i

Abstract

Lines provide important information in images and line detection is crucial in many

applications. However, most of the existing algorithms focus only on the extraction of line

positions, ignoring line thickness. In this thesis, we aim to address this issue. We describe a

general method for wide line detection and apply this method to solve two practical line

detection problems.

In the first section, we propose a novel wide line detector to extract the line entirely. In

contrast with the traditional directional-derivative-based edge and line extraction method,

our wide line detector is based on isotropic nonlinear filtering without any derivatives and

consequently is more robust to noise. We develop an approach for dynamic selection of

parameters of the proposed wide line detector. We also introduce a general scheme for

analyses of this wide line detector further. A sequence of tests is conducted on a variety of

image samples. The experimental results demonstrate that the proposed wide line detector

works very well for a range of images containing lines of different widths, especially for

those where the width of lines varies greatly and where the lines run close together or cross

each other.

We then address the first application of our wide line detector: palm-line based palmprint

recognition. We present a novel palm-line feature extraction method for personal

identification. As compared to previous work on palm line extraction, the proposed wide line

detector-based method extracts not only structure features but also strength features of palm

lines. We introduce a translation-invariant scheme for palm-line feature matching. We also

develop an experimental scheme to find out the optimal combination of parameters for the

proposed palm-line feature extraction method. An extensive test is conducted on a public

palmprint database. Experimental results show that the performance of the proposed

palm-line feature extraction method is comparable with the state-of-the-art algorithms of

palmprint identification and thereby palm-line features can be used to recognize palmprints.

Finally, we for the first time attempt to extract tongue cracks, one of pathological features

in tongue diagnosis. We propose a framework for automatic tongue crack extraction. We

derive a tongue crack detection scheme based on the wide line detector which extracts the

whole of the line by employing an isotropic nonlinear filter. The wide line detector describes

the relationship between the size of the isotropic filter, i.e. the scale of this detector, and the

width of detected lines. Due to the large range of widths of tongue cracks, the maximum

widths of cracks vary greatly with different tongue images and consequently the sizes of the

ii

isotropic filters should be very different. To implement the proposed scheme totally

automatically, we design an adaptive algorithm of line width estimation. The proposed

scheme has been tested on a set of typical cracked tongue samples and our experimental

results show the promising performance of our automatic tongue crack extraction scheme.

iii

List of Publications

The following technical papers have been published or are currently under review based on

the result generated from this work.

1. Laura Liu, David Zhang, and Jane You, “Detecting Wide Lines Using Isotropic

Nonlinear Filter,” IEEE Trans. Imag. Processing, vol. 16, no. 6, pp. 1584-1595,

2007;

2. Laura Liu and David Zhang, “Adaptive Detection of Cracks in Tongue Images,”

submitted to IEEE Trans. Medical Imaging,;

3. Laura Liu and David Zhang, “Palm-Line based Personal Recognition,” submitted to

Pattern Recognition;

4. Laura Liu and David Zhang, “Tongue crack extraction,” accepted by 1st Int’l Conf.

Medical Biometrics, Hong Kong, Jan. 4-5, 2008;

5. Laura Liu and David Zhang, “Palm-Line Detection,” ICIP 2005, pp. 269-272,

Genova, September 11-14, 2005;

6. Li Liu and David Zhang, “A Novel Palm-Line Detector,” the 5th International

Conference on Audio- and Video-based Biometric Person Authentication, pp.

563-571, New York, July 20-22, 2005;

7. Li Liu and David Zhang, “A Novel Palm-Line Detector,” the 6th ACM Postgraduate

Research Day, pp. 24-29, March 12, 2005.

i

Acknowledgements

I would like to take this opportunity to express my sincere gratitude to everyone who

generously gave me their support.

On the first place, I would like to express my gratitude and appreciation to my Supervisor,

Prof. David Zhang, for his endlessly patient guidance throughout my research studies. My

Ph.D. studies would have never been completed without his encouragement, help, and good

advice. His immense enthusiasm for research is extremely motivating. The discussions with

him have not only contributed significantly to this work, but also have made lasting

influences in me.

I was fortunate to share my office with Guang Ming Lu, Adams Kong and Michael Wong

during my initial days, from whom I have learned quite a lot. I also admire the selfless

attitudes of them. They were always ready to advice and help.

I really appreciate the open and friendly environment at Biometrics Lab. Specifically, I

would like to thank Dr. Jane You, Dr. Xiang Qian Wu and Dr. Wang Meng Zuo for the

support and constructive comments they gave me. It was wonderful to be with encircled by

so many nice and smart people like Dr. Lei Zhang, Dr. Da Cheng Tao, Dr. Jian Yang, Dr.

Ajay Kumar, Denis Guo, Jerry Zhao, Kenneth Li and Vivek.

My special thanks goes to all my friends in Hong Kong, specifically Annie, Qinqin, Dayu,

Helen and Byron. They made my time here very lively. I will definitely miss the discussions

and the fun.

I would like to dedicate this work to my parents. Their love, constant support and

encouragement made me what I am.

ii

Table of Contents

Abstract......................................................................................................................... i

List of Publications..................................................................................................... iii

Acknowledgements....................................................................................................... i

1 Introduction ............................................................................................................1 1.1 Motivation...................................................................................................1 1.2 Statements of Originality ............................................................................2 1.3 Organization of this thesis...........................................................................3

2 Literature Review...................................................................................................6 2.1 Overview of line detection..........................................................................6

2.1.1 Hough transform ..............................................................................6 2.1.2 Parallel edge extraction....................................................................8 2.1.3 Hessian-based ridge detection..........................................................9

2.2 Review of wide line detection.....................................................................9 2.2.1 Edge-based line finder ...................................................................10 2.2.2 Ridge-based line detector...............................................................11 2.2.3 Line operator ..................................................................................12

2.3 Review of palmprint recognition ..............................................................13 2.3.1 Palmprint features ..........................................................................14 2.3.2 Palmprint recognition and problem statement ...............................15 2.3.3 Representative methods of palmprint recognition .........................19

2.4 Review of tongue crack detection .............................................................23 2.4.1 Review of computerized tongue diagnosis ....................................23 2.4.2 Tongue crack ..................................................................................25

2.5 Conclusions...............................................................................................26

3 Wide Line Detection.............................................................................................28 3.1 Introduction...............................................................................................28 3.2 Model design.............................................................................................29

3.2.1 1D line profile model .....................................................................29 3.2.2 2D line detection ............................................................................30

3.3 Line detection method...............................................................................33 3.4 Parameter selection ...................................................................................36

3.4.1 Radius of circular mask, r ..............................................................37 3.4.2 Brightness contrast threshold, t ......................................................43

3.5 Experimental results..................................................................................48 3.5.1 Synthesized image..........................................................................48 3.5.2 Real image......................................................................................48

3.6 Conclusion and discussions ......................................................................51

4 Analyses of the Wide Line Detector....................................................................56

iii

4.1 Introduction...............................................................................................56 4.2 Background ...............................................................................................58

4.2.1 Signal-to-noise ratio .......................................................................58 4.2.2 ROC curve......................................................................................58

4.3 Core function.............................................................................................60 4.3.1 SECH v.s. EXP...............................................................................60 4.3.2 The power of the hyperbolic secant function.................................64

4.4 Radius of circular mask.............................................................................66 4.4.1 Operating radius v.s. real radius.....................................................66 4.4.2 Relationship of mask radius and detected line width.....................68

4.5 Line orientation .........................................................................................72 4.6 Time complexity .......................................................................................74 4.7 Robustness to impulse noise .....................................................................74 4.8 Summary ...................................................................................................79

5 Palmprint Recognition by Using Line Features ................................................80 5.1 Introduction...............................................................................................80

5.1.1 Palm lines .......................................................................................82 5.1.2 Review ...........................................................................................83

5.2 Line-like feature extraction.......................................................................84 5.3 Palm-line feature matching .......................................................................90 5.4 Experimental results..................................................................................91

5.4.1 Palmprint database .........................................................................91 5.4.2 Parameters for the palm-line feature based palmprint recognition 91 5.4.3 Palmprint matching and parameter selection .................................92 5.4.4 Verification.....................................................................................98 5.4.5 Identification ................................................................................100

5.5 Conclusion and discussions ....................................................................101

6 Automatic Extraction of Cracks on Tongue Images .......................................102 6.1 Introduction.............................................................................................102 6.2 Methodology of crack extraction ............................................................105

6.2.1 Preprocessing ...............................................................................107 6.2.2 Extracting tongue cracks ..............................................................107 6.2.3 Post-processing ............................................................................112

6.3 Adaptive line width estimation ...............................................................114 6.4 Experimental results and analysis ...........................................................118

6.4.1 Performance evaluation................................................................119 6.4.2 Experimental results.....................................................................120

6.5 Conclusion and discussion ......................................................................129

7 Conclusion...........................................................................................................130 7.1 Main contributions ..................................................................................130 7.2 Future Work.............................................................................................132

Bibliography .............................................................................................................134

iv

Lists of Figures

Fig. 1.1 The framework of this thesis. ................................................................................. 5

Fig. 2.1 Operation of the line operator. (left) Average intensity, L (indicated by the various

shades of gray), is determined for a number of orientations. (right) Line strength,

S, is obtained as the difference between the maximum value of L (dark-gray

shaded points) and the average intensity, N, of a square region aligned with the

direction of maximum L (light-gray shaded points). [4] ...................................... 13

Fig. 2.2 Palmprint features. (a) Principal lines and datum points. (b) Wrinkles, ridges and

delta points............................................................................................................ 14

Fig. 2.3 Block diagram of palmprint recognition architecture........................................... 18

Fig. 2.4 The main steps of preprocessing. (a) Original image, (b) binary image, (c)

boundary tracking, (d) building a coordinate system, (e) extracting the central part

as a subimage, and (f) preprocessed result. [50]................................................... 20

Fig. 2.5 Flowchart of the automatic tongue diagnosis system in TCM. [8,83].................. 24

Fig. 3.1 Four circular masks at different positions on a line image based on the 1D ideal

line model IL as in (3-1). ...................................................................................... 31

Fig. 3.2 Five circular masks at different positions of a line image based on the 1D

common line profileGL as in (3-2). ..................................................................... 31

Fig. 3.3 Illustration of gray-level relations between three regions. IGr , IIrG and IIIGr

are gray levels of the line part, the edge region and the background, respectively.

The difference of the gray levels between the line ( IGr ) and the background

( IIIGr ) is larger than the brightness contrast threshold t (a) with or (b) without

larger than t×2 . (i), (ii), (iii) and (iv) show the corresponding relations in (3-4),

respectively. .......................................................................................................... 32

Fig. 3.4 Brightness difference versus the similarity functions defined in (3-3) and (3-11),

respectively. Here the brightness contrast threshold t is set to 10. ....................... 35

Fig. 3.5 Illustration of Proposition 1 and its proof............................................................. 39

Fig. 3.6 Illustration of the inequality relation about the ratio of the width of the line

detected to the radius of a circle mask with normalized constant weighting........ 41

Fig. 3.7 (a) A segmented palmprint image. Palm-line response images obtained using

v

brightness contrast thresholds t of (b) 6, (c) 7, (d) 8, (e) 9, (f) 10, (g) 11, (h) 15, (i)

20, and (j) 25......................................................................................................... 46

Fig. 3.8 (a) A test image including straight lines and curves of different widths. The line

detection results obtained using (b) the edge-based line finder, (c) the ridge-based

line detector, and (d) the proposed wide line detector. ......................................... 47

Fig. 3.9 (a), (b) Aerial images and (c) an X-ray image taken from [3]. (d)-(f) The

extraction results of line positions and line widths reported in [3] where line

positions are displayed in white with the corresponding edges displayed in black.

(g)-(i) The corresponding line detection results obtained using our wide line

detector are drawn in white. ................................................................................. 53

Fig. 3.10 The segmented palmprint images (first row) and the palm-line detection results

obtainedusing the edge-based line finder (second row), the ridge-based line

detector (third row), and our wide line detector (last row). Detected lines are

displayed in black. ............................................................................................... 54

Fig. 3.11 Segmented tongue images (first row) and crackle detection results obtained using

the edge-based line finder (second row), the ridge-based line detector (third row)

and the proposed wide line detector (last row). Detected crackles are displayed in

red. ....................................................................................................................... 55

Fig. 4.1 The ROC space and plots of the four prediction examples. [97].......................... 59

Fig. 4.2 Brightness difference versus the similarity formulae defined in (4-2), (4-3), and

(4-4), respectively. Here the brightness contrast threshold t is set to 10, 5=JS for

(4-3), and 6=JE for (4-4).................................................................................. 61

Fig. 4.3 (a) A test image including straight lines and curvilinear structures of different

widths. (b) The ROC curves of (a) for the 0-1 function, the exp to 6th power

formula, and the sech to 5th power formula. ......................................................... 63

Fig. 4.4 The ROC curves of Fig. 4.3a for different functions and different weighting. .... 65

Fig. 4.5 (a) A synthesized image with a bright line of 5 pixels wide. The pixel values are

marked. (b) and (c) The line response images by using the 0-1 function and the

SECH to 5th power function, respectively. The line responses on the center pixel

and at the most left pixel are shown. .................................................................... 65

Fig. 4.6 An example of circular mask approximated by a square kernel of 1515× .......... 67

Fig. 4.7 The plots of WMSB mass of lines with width of (a) 5 pixels, (b) 15 pixels, and (c)

25 pixels, respectively........................................................................................... 71

vi

Fig. 4.8 The line with orientation of (a) 15 degree, (b) 30 degree, (c) 60 degree, and (d) 75

degree, respectively. ............................................................................................. 71

Fig. 4.9 The test image (Fig. 4.3a) is added impulse noise with the noise density of (a)

0.01 and (b) 0.1, respectively. Line strength images by using our wide line

detector to (a) and (b) are shown in (c) and (d), respectively. (e) and (f) are final

results of line detection by performing morphological operations to (c) and (d),

respectively. .......................................................................................................... 75

Fig. 4.10 Line detection results of the noisy image Figure 4.9a using (a) Koller’s

edge-based line finder [26] and (b) Steger’s ridge-based line detector [3]........... 76

Fig. 4.11 Filter the noisy image Figure 4.9(a) using median filters with three different

neighbors: (a) a 33× square, (b) a 31× horizontal line, and (c) a 51× horizontal

line. ....................................................................................................................... 78

Fig. 5.1 The main patterns in a palmprint. [13] ................................................................. 82

Fig. 5.2 Brightness difference versus the similarity defined in the core functions (5-1),

(5-4), and (5-5), respectively. Here the brightness contrast threshold t is set to 10.

.............................................................................................................................. 85

Fig. 5.3 A 3D plot of the WMSB mass given a test image with a 3 pixels wide line. ....... 86

Fig. 5.4 The palmprint sub-images (the first row) with the size of 128128× , the

corresponding line-strength images (the second row) using the wide line detector,

the palm-line feature images (the third row) via thresholding the line-strength

images, and the post-processed palm-line feature images (the last row) with the

size of 6464× .................................................................................................... 87

Fig. 5.5 Palm-line feature extraction results using the WLD-based palm-line feature

extraction method with different brightness contrast thresholds t and different

radii of the circular mask r. For 0=t , the core function defined in (5-5) is

employed. ............................................................................................................. 89

Fig. 5.6 EER (%) values for different combinations of brightness contrast threshold and

radius of circular mask. Here the standard deviation of Gaussian smoothing filter

is 75.0=σ and the translation range is 2=s . ................................................... 93

Fig. 5.7 EER (%) values for different parameter combinations of circular mask radius and

translation range given the standard deviation of Gaussian smoothing filter (a)

0.1=σ and (b) 25.1=σ , respectively. Here the brightness contrast threshold

is 0=t . ................................................................................................................. 96

vii

Fig. 5.8 Genuine and impostor distributions for the optimal parameter combination. ...... 98

Fig. 5.9 Verification performance comparison on PolyU Palmprint Database. ................. 99

Fig. 6.1 The diagram of tongue crack extraction procedure using the WLD................... 106

Fig. 6.2 Preprocessing of tongue crack extraction. (a) Captured tongue image, (b) contour

tongue image with the centroid and corresponding contour, (c) tongue body mask,

and (d) extracted tongue body image. ................................................................ 108

Fig. 6.3 Tongue crack extraction. (a) The ground truth for Fig. 6.2d, (b) The line-strength

image using the wide line detector (WLD), (c) tongue crack image obtained by

postprocessing (b), and tongue crack extraction results using (d) the Line Operator

(LO) and (e) Steger’s method, respectively. ....................................................... 109

Fig. 6.4 Illustration of the line width estimate. The first row is the three dark line models.

The second row shows the corresponding Gaussian smooth profiles. The last row

is the first-order derivatives of Gaussian (DoG) profiles shown in the second row.

The line width can be obtained by calculating the distance between the pair of

minimum and maximum of DoG filtered results along the line profile. ............ 115

Fig. 6.5 Line width estimation algorithm......................................................................... 117

Fig. 6.6 (a) The vertical cracks with (b) the ground truth and extraction results by using (c)

WLD, (d) LO, and (e) Steger’s method, respectively. ........................................ 121

Fig. 6.7 (a) The horizontal cracks with (b) the ground truth and extraction results by using

(c) WLD, (d) LO, and (e) Steger’s method, respectively.................................... 123

Fig. 6.8 (a-b) Two irregular cracks with (c-d) the corresponding ground truth and

extraction results by using (e-f) WLD, (g-h) LO, and (i-j) Steger’s method,

respectively. ........................................................................................................ 126

Fig. 6.9 Box-and-whisker plots of the PM values of three methods for all test cracked

tongue images. .................................................................................................... 128

viii

Lists of Tables

Table 2.1 Edge and Line detection methods. ..................................................................... 7

Table 2.2 Comparison of biometric techniques [46,56]. A low ranking indicates poor

performance in the evaluation criterion whereas a high ranking indicates a very

good performance............................................................................................. 16

Table 2.3 Comparison of technology risk rating [57]. ..................................................... 17

Table 2.4 Seven types of tongue cracks. [75]................................................................... 27

Table 3.1 The deviation of function PtyxIyxIh )/),(),((sec 00− from (3-3). Here c is

the subtraction of (3-11) from (3-3), and c is the absolute value of c.......... 35

Table 3.2 Relationship between radii of Gaussian masks and approximately critical

widths of lines (ACLW) detected. .................................................................... 42

Table 4.1 Look up table of core functions 1s and 2s with different powers and the

deviation of the two core functions from 0s ..................................................... 62

Table 4.2 Square kernel and the corresponding operating radius and real radius. Here the

operating radius is half the number of pixels along x or y-direction excluding

the center pixel. ................................................................................................ 67

Table 4.3 The values of x given different widths and different radii. Here the operating

radius is half the number of pixels along x or y direction excluding the center

pixel. 0L is the line pixel where WMSB mass of line pixels reaches the

maximum, while 0B is the background pixel where the WMSB mass of

background pixels reaches the minimum. ........................................................ 69

Table 4.4 The calculated φ . Here opR is the operating radius which is half the number of

pixels along x or y-direction excluding the center pixel................................... 73

Table 4.5 Comparisons of calculations per pixel for different line detection methods. The

size of the convolving kernel is NN × . .......................................................... 74

Table 5.1 Equal error rates (%) for different brightness contrast thresholds (t) and

different radii of circular masks (r). Here the standard deviation of Gaussian

smoothing filter is 0.75 and the translation range is 2. For t larger than 0, the

ix

core function defined in (5-1) is applied. For 0=t , the core function defined

in (5-5) is applied. ............................................................................................ 93

Table 5.2 Equal error rates (%) for different translation ranges (s) and different radii of

circular masks (r). Here 0=t and the standard deviation of Gaussian

smoothing filter takes two values, 1 and 1.25. ................................................. 95

Table 5.3 Equal error rates (%) for different radii of circular masks (r) and different

scales of Gaussian smoothing filter with 0=t and 5=s . The core function

defined in (5-5) is used..................................................................................... 97

Table 5.4 Comparison of our method with four representative palmprint verification

methods on PolyU database. ............................................................................ 99

Table 5.5 Comparison of identification accuracy on two registration databases. .......... 101

Table 6.1 Comparison of the relationship between radii of different profiles and

approximately critical widths of detected lines (ACWL). ............................. 113

Table 6.2 The estimation results of maximum widths of cracks by applying the algorithm

described in Figure 6.5. The true widths of cracks are also listed for reference.

........................................................................................................................ 117

Table 6.3 Comparisons of performance evaluation between different methods used in Fig.

6.3.................................................................................................................... 120

Table 6.4 Comparisons of performance evaluation between different methods used in Fig.

6.6.................................................................................................................... 122

Table 6.5 Comparisons of performance evaluation between different methods used in Fig.

6.7.................................................................................................................... 124

Table 6.6 Comparisons of performance evaluation between different methods used in Fig.

6.8a. ................................................................................................................. 127

Table 6.7 Comparisons of performance evaluation between different methods used in Fig.

6.8b.................................................................................................................. 127

Table 6.8 Comparisons of average performance evaluation between different methods.....

........................................................................................................................ 128

Table 6.9 Paired t-test results of different methods. The p values are calculated using the

paired t-test of the hypothesis that two matched samples in the two vectors

come from distributions with equal means. p<0.05 was considered statistically

significant. ................................................................................................................ 128

1

Chapter 1

Introduction

The objective of this chapter is to introduce the general concepts of line detection, including

the characteristics of lines in digital images and applications of line detection. We also

address the originality and the organization of this thesis.

1.1 Motivation

Lines, a generic term without making distinction between straight lines and curvilinear

structures, usually convey much relevant information of an image like edges [1,2]. Hence it

is important to detect lines reliably and effectively.

Line detection in digital images is an important low-level operation in image analysis and

computer vision. In photogrammetric and remote sensing tasks, it can be used to extract

linear features, such as roads, railroads, and rivers, from satellite or low-resolution aerial

imagery, which can be used for the capture or update of data for geographic information

systems [3]. It is also extensively used in medical imaging for extracting anatomical features

such as linear structures in mammograms [4], blood vessels from an X-ray angiogram [5] or

a retina image [6], the bones in the skull from a CT or MR image [7], and cracks on a tongue

surface in TCM [8]. In addition, line detection is useful in, for example, extracting strokes in

character recognition [9,10], in estimating motion and structure from multiple images [11,12],

and in detecting biometric traits for personal authentication [13].

A large number of line detection algorithms have been proposed, most of which focused

on locating line positions without considering line widths. However, a digital image line

generally appears as a straight line or a curvilinear structure with one or more pixels wide, i.e.

a thin/narrow or thick/wide line. Since width is one of the predominant and most informative

features that characterize a line, it is important not only to extract line locations but also to

2

detect the complete line. In this thesis, we address this issue by proposing a general method,

the wide line detector (WLD), which can extract the full cross-sectional extent of lines at

each location along them. We also study two applications of the proposed method: palm-line

based palmprint recognition and adaptive tongue crack detection.

1.2 Statements of Originality

Figure 1.1 illustrates the framework of this thesis as well as the corresponding contributions

which are claimed to be original as follows:

1. A novel wide line detector using an isotropic nonlinear filter is presented. This detector

is based on the isotropic responses via circular masks. Unlike most existing edge and

line detectors which use directional derivatives, our proposed wide line detector applies

a nonlinear filter to extract a line completely without any derivative.

2. A model for the common line profile, named the edge-based bar-shaped line, is defined

to design the wide line detector.

3. The dynamic selection of parameters is developed to automatically determine the two

parameters – the brightness contrast threshold and the radius of circular mask – of the

proposed wide line detector for an input image.

4. A general scheme is introduced for analyses of the proposed wide line detector. The

optimal core function is determined for this detector by evaluating the performance of

various formulae.

5. A novel palm-line feature extraction method based on our wide line detector is proposed

for palmprint recognition. This palm-line feature extraction method can detect line-like

features which convey both structure features and strength features of palm lines.

6. A translation-invariant similarity measure is introduced for palm-line feature matching

which can be implemented reliably and effectively.

7. An experimental scheme is designed to determine the optimal combination of

3

parameters for the proposed palm-line feature based palmprint recognition methodology,

which are the brightness contrast threshold and the radius of circular mask for the wide

line detector, the Gaussian smoothing filter scale for post-processing, and the translation

range for palm-line feature matching.

8. A framework is proposed for adaptive tongue crack detection.

9. An adaptive tongue crack detection scheme is derived based on the proposed wide line

detector. This scheme allows totally automatic extraction of tongue cracks

10. An algorithm of maximum line width estimation is designed to determine the maximum

width of tongue cracks in a tongue image, which is related to the radius of the circular

mask, one of parameters for the proposed wide line detector.

1.3 Organization of this thesis

Following the global introduction, the thesis proceeds in Chapter 2 with an overview of line

detection techniques, palmprint recognition, and tongue cracks. Special attention is given to

the classic wide line detection approaches and palmprint recognition algorithms which are

compared to our proposed methods in the thesis.

The subsequent parts (Chapters 3-6) present the scientific contributions of the research.

All the chapters correspond to work that has been published or is currently under review in

peer-reviewed journals.

In Chapter 3, we concentrate on the detection of the complete line. We present a wide line

detector to extract the full cross-sectional extent of lines at each location along them. In

contrast with the traditional directional-derivative-based edge and line detector, the proposed

wide line detector applies an isotropic nonlinear filter to extract a line completely without

any derivative. A dynamic selection of parameters is developed by the analysis of robustness

of the proposed wide line detector. In addition, this chapter investigates the relationship

between the size of circular masks and the width of detected lines.

4

We then analyze the proposed wide line detector in Chapter 4. The optimal core function

for the proposed wide line detector is determined by comparing the performance of various

formulae and the results show the power of the hyperbolic secant function which is

employed as the core function in Chapter 3. The relationship between the real radius and

operating radius is described and the restriction on the real radius presented in Chapter 3 is

illustrated. The calculation of line orientation defined in Chapter 3 is also illustrated to show

its reasonableness. In addition, a comparative study is conducted to demonstrate the

robustness of our method to impulse noise.

In Chapter 5, we address the first application of the wide line detector, a novel palm-line

feature extraction method for palmprint recognition. This wide line detector based method

can extract both structure features and strength features of palm lines. An isotropic nonlinear

filter is employed to calculate the line strength of palmprint. Palm-line feature images are

obtained via binarilization of line strength images. A Gaussian smoothing filter serves as

post-processing for palm-line feature image denoise. A translation-invariant similarity

measure is introduced for palm-line feature matching. An experimental scheme is also

designed to determine the optimal combination of parameters for the proposed method.

In Chapter 6, we, for the first time, attempt to detect tongue cracks, one of pathological

features in tongue diagnosis. A framework is described for adaptive tongue crack detection

and consequently an adaptive tongue crack detection scheme is derived based on the

proposed wide line detector. This scheme can extract tongue cracks totally automatically. A

novel algorithm of maximum line width estimation is also designed to automatically

calculate the maximum width of cracks for an arbitrary input tongue image; the maximum

width of cracks determines the radius of circular mask, one of the parameters required for the

proposed wide line detector.

Finally, we give the conclusions of our work in Chapter 7, where some suggestions for

further development are also provided.

5

Fig. 1.1 The framework of this thesis.

Performance Evaluation

4. A general scheme is introduced for analyses of the proposed wide line detector.

Wide Line Detector

1. A novel wide line detector using an isotropic nonlinear filter is presented;

2. A model for the common line profile is defined;

3. The dynamic selection of parameters is developed.

Adaptive Tongue Crack Detection

9. An adaptive tongue crack detection scheme is derived;

10. An algorithm of maxi- mum line width estima- tion is designed.

Palm-Line based Palmprint Recognition

5. A palm-line feature extraction method is proposed based on WLD for palmprint recognition;

6. A translation-invariant similarity measure is introduced;

7. An experimental scheme is designed to determine the optimal parameter combination.

Our Proposed Method Applications Analyses

8. A framework for the adaptive tongue crack detection is proposed;

6

Chapter 2

Literature Review

In this chapter, we introduce the general concepts and methods of line detection. We briefly

review some well-known line detection techniques which consider line width. We also

review the methods for palmprint recognition which will be compared to our proposed

method in Chapter 5. We finally introduce the concepts of tongue cracks.

2.1 Overview of line detection

Line detection is considered one of the most fundamental tasks in image analysis and

computer vision. Consequently, much research has been done in this area and a considerable

body of literature has been accumulated. Table 2.1 illustrates the typical techniques used for

line detection. Surveys of edge and line detection may be found in [133, 135].

Most work on line detection can be classified into three primary categories: Hough transform

(HT), parallel edge extraction, and Hessian-based ridge detection. In this section, we will

introduce and discuss the three techniques for line detection.

2.1.1 Hough transform

The Hough transform [14-15, 92-93], which is a widely used line detection method [136], is

the classical technique for finding analytically defined curvilinear structures (e.g., straight

lines, circles, ellipses etc.). It transforms a binary image into Hough parameter counting

space. Any straight line in the image is represented by a single point in the parameter space

and any part of this straight line is transformed into the same point. The main idea of the

Hough transform is to determine all the possible line pixels in the image, to transform all

lines that can go through these pixels into corresponding points in the parameter space, and

to detect the points in the parameter space that frequently resulted from the Hough transform

7

Table 2.1 Edge and Line detection methods.

Category Methods Description

Hough Transform Hough Transform Voting in the dual plane.

Roberts operator ⎥⎦

⎤⎢⎣

⎡−

=10

011h , ⎥

⎦

⎤⎢⎣

⎡−

=0110

2h

Prewitt operator⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−−=

111000111

1h , ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−−

=101101101

1h

Sobel operator ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−−=

121000121

1h , ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−−

=101202101

1h

1st derivative

Canny edge detection

Optimal for step edges by the first derivative of Gaussian smoothing filter with standard deviationσ .

Laplacian of Gaussian (LoG)

A second derivation of a smoothed 2D function, non-directional (isotropic)

Mexican hat The inverted LoG operator

Difference of Gaussians (DoG)

The difference of two Gaussian averaging masks with substantially different σ .

2nd derivative

Ridge detection Local maximum or minimum in the direction of the main principal curvature, the interior of elongated

objects in the image domain.

Thresholding Adaptive thresholding

Segmentation using variable thresholds, the threshold value varies over the image as a function of local image

characteristics.

8

of lines in the image [16]. Although the original Hough transform [14] was designed to

detect straight lines and curves, this original method can be used to detect any analytically

defined shape. The Hough transform is particularly useful when the curves one is looking for

are sparsely digitized, have “holes” and/or the images are noisy.

If the analytic expression of the desired curves is known, the Hough transform works very

well. Unfortunately, this is not often true in practice. In this case, a generalized Hough

transform [17-19] can offer the solution. This method constructs a parametric curve

description based on sample situations detected in the learning stage and can be used to

detect arbitrary shapes. However, when a complex curvilinear structure needs to be detected,

the Hough transform becomes quickly so high dimensional that it is not feasible. Moreover,

although the generalized Hough transform can be used to detect arbitrary curvilinear

structures in theory, it requires the complete specification of the exact shape of the target

object to achieve precise segmentation [16], which is often difficult and not available for

complex curvilinear structures in practice.

2.1.2 Parallel edge extraction

The second technique is based on edge extraction. It treats lines as objects with parallel

edges [20-26,94,134] and accordingly adopts edge detection for preprocessing. It is common

to first find all edges in the image and then analyze the edge image to find the line by

detecting parallel opposing edges. The edge detection algorithm used in the early stage in

most cases [22,26] is the first derivative of the Gaussian, a well known edge detector [27].

Actually, this technique converts the problem of line detection to edge detection and thus

strongly depends on reliable edge detection. Due to the first derivative of the Gaussian used

for edge extraction, this line detection technique is sensitive to image noise. For the parallel

edge extraction based line detection technique, the detection of the line is now a two step

process: edge detection and line finding. If an error is made during the edge detection stage,

it cannot be corrected in the line finding stage.

9

2.1.3 Hessian-based ridge detection

For the final technique, lines are regarded as ridges and valleys in the image [28]. A ridge

point is differential-geometrically defined as location for which the gray value assumes a

local maximum or minimum in the direction of the main principal curvature which

corresponds to the maximum eigenvalue of the Hessian [29,30]. Hence, this technique

extracts ridges by computing the eigen-decomposition of the Hessian at each image pixel and

find line points by selecting pixels that have a high second directional derivative

perpendicular to the line direction [30-35]. Ridge strength can be measured by the LA norm−γ

index [30], which is designed to minimize the response to blobs.

The advantage of the Hessian-based ridge detection technique is that lines can be detected

with a high accuracy [29]. However, this technique usually leads to multiple responses to a

single line and returns wrong line locations if the line has different lateral contrast [3].

Although this technique can be iterated through scale-space to obtain a coarse estimate of the

line width [30], the line position at the optimal scale for width estimation will in general be

severely biased. In addition, this approach is sensitive to noise due to the use of second order

of derivatives.

2.2 Review of wide line detection

The importance of detecting wide lines, i.e. the full cross-sectional extent of lines, is often

underestimated in line detection, but it may be as significant as the location of line positions.

In the past decade, there has been increasing interest in the wide line detection [3,4,26,36-39]

and the techniques developed in the literature can be divided into the three categories

introduced in Section 2.1.

For the Hough transform, since the analytic expression of desired lines is required, the

wide/thick line detection based on HT only focuses on straight lines/bands [37,38]. Such

approaches are expected to be slow due to a large number of votes and require a large

10

amount of memory. Also, it does not seem to be able to handle straight lines of non-uniform

brightness and width as well as curvilinear structures.

One possible powerful approach for wide line detection is to use edge detection followed

by a method for detecting parallel opposing edges [25,26]. The other is to apply ridge

extraction at a proper scale to detect line positions as well as line width [3]. However,

dedicated line detectors are generally more successful [4,36].

The adaptive thresholding technique, which is widely used for document image analysis

[128-131], can also be used to detect edges and segment wide lines [132]. However, it

appears that none could extract the wide line well with a set of operating parameters when

the background is too complex, i.e., the illumination changes dramatically and there are too

much structured noise.

In this section, we introduce three specific wide line detection approaches for our analysis,

[3], [4], and [26], which have been applied in a number of papers [39-44] and will be

compared to our proposed methods in the following Chapters.

2.2.1 Edge-based line finder

In their work, Koller et al. [26] aimed to propose an algorithm which is independent of scale

and does not involve the specification of width parameters to detect curvilinear structures of

different widths and orientations. This algorithm first calculates the line direction by

analyzing the directional derivatives at the appropriate scales and then employs an edge

detector, the first derivative of the Gaussian, perpendicularly to the line direction to detect

the parallel opposing edges of the line. To overcome the multiple line response and the

sensitivity to edges, the response of the two specially tuned edge detection filters is

combined in a nonlinear way. This edge-based line finder algorithm can be implemented by

five steps:

Step 1: Create the scale-space image ss GLL ⊗= , where L is the input image and sG is the

Gaussian filter with its variance set equal to the scale parameter s;

11

Step 2: Calculate the gradient sL∇ ;

For all points x :

Step 3: Determine the direction )sin,(cos αα=od , where

)(2)2(tan 1yyxxxy LLL −=− α ;

Step 4: Obtain the edge responses ddsxLR sl ⋅+∇= )( and ddsxLR sr ⋅+−∇= )( ;

Step 5: Calculate the filter response ))(,)(min(),( rrllrl RRsignRRsignRRF ⋅⋅= , where

1)( =xsign for 0>x .

The advantage of this algorithm is that, since derivatives of Gaussian kernels are used, it

can detect lines of arbitrary widths by iterating in scale space and selecting as the line width

the scale that yields the maximum of a scale-normalized response. However, since special

filters need to be constructed for several or even all possible line directions, the edge-based

line finder algorithms are computationally very expensive. Furthermore, it obtains a coarse

estimate of the line width by iteration through the scale space, which makes the algorithm

even more expensive.

2.2.2 Ridge-based line detector

A well-founded algorithm for the line detection is given by Steger [3]. He proposes an

explicit model for lines and their surroundings and carries out a scale-space analysis for this

line model. This analysis leads to an algorithm which can extract lines and line widths with

high precision. In this algorithm, an input image is first convolved with a Gaussian kernel,

and then each pixel is assumed to be at the center position of a curvilinear structure. To test

whether the assumption is correct for the pixel under consideration, the first and second

directional derivatives of the Gaussian smoothed image are computed along the local line

direction which is the main principal curvature corresponding to the maximum eigenvalue of

the Hessian. A line point is detected at the zero-crossing of the first derivative of the image

taken in the direction of the eigenvector of the Hessian matrix, the Hessian being given by

12

the local second order derivatives:

⎥⎦

⎤⎢⎣

⎡=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

∂∂

∂∂∂

∂∂∂

∂∂

=yyyx

xyxx

LLLL

yL

xyL

yxL

xL

yxH

2

22

2

2

2

),( . (2-1)

The width (w) of the curvilinear structure to be found depends on the scale (σ ) of the

Gaussian kernel which should satisfy

3w

≥σ . (2-2)

This ridge-based line detector overcomes the problem that the ridge-based line detection

approach will return inaccurate line locations when the contrast on one side of the line is

different from the contrast on the other side of the line. Since Gaussian kernels are used to

measure the derivatives of the image, the line detector can scale to lines of arbitrary widths.

However, since this approach extracts lines as the maxima of the magnitude of the second

directional derivatives, it can detect only salient lines. Moreover, this line detector will fail

when the curvilinear structures cross each other because the direction of a line is estimated

by an eigenvector corresponding to the maximal absolute value of the Hessian matrix

eigenvalue. In addition, once the selected σ becomes so large that neighboring lines start

to influence each other, the line model will not hold and the results will deteriorate.

2.2.3 Line operator

Taylor et al describe a line operator [4,45], the principle of which is illustrated in Fig. 2.1.

The Line Operator improves the line signal to background noise ratio by taking the average

gray level, L, of the pixels lying on an orientated local line passing through the target pixel

and subtracting the average intensity, N, of all the pixels in the locally orientated

neighborhood. The values of pixels falling on the border of the line or neighborhood are

weighted according to the area of the relevant pixel falling within the line or neighborhood.

The line-strength S is calculated by S = (L-N) and compared for n orientations. Line

direction is obtained from the orientation producing the maximum line strength. Line scale

13

can be obtained by applying this algorithm at multiple scales either by subsampling the

image or changing the local area size. For each pixel, the scale producing the maximum line

strength is taken as the detected line scale.

This algorithm is simple and effective for line detection. Its sensitivity makes the Line

Operator suitable to detect low-contrast lines and narrow lines. However, the detection

results may be corrupted by image noise or changes of contrast.

2.3 Review of palmprint recognition

In this section, we first introduce the palmprint features and then provide a short review on

palmprint recognition followed by the description of problem statement. We also briefly

review on some well-known palmprint recognition methods which will be compared to our

methods in Chapter 5.

Fig. 2.1 Operation of the line operator. (left) Average intensity, L (indicated by the various

shades of gray), is determined for a number of orientations. (right) Line strength, S, is

obtained as the difference between the maximum value of L (dark-gray shaded points) and

the average intensity, N, of a square region aligned with the direction of maximum L

(light-gray shaded points). [4]

14

(a) (b)

Fig. 2.2 Palmprint features. (a) Principal lines and datum points. (b) Wrinkles, ridges and

delta points.

2.3.1 Palmprint features

Biometrics, which deals with the problem of identifying a person based on human physical

and behavioral characteristics, is a better alternative to conventional authentication

approaches due to the inherency, universality, and uniqueness of biometric features [46].

Palmprpint, one of biometric features, is relatively stable and unique physical characteristic

[47]. As shown in Fig. 2.2, in a palmprint, there exists rich and useful information which can

be categorized as follows:

Principal Lines: Principal lines consist of hear line, head line and life line. They are the

most visible palm lines in a palmprint. Both the location and form of principal lines are

very important physiological characteristics for identifying individuals because they

vary little over time [48].

Wrinkles: Wrinkles are generally thinner and more irregular than principal lines.

15

They are classified as strong wrinkles and weak wrinkles so that more detail features

can be acquired.

Datum points: Datum points are two endpoints of head line and heart line which

intersect the both sides of palm. These provide a stable way to register palmprints.

Delta points: Delta point is defined as the center of a delta-like region in the palmprint

and provides stable and unique measurement for palmprint recognition [48].

Ridges: The palmprint is basically composed of ridges which are also a significant

measurement [48].

Compared with fingerprint, the most widely used biometric feature, palmprint contains not

only fingerprint-like features such as delta points and ridges but also additional distinctive

features such as principal lines and wrinkles. Therefore, it is possible to build a highly

accurate biometric system by palmprint.

2.3.2 Palmprint recognition and problem statement

Palmprint recognition, as a relatively new biometric technique, has drawn more and more

attention in the past few years. The comparison of various biometric techniques summarized

in Table 2.2 indicates that palmprint, on average, is more suitable than other biometrics for

personal recognition. Furthermore, the hand-scan technology is low risk rating in general, as

shown in Table 2.3. Moreover, compared with other hand-based biometrics such as

fingerprint and hand geometry, palmprint is more user-friendly, more cost effective, and

requires fewer data signatures but has a higher accuracy [13].

Palmprint recognition systems can be classified into two categories: offline and online

[50]. An offline system usually processes previously captured palmprint images, which are

often obtained by inked palms before digitization. An online system captures palmprint

images using a palmprint capture sensor that is directly connected to a computer for

real-time processing. Much research has done on offline palmprint images and some useful

results have been obtained [48,51-55]. Recently, several researchers have started working on

online palmprint recognition.

16

Table 2.2 Comparison of biometric techniques [46,56]. A low ranking indicates poor

performance in the evaluation criterion whereas a high ranking indicates a very good

performance.

17

Table 2.3 Comparison of technology risk rating [57].

Biometrics Verification

/Identification

Overt

/Covert

Behavioral

/Physiological

Give

/Grab Risk

Rating

Facial-scan high high medium high high

Finger-scan high medium high medium high

Hand-scan low low medium low low

Iris-scan high low high medium medium

Keystroke-scan low medium low low low

Retina-scan high low high low medium

Signature-scan low low low low low

Voice-scan low high low medium medium

A biometric system may operate either in verification mode (one-to-one matching) or

identification mode (one-to-many matching) [56]. In this thesis, we use the generic term

recognition without making a distinction between verification and identification. In a

palmprint recognition system, there are two stages: enrolment and recognition. Both stages

comprise three subsystems: palmprint image acquisition, palmprint image preprocessing and

feature extraction. Recognition stage consists of an additional subsystem - palmprint

matching. Figure 2.3 illustrates the block diagram of palmprint recognition architecture.

Problem statement

The key issue of palmprint recognition is how to characterize a palmprint stably and

effectively. Various palmprint representations have been proposed for recognition, such as

point features [51,58], line features [48,59-62], energy features [55,63], Fourier-domain

representation [64,65], algebraic representation [66-68], texture features [50,69-71], wavelet

signatures [13], etc. Since Zhang et al [50] extracted the texture features to describe a

palmprint and established an efficient and effective on-line palmprint recognition system,

texture feature has become the most popular representation used for palmprint recognition

and have achieved good performance in terms of speed and accuracy.

18

Fig. 2.3 Block diagram of palmprint recognition architecture.

Actually, it is the line feature that plays the most important role in palmprint recognition.

In [60,61], Wu et al for the first time made use of palm line structural features for

recognition. Observing palmprint, we can find that principal lines are very strong and look

wider than wrinkles. That is, many palm lines are not one pixel wide lines and have different

strength or width. The strength feature, or width information, of palm lines is very important

to characterize a palmprint clearly especially when different palmprints have similar line

structures. Hence, not only the structure feature but also the strength feature of palm lines is

necessary and important for palmprint recognition. In Chapter 5, we will describe our

proposed method for palmprint recognition by extracting both structural features and

strength features of palm lines.

19

2.3.3 Representative methods of palmprint recognition

In this subsection, we will briefly introduce the representative palmprint recognition

approaches which will be compared to our proposed method in Chapter 5.

PalmCode

PalmCode [50] is a 2D Gabor phase coding scheme for palmprint recognition. In the

preprocessing, a finger-gap-based algorithm is proposed to segment a normalized subimage

for reliable feature measurements. The five major steps (see Fig. 2.4) of the preprocessing

are [50]:

Step1: Apply a lowpass filter to the original image and convert the convolved image to a

binary image, as shown in Fig. 2.4b.

Step 2: Extract the boundaries of the holes, )2,1(),,( =iyFxF jiji , between fingers, as

shown in Fig. 2.4c.

Step 3: Compute the tangent of the two gaps. If there is a line ( cmxy += ) passing through

a pair of points on ),( 11 jj yFxF and ),( 22 jj yFxF satisfies the inequality,

cxmFyF jiji +≤ , for all i and j (see Fig. 2.4d), then the line is considered to be the tangent

of the two gaps.

Step 4: Line up the pair of points determining the tangent of the two gaps to get the y-axis of

the palmprint coordinate system. The origin of the coordinate system is the midpoint of the

two points (see Fig. 2.4d).

Step 5: Extract a subimage of a fixed size (normally 128128× ) based on the coordinate

system (see Fig. 2.4e). The subimage should be located at a certain area of the palmprint

image for feature extraction. The preprocessed palmprint image (the normalized subimage) is

shown in Fig. 2.4f).

20

(a) (b)

(c) (d)

(e) (f)

Fig. 2.4 The main steps of preprocessing. (a) Original image, (b) binary image, (c)

boundary tracking, (d) building a coordinate system, (e) extracting the central part as a

subimage, and (f) preprocessed result. [50]

The preprocessing aligns different palmprint images for matching and accordingly

required by any palmprint recognition method. In Chapter 5, we apply this preprocessing

algorithm to obtain the normalized subimage for our proposed method and the palmprint

recognition approaches employed to compare with our method.

In the stage of feature extraction, the normalized subimage is convolved with an adjusted

circular Gabor filter [50]

21

{ })sincos(2exp2

exp2

1),,,,( 2

22

2 θθπσπσ

σθ uyuxiyxuyxG +⎭⎬⎫

⎩⎨⎧ +−= , (2-3)

where 1−=i , 0916.0=u is the frequency of the sinusoidal wave, 4πθ = controls

the orientation of the function, 6179.5=σ is the standard deviation of the Gaussian

envelope. The signs of the filtered images are coded as a feature vector, which has been used

for iris recognition [72].

In palmprint matching, two PalmCodes are measured using the normalized hamming

distance. Due to imperfect preprocessing, translation is needed to get the final matching

score.

Competitive code (CompCode)

Competitive coding scheme [70] attempts to utilize the orientation information of palm lines

for palmprint recognition. Six orientations are specified for the competition according to the

neurophysiological findings [73]. The normalized subimage is convolved with the real parts

of the neurophysiology-based Gabor functions [73] along the six orientations, respectively,

to obtain the corresponding filter response of the palm line which is modeled in an

upside-down Gaussian shape. The orientation information of the palm line is determined by

applying a winner-take-all rule on the filtered results.

In the stage of palmprint matching, an angular distance is designed for comparing two

Competitive Codes. To implement real-time palmprint recognition, three bits are used to

represent an orientation. Based on this bit representation, a more effective and efficient

angular distance is defined for matching the Competitive Code.

Ordinal code

Sun et al [71] propose the orthogonal line ordinal features based on ordinal measures. This

method qualitatively compares two elongated, line-like image regions which are orthogonal

in orientation. The weighted average intensity of a line-like region is obtained using 2D

22

Gaussian filter [71]

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟⎠

⎞⎜⎜⎝

⎛ +−−⎟⎟

⎠

⎞⎜⎜⎝

⎛ +−=

22sincossincosexp),,(

yx

yxyxyxfδ

θθδ

θθθ , (2-4)

where θ denotes the orientation of 2D Gaussian filter, xδ and yδ denote the filter’s

horizontal scale and vertical scale, respectively. The scale ratio yx δδ should be higher

than 3 to make its shape like a line.

The orthogonal line ordinal filter, comparing two orthogonal line-like palmprint image

regions, is specially designed as follows [71]:

)2

,,(),,()( πθθθ +−= yxfyxfOF . (2-5)

For each local region in normalized subimage, three ordinal filters, )0(OF , )6(πOF ,

and )3(πOF , are performed on it to obtain three bit ordinal codes based on the sign of

filtering results. Finally, three ordinal templates named as ordinal code are obtained as the

feature of the input palmprint image. The matching metric is also based on Hamming

distance.

Palm-line structural features

In [61], Wu et al extract palm line structural features by using a set of directional line

detectors. They consider palm line as a kind of roof edge of which the position is determined

by the zero-crossing of their first-order derivative and the strength can be reflected by the

magnitude of their second derivative. Consequently, theθ -directional line detectors consist

of two filters which are convolution results of a 1D Gaussian smoothing filter in θ

direction with the first-order and the second-order derivatives of a 1-D Gaussian function in

2/πθ + direction, respectively. Four sets of directional line detectors in °0 -, °45 -, °90 -,

and °135 -directions are employed to extract the corresponding directional line images.

Finally, the palm line image is obtained by combining the four directional line images.

23

For palm-line matching, the palm line image is represented by the chain code [74]. The

chain code of a palm line is obtained by line tracing. The similarity of two palm line images

is measured by the ratio of the number of matched line points to the total number of line

points in two palm line images.

This palm-line extraction method achieves a good performance on a large-scale palmprint

database and considers only the structure features of palm lines. As discussed above, the

strength features, or width information, of palm lines is also very important to characterize a

palmprint clearly. Therefore, the performance can be improved further when considering the

strength features of palm lines, which will be addressed in Chapter 5.

2.4 Review of tongue crack detection

In this section, we first review the computerized tongue diagnosis and then introduce some

concepts of tongue cracks.

2.4.1 Review of computerized tongue diagnosis

Traditional Chinese Medicine (TCM) spans thousands of years and its practitioners have

accumulated very rich practical experiences in diagnostic methods. Tongue diagnosis [75,76]

ranks as one of the most important and widely used diagnostic methods in traditional

Chinese medicine. This method has proved, in practice, to be very valuable in clinical

applications and self-diagnosis. Furthermore, tongue diagnosis is a non-invasive technique

that is in accord with the most promising direction in the 21st century: no pain and no injury.

Traditional tongue diagnosis, however, has a very limited application in clinical medicine

due to its qualitative, subjective, and experience-based nature. Recently, researchers have

developed various methods and systems [8,77-86] to circumvent these problems. An

automatic tongue diagnosis system has been presented in [8,83] based on modern techniques

of image processing and pattern recognition, as illustrated in Fig. 2.5. A set of quantitative

and objective features and measurements have been developed according to the theories of

traditional tongue diagnosis. As many descriptive features in tongue diagnosis indicate some

24

implicit connections between color-related and texture-related features, various chromatic

features and textural features have been investigated for computerized tongue diagnosis.

In the aspect of extraction of chromatic features, Chiu [78] choose the HSL color model to

represent the color of tongue using saturation and luminance of the pixels inside the tongue

image. Yang [82] converts the tongue image from the color space of RGB to L*a*b so that

the color feature can be represented with only two parameters, *a and *b. Li and Yuen [80]

segment the tongue image into square blocks of 3636× , each represented by the mean of

its color pixels as three attributes using color values only in RGB color space and in CIE

LUV color space. Further, they investigate the color matching of tongue images by defining

a total of 10 different metrics in four color spaces (RGB, HSV, CIELUV, and CIELAB) [81].

Pang et al. [8,83-84] extract quantitative color features from four color spaces (RGB,

CIEYxy, CIELUV, and CIELAB) and use the mean and standard deviation of the colors of

pixels within the whole tongue region in all the four color spaces as the metrics for color.

Fig. 2.5 Flowchart of the automatic tongue diagnosis system in TCM. [8,83]

25

In the aspect of extraction of textural features, Chiu et al. [77] propose a structural texture

recognition algorithm which used certain features such as spatial gray-tone dependency

matrices (SGTDM) and Fourier power spectrum to verify or identify certain properties of

coating on the tongue. They further develop some SGTDM-based textural features such as

angular second moment, contrast, correlation, variance and entropy to determine the grimy

coating of a tongue [78]. Yuen et al. [79] apply the Gabor wavelet opponents color features

for tongue texture analysis, which contained both the multi-channel frequency properties and

color features. Yang [82] represents the texture features using Entropy and Energy functions

of a gray-level co-occurrence matrix. Pang et al. [8,83-84] employ two feature-based texture

descriptors, which are the second-order moment and the contrast measure of the gray-level

co-occurrence matrix, to extract different textural features from tongue images.

All of above methods have obtained encouraging results. However, none of them

considered physical and quantitative features in tongue diagnosis which have significant

pathological meanings. In Chapter 6, we will attempt to extract such feature and focus on

detecting tongue cracks, one of pathological features in tongue diagnosis.

2.4.2 Tongue crack

A cracked tongue [75] is frequently seen in clinical practice. The cracks on the tongue’s

surface resemble those that develop in soil after a prolonged period of drought. These cracks

can vary greatly in number and depth. They can be barely visible lines or extremely deep

fissures.

In general, there are no cracks in a normal tongue. The formation of cracks in the tongue

body may represent a lengthy pathological process. The most common cause of cracks is

dryness from exhaustion of the body fluids or yin. The clinical significance of cracks

depends on the tongue body color, the location of the cracks and their shape and depth. For

example, cracks in a pale tongue body can originate from a deficiency of blood. In the case

of deep cracks, besides deficiency of blood, there may also be injury to the fluids. A single,

small crack on the tongue body is less significant than cracks that are distributed over the

26

entire body of the tongue. In [75], tongue cracks are divided into seven types according to

the location and shape. Table 2.4 illustrates the seven types and their clinical significance in

tongue diagnosis. A common type of cracked tongue has a deep crack in the center reaching

to the tip, reflecting hyperactivity of Heart fire.

In spite of the clinical significance of the tongue crack, little work has been done on it.

Therefore, in Chapter 6, we will address the issue of tongue crack detection for tongue

diagnosis.

2.5 Conclusions

This chapter has introduced the primary techniques for line detection. We have reviewed

some well-know wide line detection approaches such as Koller’s algorithm [26], Steger’s

approach [3], and the line operator [4]. We have overviewed palmprint recognition and

reviewed the state-of-the-art palmprint recognition methods. We have also overviewed the

computerized tongue diagnosis and introduced the concepts of tongue cracks. In the

following chapters, we will present our proposed methods and compare them to those

existing approaches described in this chapter.

27

Table 2.4 Seven types of tongue cracks. [75]

Crack Type Clinical Significance Illustration

Horizontal cracks yin deficiency

Cracks like ice floes

yin deficiency from old age

Irregular cracks Stomach yin deficiency

Transverse cracks on sides

Spleen qi deficiency

Vertical cracks in center

Heart yin deficiency or blazing Heart fire

Transverse cracks behind tip

Lung yin deficiency

Very deep central crack with other small cracks

Kidney yin deficiency with heat

28

Chapter 3

Wide Line Detection

In this chapter, we present a novel wide line detector using an isotropic nonlinear filter.

Unlike most existing edge and line detectors which use directional derivatives, our proposed

wide line detector applies a nonlinear filter to extract a line completely without any

derivative directly used. The detector is based on the isotropic responses via circular masks.

A general scheme for the analysis of the robustness of the proposed wide line detector is

introduced and the dynamic selection of parameters is developed. In addition, this chapter

investigates the relationship between the size of circular masks and the width of detected

lines. A sequence of tests has been conducted on a variety of image samples and our

experimental results demonstrate the feasibility and effectiveness of the proposed method.

3.1 Introduction

The analysis of images in the fields of pattern recognition and computer vision generally

requires the detection of lines, also called curvilinear structures, from grayscale images. Line

detection plays an important role for the success of higher-level processing such as matching

and recognition [40,87-91]. Most of existing line detection methods focus on locating line

positions. Although the line position detection is important, it would be useful if all the line’s

pixels (i.e., the pixels that comprise the full cross-sectional width) were also extracted.

A line, mathematically, is a one-dimensional figure without thickness, but an image line

generally appears as a line of one or several pixels wide, i.e., as a thin/narrow or thick/wide

line, having linear or curvilinear structures. In image processing and pattern recognition

applications, line thickness or a line’s full cross-section is important in, for example,

segmenting multiple orientation lines [39], in recognizing roads, railroads, or rivers from

29

satellite or aerial imagery [20,34], in extracting anatomical features in medical imaging for

diagnoses [4,8,28], and in detecting biometric traits for personal authentication [13]. It is

thus important to detect not simply the line edges but rather the whole of the line.

In this chapter, we present a robust method to detect the whole of the line, which we call

the wide line detector. This wide line detector is implemented by employing a nonlinear

filter without the direct use of any derivative. Isotropic responses are obtained by using

circular masks which contain either a normalized constant weighting or a Gaussian profile.

We restrict the sizes of circular masks so as to ensure that lines of different widths can be

extracted in their entirety. We also design a line model which can analyze the robustness of

the proposed wide line detector and which allows the automatic selection of parameters.

The chapter is organized as follows. Section 3.2 introduces the line model and the relevant

design issues. Section 3.3 presents the isotropic nonlinear filter based line detection method.

In Section 3.4, we analyze the robustness of the proposed method and show how to

automatically select parameters. Section 3.5 describes the results of our experiments. Section

3.6 offers our conclusion.

3.2 Model design

In this section, we first introduce the models for line profiles in 1D and then describe the

design issues for the proposed line detection method with particular reference to 2D line

detection.

3.2.1 1D line profile model

Many line detection approaches model lines in 1D as bar-shaped [26], i.e., the ideal line of

width w×2 and height h is assumed to have a profile given by [3]

⎩⎨⎧

>≤

=wxwxh

xIL,0,

)( . (3-1)

However, the flatness of this profile is rarely found in real images. Generally speaking, in

30

terms of different gray levels, there are three regions in a line image: the line part having a

gray level IGr , the edge region having a gray level IIrG , and the background having a gray

level IIIGr . As an example, consider a bright line on a dark background, then we get

IIIIII rr GGGr >> . In this chapter, therefore, a model for the common line profile in 1D, the

edge-based bar-shaped line, is defined as

⎪⎩

⎪⎨

⎧

><<

≤×=

e

el

l

wx wxwb

wxhxGL

,0,,1

)( , (3-2)

where 0>> le ww and ]1,0[∈b and h is a scale or a vector, which represents height in the

1D case and intensity in the 2D case. For a bright line, also called a positive line, 0>h .

For a dark line, also called a negative line, 0<h .

3.2.2 2D line detection

We now address the design issues for the proposed line detection method. Fig. 3.1 shows a

dark line ( 0<h ) in 2D based on the 1D ideal line model IL as in (3-1). A circular mask is

shown at four image positions in Fig. 3.1. The detector groups pixels whose brightness is

similar to the brightness at the center of the mask into a weighted mask having similar

brightness (WMSB). This similarity can be measured by:

⎩⎨⎧

>≤

=tyx-IyxIiftyx-IyxIif

tyxyxs),(),( ,0),(),( ,1

),,,,(00

0000 , (3-3)

where ),( 00 yx is the coordinate of the center, ),( yx is the coordinate of any other pixel

within the mask, ),( yxI is the brightness of the pixel ),( yx , and t is the brightness contrast

threshold. The summation of the outputs s within the circular mask gives the mass of WMSB.

According to (3-3), when the center of the mask moves to a line on the image, the WMSB

reaches the global maximum as the mask lies in a flat region of the image (as the mask a

shown) and decreases when the center of the mask is very near a straight edge (as shown in

the mask b) and decreases even further when very near the straight edge while remaining

31

Fig. 3.1 Four circular masks at different positions on a line image based on the 1D ideal line

model IL as in (3-1).

Fig. 3.2 Five circular masks at different positions of a line image based on the 1D common

line profileGL as in (3-2).

nonetheless in the line region (as shown in the mask d). Therefore, the smaller the WMSB

mass, the larger the feature response. This is similar to the idea used for edge extraction and

corner detection in [49]. Hence, to detect a line completely, the WMSB mass of any pixel on

the line should be less than that of any background pixel.

Now let us consider a general situation: a line with an edge region in 2D based on the

common 1D line profileGL as in (3-2). Fig. 3.2 provides an illustration in which a dark line

a

b c

d e

Dark line

Gray edge

Bright background

Circle mask

Mask center a

bc d Dark line

Bright background

32

Fig. 3.3 Illustration of gray-level relations between three regions. IGr , IIrG and IIIGr

are gray levels of the line part, the edge region and the background, respectively. The

difference of the gray levels between the line ( IGr ) and the background ( IIIGr ) is larger than

the brightness contrast threshold t (a) with or (b) without larger than t×2 . (i), (ii), (iii) and

(iv) show the corresponding relations in (3-4), respectively.

is bounded by a gray band against a white background. In proximity to the lines are five

circular masks. According to (3-3), in order to completely detect the line it is necessary that

tGrGr >− IIII . It is obvious that no matter what value b and h take in (3-2), the three

different gray level regions (Fig. 3.3) have only four relations:

(i)⎪⎩

⎪⎨⎧

>−

≤−

tGrGr

tGrGr

IIIII

III (ii)⎪⎩

⎪⎨⎧

>−

>−

tGrGr

tGrGr

IIIII

III

(iii)⎪⎩

⎪⎨⎧

≤−

≤−

tGrGr

tGrGr

IIIII

III (iv)⎪⎩

⎪⎨⎧

≤−

>−

tGrGr

tGrGr

IIIII

III .

(3-4)

Now the question is how the edge region affects the WMSB mass of the line and the

background pixels and thereby influences line detection. These matters will be considered in

Section 3.4.2.

(ii) IIGr

(i) IIGr

IIIGr

IGr

t

t (iv) IIGr

(iii) IIGr

(i) IIGr

IIIGr

t

t (iv) IIGr

IGr

(a) (b)

33

3.3 Line detection method

The wide line detector is implemented to give isotropic line responses by applying a set of

rules in a circular mask. Using a square kernel, the circular mask is digitally approximated

by either with a constant weighting

⎩⎨⎧ ≤−+−

=otherwise

ryyxxifryxyx

0)()(1

),,,,(22

02

000ω , (3-5)

or with a Gaussian profile

2

20

20

2)()(

00 ),,,,( ryyxx

eryxyx−+−

−=ω , (3-6)

where r is the radius of the circular mask. The normalization of the circular mask is obtained

by the rule

∑+≤≤−+≤≤−

=

ryyryrxxrx

ryxyx

0000 ,

000 ),,,,(ω

ωω . (3-7)

As is usual when locally processing an image, the mask is centered on each pixel in the

image and the brightness of any other pixel within the mask is compared with that of the

center pixel. The comparison is determined by the rule defined in (3-3) along with a

weighting function 0ω :

),,,,(),,,,(),,,( 0000000 tyxyxsryxyxyxyxc ×= ω , (3-8)

where c is the output of the weighting comparison. This comparison is done for each pixel

within the mask. The WMSB mass of the center ),( 00 yx is given by

∑+≤≤−+≤≤−

=

ryyryrxxrx

yxyxcyxm

0000 ,

0000 ),,,(),( . (3-9)

The initial line response L is the inverse WMSB mass obtained by

34

⎩⎨⎧ <−

=otherwise

),(m if0

),(),( 0000

00

gyxyxmgyxL . (3-10)

Here g is the geometric threshold and 2/maxmg = , where maxm is the maximum value

which m can take (usually 2max rm π= ). The fixed threshold g for (3-10) is the theoretical

optimum which is shown in the later analyses.

According to (3-3), the comparison s varies dramatically when a slight change of the

brightness difference occurs very near the brightness contrast threshold t. In order to produce

a smooth profile near the brightness contrast threshold, a hyperbolic secant function was

used to give a much more stable and sensible version of (3-3) and is defined as:

500

00),(),(

sec),,,,( ⎟⎠⎞

⎜⎝⎛ −

=t

yxIyxIhtyxyxs , (3-11)

where xx eexh

−+=

2)(sec . The use of the 5th power introduces the minimum difference

from (3-3), as shown in Table 3.1. This equation is plotted along with (3-3) in Fig. 3.4 where

t is set to 10. It can be seen that, compared with (3-3), (3-11) produces a smoother profile

and does not have too large an effect on s as a pixel’s brightness changes slightly. This

equation makes a trade-off between stability about the threshold and the original requirement

of the function, which is to take pixels having intensities similar to that of the center together

into the mass of the circular mask.

Although the wide line detector is isotropic and can detect the whole of a line without the

need to find the direction of line pixels, line direction is still necessary either for

post-processing or for application requirements. From (3-10), the direction of a pixel with a

non-zero line response is determined by finding the longest axis of symmetry:

⎪⎪⎩

⎪⎪⎨

⎧

−

≥=

−

−

otherwisetan

0 ftan

1

1

m

m

mm

m

xy

dixy

φ , (3-12)

35

Fig. 3.4 Brightness difference versus the similarity functions defined in (3-3) and (3-11),

respectively. Here the brightness contrast threshold t is set to 10.

Table 3.1 The deviation of function PtyxIyxIh )/),(),((sec 00− from (3-3). Here c

is the subtraction of (3-11) from (3-3), and c is the absolute value of c.

P C c

2 2.6690 2.6690

3 1.0693 1.0693

4 0.4173 0.4173

5 0.0705 0.0705

6 -0.1427 0.1427

7 -0.2863 0.2863

8 -0.3893 0.3893

9 -0.4666 0.4666

10 -0.5264 0.5264

36

∑+≤≤−+≤≤−

−=

ryyryrxxrx

m yxyxcxxx

0000 ,

002

0 ),,,()( , (3-13)

∑+≤≤−+≤≤−

−=

ryyryrxxrx

m yxyxcyyy

0000 ,

002

0 ),,,()( , (3-14)

∑+≤≤−+≤≤−

−−=

ryyryrxxrx

m yxyxcyyxxd

0000 ,

0000 ),,,())(( , (3-15)

where ⎥⎦⎤

⎜⎝⎛−∈

2,

2ππφ . The value of φ is exactly correct only for lines parallel to one of

the coordinate axes or at an angle of 4π to a coordinate axis. In other cases, deviations of

the calculation of φ will occur. However, such deviation of φ from the line orientation is

small and can be ignored.

In some cases, only dark or bright lines are required, for example, with reference to blood

vessels in X-ray images (dark lines generally required) and aerial images (bright lines

generally required). Introducing a step function, )(∆Θ , we can implement the wide line

detector to extract bright or dark lines according to need:

5

00)(sec),,,,( ⎟⎠⎞

⎜⎝⎛ ∆∆Θ

=t

htyxyxs , (3-16)

where ⎩⎨⎧ >∆

=∆Θelse,0

0,1)( and

⎩⎨⎧

−−

=∆linebright if),(),(

linedark if),(),(

00

00

yxIyxIyxIyxI

.

3.4 Parameter selection

The proposed line detection method requires two parameters – the radius of the circular

mask, r, and the brightness contrast threshold, t. In this section, we provide analyses to show

how the two parameters affect the line detection result and then present approaches for

automatically selecting the two parameters so that the proposed method is robust.

37

3.4.1 Radius of circular mask, r

Obviously complete line detection requires that the circular mask should at least be bigger

than the line width. The radius of the circular mask, r, must therefore be restricted so as to

ensure that the whole of the line can be detected using the inverse WMSB mass. In this

subsection, we analyze the relationship between the radius of a circular mask, r, and the

width of the line detected, w×2 , first with regard to circular masks with a normalized

constant weighting and then those with a Gaussian profile.

Circular Mask with Normalized Constant Weighting

In this subsection, we employ the line mode IL to discuss the relationship between the size of

circular mask with constant weighting and the width of detected line.

Definition 1 Given an image region I and a line L of width w×2 , for any given

point Ip∈ , the distance of p to L, Lpd , is defined by the rule

{ }22 )()(),(,|),(minmLmLmmm ppppLmLL

Lp yyxxppdLpppdd −+−=∈∀= , (3-17)

where mL is the middle axis of L in the line direction.

Definition 2 Let C denote a circle region with radius r in an image. The mass of point 0p ,

the center of the circle region, is defined as

∫∫=C

pp dxdysM0

, (3-18)

⎪⎩

⎪⎨⎧

>

≤=

t-IIift-IIif

spp

ppp

0

0

,0 ,1

, (3-19)

where p is any other point in the circle region C and pI is the intensity of point p.

Proposition 1 Denote the background { }LyxIyxyxB ∉∈= ),(,),(|),( . For each

,Lpl ∈ ,Bpb ∈ if tIIbl pp >− , there exist

38

(1) lpM is monotonically decreasing relative to L

pld and }|max{ LpMM lpp lL

∈= for

each mL Lp ∈ .

(2) bpM is monotonically increasing relative to L

pbd and }|min{ BpMM bpp bB

∈= for

each { }wdpp LpbB b=∈ | .

Proof. Assume that the center of circular region C is the coordinate origin. Rotate the

coordinate axes about the origin so that the y-axis is parallel to mL , as shown in Fig. 3.5. We

define 11 pxw = and

22 pxw = , where { }LCpxx pp I∈= |max1

and

{ }LCpxx pp I∈= |min2

are the x-coordinates of the right- and left-most intersection

points of the circle region C and the line L, respectively. As there exists tIIbl pp >− , for

each BpLp bl ∈∈ , , according to (3-18) and (3-19), we can get ∫∫=LC

p dxdyMl

I

1 and

∫∫=BC

p dxdyMb

I

1 .

(1) For each Lpl ∈ , when the circle C is centered on lp (as shown in Fig. 3.5a), we

have

∫∫∫ ∫ −+−==−

−−

211

2

22

22 0

22

0

22 221wwx

x

xr

xrp dxxrdxxrdydxM p

pl

⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪

⎨

⎧

−≤+⎥⎥

⎦

⎤

⎢⎢

⎣

⎡⎟⎠⎞

⎜⎝⎛−+

−>

⎥⎥

⎦

⎤⎟⎠⎞

⎜⎝⎛ −

−−

+

⎢⎢

⎣

⎡ −+⎟

⎠⎞

⎜⎝⎛−+

=

rwwrr

wr

wr

wr

rww

rww

rww

rww

rw

rw

rwr

2211arcsin

2212

2arcsin1arcsin

12

21112

12

11

12

1112

π

(3-20)

where ww ≤≤ 10 . For convenience, denote

39

Fig. 3.5 Illustration of Proposition 1 and its proof.

21arcsin)( xxxxf −+= , (3-21)

where 10 ≤≤ x . Then the equation (3-20) can be rewritten as

⎪⎪⎩

⎪⎪⎨

⎧

−≤⎥⎦⎤

⎢⎣⎡ +

−>⎥⎦⎤

⎢⎣⎡ −+

=12

21)(

12)2()(

2

2

rwxxfr

rwxx

rwfxfr

Mlp

π,

where rwx 1= . It is obvious that the derivative 0≥′lpM . Therefore,

lpM is

monotonically decreasing relative to Lpl

d . Hence, when mL Lp ∈ , 0=LpL

d and LpM

takes the maximum value

⎟⎠⎞

⎜⎝⎛=−+=

rwfrwrw

rwrM

Lp2222 22arcsin2 . (3-22)

(2) For each Bpb ∈ , when the circle C is centered on bp (as shown in Fig. 3.5b), we

have bpb L

BCp SrdxdyM −π== ∫∫ 21

I

and

x

y

1w2w

1px2px

mL

L

C bpM

bpLS

y mL

x

1w

2w

1px2px

L

ClpM

(a) (b)

40

⎪⎪⎩

⎪⎪⎨

⎧

−<⎥⎦⎤

⎢⎣⎡ −+

−≥⎥⎦⎤

⎢⎣⎡ −

=

−+== ∫ ∫−

−−

rwxxfx

rwfr

rwxxfr

ww

xrxrxrdxdyS p

pbp

x

x

xr

xrL

21)()2(

21)(21

arcsin1

2

2

1

22221

2

22

22

π ,

where rwx 1= . It is obvious that 0<′bpLS . Therefore,

bpM is monotonically increasing

relative to Lpb

d . Hence, for each { }wdpp LpbB b=∈ | , L

pbd reaches the minimum value w,

and bpM takes the minimum value

⎪⎪⎩

⎪⎪⎨

⎧

>⎥⎦⎤

⎢⎣⎡ −

≤=−=

wrrwfr

wrrSrM

bpB Lp2)2(

221

2

2

2

π

ππ . (3-23)

□

The meaning of Proposition 1 is that, no matter what size of the circular mask, the smaller

the distance of the pixel to L, the larger the WMSB mass if the pixel is on the line, while the

smaller the WMSB mass if the pixel on the background. Consequently, pixels on the middle

axis of a line take the local maximum value of the WMSB mass, whereas pixels on the

background very near the edges of the line take the local minimum WMSB mass. As

mentioned in Section 3.2.2, in order to detect a line completely, the maximum of the WMSB

mass that the line pixel can take should be less than the minimum that the background pixel

can take. Therefore, according to Proposition 1 and its proof, from (3-22) and (3-23), we get

⎪⎩

⎪⎨

⎧

<≤<

<<<+

121

21)(2

210)2()(2

xxf

xxfxf

π

π, (3-24)

where rwx = .

41

Fig. 3.6 Illustration of the inequality relation about the ratio of the width of the line detected

to the radius of a circle mask with normalized constant weighting.

Figure 3.6 illustrates the inequality relations defined by (3-24). We can see that only

43.0≤x meets the inequality. Given the line width, the smaller the x value, the larger the

mask size r. There is a trade-off to be made here as a smaller ratio means a slower detection

yet the use of a larger ratio and therefore a smaller mask will undermine line detection.

Hence, we set 4.00 =x by experience. The relationship between the width of detected line,

w×2 , and the radius of a constant weighting circular mask, r, is

wr 5.2≥ . (3-25)

According to (3-22), the maximum of WMSB mass which line pixels can take is

)(2 02 xfrM

Lp = . Therefore, the geometric threshold g used in (3-10) is equal to

5.0)(2)(2 02

02 ≈π=π= xfrxfrg .

42

Table 3.2 Relationship between radii of Gaussian masks and approximately critical

widths of lines (ACLW) detected.

Circular Mask with Gaussian Profile

Now we discuss the relationship between the width of the line detected and the size of a

circular mask with a Gaussian profile. Although Proposition 1 is for a constant weight, it is

evident that we can get the same conclusion for a Gaussian weight. That is, the WMSB area

of a line reaches a local maximum when the line passes through the center of the circular

mask. Assume that a circle C with a radius r has a density )2/()( 222 ryxe +− and a line of

width w×2 traverses the center of the circle. Let CL denote the part of the line within the

circle. According to the definition of line response [see (3-10)], if a line of width w×2 is to

be completely detected by using a Gaussian mask with radius r, it requires

∫∫∫∫+

−+

−<

C

ryx

L

ryx

dxdyedxdyeC

2

22

2

22

22

21

, (3-26)

which is equivalent to,

Radius of Gaussian

mask ACLW Digital

ACLW

3 2.6 2

4 3.5 3

5 4.4 4

6 5.3 5

7 6.2 6

8 7.1 7

9 7.9 8

10 8.8 8

11 9.7 9

12 10.6 10

13 11.5 11

14 12.4 12

15 13.2 13

43

∫ ∫∫ ∫−

+−−

+−

<r xr

ryx

w xrr

yx

dxdyedxdye0 0

20 0

222

2

2222

2

22

21

, (3-27)

The right hand side can be simplified as

)1(2

21220 0

20 0

2 2

222

2

22

−−−

+−

−== ∫ ∫∫ ∫ erdeddxdyer

rr xr

ryx πρρθ

π ρ

, (3-28)

Therefore,

)1(4

212

0 02

222

22

−−+

−−<∫ ∫ erdxdye

w xrr

yx π. (3-29)

This equation determines the relationship between the width of the line detected and the

radius of a circular mask with a Gaussian profile. Given a mask with a radius r, the critical

width of the line detected is obtained when the left and right arguments of (3-29) are equal.

As the analytic form of the left function is not available, we provide only the approximate

critical width of the line detected as shown in Table 3.2, as well as the corresponding digital

approximations. Therefore, given a Gaussian profile mask of radius r, a line is definitely

detected if it is not wider than the digital approximation of the corresponding critical width.

3.4.2 Brightness contrast threshold, t

Ideally, a line is defined as the profile of two distinctive regions as described in Section 3.2.1

(see Fig. 3.1). However, in general, there are shaded areas between the two distinctive

regions, as shown in Fig. 3.2. Here, we call such area as the edge region. Therefore, we have

to take into account the influence of the edge region on the WMSB mass, which is related to

the brightness contrast threshold that defines the minimum contrast of the detected features.

In this subsection, we first analyze the relationship between the brightness contrast threshold

and the WMSB mass and then give the automatic selection of a proper t.

Proposition 2 Given a line L of width w×2 bounded by an edge region of width e denoted

by { }weewdwIyxyxE Lyx <<+≤≤∈= ,,),(|),( ),( and a circle C of radius r with the

constraint rw 4.0≤ . Define the background { }ELyxIyxyxB ∪∉∈= ),(,),(|),( . For each

44

Lpl ∈ , Epe ∈ , Bpb ∈ , if (i) tIIbl pp >− and (ii)

bl pp MM < , there exists

⎪⎩

⎪⎨⎧

>>−<

otherwiseMMtIIifMM

le

bele

pp

pppp . Here the sign “<< ” means much less than.

Proof. From Proposition 1, condition (ii) can be rewritten as BL pp MM < . As discussed

in Section 3.2.2, there are only four relations between three different gray-level regions:

Case 1: tIIbe pp >− and tII

el pp ≤− . Suppose ELL U=' , then 'L is a line with a

width of )(2 ew +× and mm LL =' . According to Definition 1, we always have '' L

pLp el

dd < .

From Proposition 1, for each '' Lpl ∈ ,

'lpM is monotonically decreasing relative to

'

'

Lp

ld .

Therefore, for each Lpl ∈ , Epe ∈ , Bpb ∈ , we get ble ppp MMM << .

Case 2: tIIbe pp >− and tII

el pp >− . From Proposition 1, for each Lpl ∈ , when

{ }wdyxEp Lyxl ==→ −

),(|),( , Lpl

d approaches the maximum value w, and lpM reaches

the minimum value ( )rwfrME

p 22=−

. From we << , we always get

( ) ( )lEe ppp MMM minmax =<

−. Therefore, for each Lpl ∈ , Epe ∈ , Bpb ∈ , we have

ble ppp MMM << .

Case 3: tIIbe pp ≤− and tII

el pp ≤− . According to (3-18) and (3-19), we have

21 rdxdyMC

peπ== ∫∫ . Obviously, for each Lpl ∈ , Epe ∈ , Bpb ∈ , we always have

ebl ppp MMM ≤< .

Case 4: tIIbe pp ≤− and tII

el pp >− . Based on Proposition 1, when 0=Lpl

d , lpM

takes the maximum value ( )rwfrMLp

22= . Suppose EBB U=' , then for each '' Bpb ∈ ,

when { }ewdyxEp Lyxb +==→ +),(|),(' , L

pb

d'

reaches the minimum w, 'b

pM takes the

45

minimum value ( )[ ]rwfrME

p 22 −=+

π . Owing to rw 4.0≤ , from Fig. 3.6, we can get

+<

EL pp MM . Therefore, for each Lpl ∈ , Epe ∈ , Bpb ∈ , we have bel ppp MMM << .

Hence, from Case 1 and Case 2, if tIIbe pp >− , we have

le pp MM < ; from Case 3 and

Case 4, if tIIbe pp ≤− , we have

le pp MM > .

□

From Proposition 2 and its proof, we conclude that for a given image, if the contrast

between the edge region and the background is less than the threshold t, the edge region can

be regarded as one part of the line; otherwise, the edge region must be regarded as one part

of the line. That is, for a given image, a large brightness contrast threshold may result in a

‘narrow’ line being detected, while a small brightness contrast threshold must result in a

‘broad’ line being detected. Therefore, the brightness contrast threshold t qualitatively

determines the width of lines detected.

Fig. 3.7 gives an example of line response images with different t. Here, dark line pixels

are extracted directly from the input segmented palmprint image (see Fig. 3.7a) by using a

constant weighting mask with a radius of 8 pixels. It can be seen that as the brightness

contrast threshold increases, the number of false response pixels and true response pixels are

both decrease. It is thus necessary to select a proper t to guarantee the detection of the whole

line. By experience, we defined t as

))(( Istdroundt = , (3-30)

where std is the standard deviation function, round means the nearest integer, and I is the

input image. According to (3-30), the brightness contrast threshold t used in Fig. 3.7a is 9.

46

Fig. 3.7 (a) A segmented palmprint image. Palm-line response images obtained using

brightness contrast thresholds t of (b) 6, (c) 7, (d) 8, (e) 9, (f) 10, (g) 11, (h) 15, (i) 20, and (j)

25.

(a)

(b) (c) (d)

(e) (f) (g)

(h) (i) (j)

47

(a) (b)

(c) (d)

Fig. 3.8 (a) A test image including straight lines and curves of different widths. The line

detection results obtained using (b) the edge-based line finder, (c) the ridge-based line detector,

and (d) the proposed wide line detector.

48

3.5 Experimental results

Our line detection method is implemented for the synthesized image and real images in

several different applications to completely detect lines of different widths. For the purpose

of establishing the effectiveness and robustness of our line detection method, the output

images of our wide line detector are compared with those of line detection approaches based

on edge extraction [26] and ridge detection [3], which are designed to extract the line width

along with the line position. For speed, the sech to the 5th power formula in (3-11) is

implemented using a look up table.

3.5.1 Synthesized image

We synthesized an image including straight lines and curves (curvilinear structures)

with different widths and different intensities. Fig. 3.8a shows the synthesized image.

Applying the proposed wide line detector we obtain the result shown in Fig. 3.8d. Here

we employed the core function defined in (3-11). The brightness contrast threshold used

is 11 according to (3-30). The maximum width in Fig. 3.8a is 5 and thus the operating

radius of circular mask is 7 according to (3-25). Fig. 3.8b and Fig. 3.8c show the line

detection results by the edge-based line finder [26] and the ridge-based line detector [3],

respectively. Since our method detects lines based on extracting the whole line while

the other two approaches detect lines based on detecting the corresponding edges of

each line pixel, we show the line detection result in the corresponding way, as shown in

Fig. 3.8b-d. It can be seen that the line detection results by using our method is more

accurate than that obtained by using either the edge-based line finder or the ridge-based

line detector.

3.5.2 Real image

Figures 3.9a-c are taken from [3] including two aerial images and one X-ray image. Figures

3.9g-i show the line detection results obtained using our wide line detector. The brightness

contrast threshold for each input image is calculated by (3-30). A circular mask with a

normalized constant weighting is used for each input image to detect lines and the

49

corresponding radius of the circular mask is determined according to (3-25) based on the

width of the widest line expected to be detected. In post-processing, we discarded very short

linear structures (<10 pixels) and very “rounded” line structures (the eccentricity < 0.75).

Figures 3.9d-f display the corresponding line extraction results reported in [3].

Figure 3.9d shows the line detection result obtained by using the ridge-based line detector.

We can see that the unjustified edge points are reported in the junction area because the line

width here exceeds the range of widths that can be detected and, further, that the estimation

of the line width of the road object in the bottom of the image is too large due to the effect of

the nearby vegetation. Figure 3.9g shows the corresponding line detection result obtained by

using our wide line detector. It can be seen that the method is able to correctly detect the

wide lines (i.e., essentially all the pixels that comprise line cross-sectional extents), even at

the junction area in the middle of the image and the road close to vegetation in the bottom

part of the image (see red circles).

The aerial image at Fig. 3.9b is more of a challenge. It contains a large area where the

model of the line does not hold, but as can be seen in Fig. 3.9h, our wide line detector

nonetheless works well. Because bright lines are needed here, we employed the equation

(3-16) as the core function of the wide line detector to suppress the dark-line response.

Comparing the line detection results obtained by the ridge-based line detection approach (see

Fig. 3.9e) and our method, we can see that the narrow line in the left upper part, which has a

width close to two, is extracted correctly by using our method, while the corresponding line

detected in Fig. 3.9e is not fully extracted as its cross-sectional extent is too narrow at some

positions. Further, the wide line in the right upper part of the image is detected completely in

Fig. 3.9h, while it is missed in Fig. 3.9e.

Fig. 3.9c is a low contrast X-ray image. Figs. 3.9f and 3.9i show the line detection results

by using the ridge-based line detector and our method, respectively. It can be seen that our

method certainly performs as well as the ridge-based line detector in delineating the

vascularstenosis in the central part, and is also able to detect some very narrow and thin

50

arteries (see red circles) which do not appear in Fig. 3.9f.

The next example, Fig. 3.10, which shows four segmented 128128× palmprint images

(the first row), is from the domain of biometrics. There are a number of reasons for

employing palmprint images to test our line detection method: (1) palm lines, referring to

principal lines and wrinkles [13], are negative lines of varying widths; (2) there are many

details on palm lines such as corners, junctions and branches; (3) some palmprints contain

complex structures along with different line widths, as shown in the last image of the first

row. This example compares the line detection results by using our method (see the last row)

with those by the edge-based line finder (see the second row) and the ridge-based line

detector (see the third row), all of which are displayed in black. We can see that all three line

detectors can extract the principal lines well, however, our method better detects details such

as the ellipse on the principal line in the first column image (see the red circle), the

intersection of two thin lines in the right parts of images of the middle two columns (see the

red circles), and the branches on the principal lines in the last column image (see red

rectangles). Further, our line detection method also outperforms the two other approaches for

the last column image, which contains complex palm lines.

Figure 3.11 displays three segmented tongue images in the first row, which followed by

the output images of the edge-based line finder (the second row), the ridge-based line

detector (the third row) and our wide line detector (the last row), respectively. The line

detection results are all displayed in red. In the first column image, there is a crackle, which

refers to a dark line in a tongue image, very thick and broad. Our line detection method

extracts this crackle correctly (see yellow circles), whereas the other two approaches not

only fail to correctly extract this crackle but, because the width of the crackle varies greatly,

miss branches of the crackle. In the middle column, the most salient crackle in the middle of

the image has an irregular structure, especially in the upper part where the width of the

crackle changes dramatically and becomes discontinuous. Again, only our method correctly

extracts the wide line and the interruption to the line (see the yellow circle). The other two

51

approaches produce unjustified edge points, and a misleadingly continuous line. The last

tongue image is the most difficult because it is low contrast and contains many line segments

of different thicknesses and widths. Comparing the corresponding three output images, it can

be seen that our method outperforms the other two approaches both in the extraction of the

wide line and in the detection of the line structures (see the yellow circles and rectangle). In

addition, because our method uses no derivative and the implementation of the circular mask

decreases the influence of the directional noise, our wide line detector gives strong noise

rejection, that is, produces false crackles caused by reflecting points much less than the other

two approaches (see all blue rectangles).

3.6 Conclusion and discussions

We have presented a novel wide line detector for extracting a whole line by using an

isotropic nonlinear filter. Unlike existing approaches, our method employs a hyperbolic

secant formula based nonlinear filter to detect the whole of the line. Isotropic responses are

obtained by using a circular mask either with a normalized constant weighting or with a

Gaussian profile. The method is robust because of the automatic selection of two

parameters – the size of the circular mask and the brightness contrast threshold. The line

detection method works very well for a range of images containing lines of different widths,

especially for those where the width of lines varies greatly. This method also works well

when the lines run close together or cross each other due to no line direction required to

estimate. Because the wide line detector is not dependent on the Gaussian kernel to detect

lines, even narrow lines can be extracted well as long as the intensity difference between the

narrow lines and the background is larger than the brightness contrast threshold.

Although the proposed line detection method focuses on extracting a whole line, the line

position, however, can be easily obtained through a thinning process. Furthermore, the

localization of lines via the detection is independent of mask sizes. In addition, the wide line

52

detector is robust against noise because there is no derivative used directly. Hence, it is

effective for practical applications in which noise is inevitable.

Finally, it should be pointed out that the proposed method requires the maximum width of

lines be estimated before detection, which is not considered in this chapter. In our method, if

given the maximum width of interested lines, the parameter r is accordingly determined and

all lines not wider than this maximum width may be detected as long as they are strong

enough. In order to apply our method fully automatically, our future work is to automatically

estimate the maximum line width for each input image. In Chapter 6, we will attempt to

achieve this aim for tongue crack detection.

53

(a) (b) (c)

(d) (e) (f)

(g) (h) (i)

Fig. 3.9 (a), (b) Aerial images and (c) an X-ray image taken from [3]. (d)-(f) The extraction

results of line positions and line widths reported in [3] where line positions are displayed in

white with the corresponding edges displayed in black. (g)-(i) The corresponding line

detection results obtained using our wide line detector are drawn in white.

54

(a) (b) (c) (d)

Fig. 3.10 The segmented palmprint images (first row) and the palm-line detection results

obtainedusing the edge-based line finder (second row), the ridge-based line detector (third row),

and our wide line detector (last row). Detected lines are displayed in black.

55

Fig. 3.11 Segmented tongue images (first row) and crackle detection results obtained using

the edge-based line finder (second row), the ridge-based line detector (third row) and the

proposed wide line detector (last row). Detected crackles are displayed in red.

56

Chapter 4

Analyses of the Wide Line Detector

In this chapter, we further analyze the wide line detector described in Chapter 3. We compare

the three choices of the core function by evaluating their performance on the synthetic image

and show the power of the hyperbolic secant function used as the core function in our wide

line detector. We describe the relationship between the real radius and operating radius and

illustrate the restriction on the real radius presented in Chapter 3. We also illustrate the

reasonableness of the calculation of line orientation given in Chapter 3. In addition, a

comparative study is conducted to demonstrate the robustness of the proposed wide line

detector to impulse noise.

4.1 Introduction

In Chapter 3, we have proposed a novel wide line detection method, wide line detector, and

proved its robustness and effectiveness by an investigation on a variety of image samples.

However, some issues should be addressed further.

First of all, the optimal core function for the wide line detector should be determined. The

core function, the measurement of brightness similarity, is the heart of the wide line detector.

In Chapter 3 a hyperbolic secant formula is used as the core function, while in our

preliminary work [95] an exponential formula is employed (3-11). Although both formulae

give a balance between the stability and sensibility of the measurement of similarity, it is

necessary to analyze the two types of core function, as well as the original brightness

similarity measurement (3-3), to determine which formula is optimal for the proposed wide

line detector. In signal detection theory, the signal-to-noise ratio is a good measure for

detection methods and ROC analysis provides tools to select possibly optimal models.

57

Therefore, we will employ the signal-to-noise ratio and the ROC curve to choose the optimal

core function for the proposed wide line detector.

Radius of circular mask is one of the two parameters of the proposed wide line detector

and plays a very important role in the detection of the complete line. In Chapter 3, we

investigate the relationship between the radius of circular mask and the width of detected

line. As this relationship is based on the real radius which is decided by the area of circular

mask and in general is not an integer, it is inconvenient in practice. Hence, we will study the

relations between the real radius and the size of square kernel which is employed to

approximate to the circular mask and thereby extend the relationship to the size of square

kernel.

Line orientation is not needed for our wide line detector. However, it is still necessary to

calculate line orientation either for post-processing or for application requirements. The

calculation of the orientation of line which is described in Chapter 3 is not exact but

approximate in most cases. We will illustrate the reasonableness of the approximation of the

calculation of line orientation.

Finally, the robustness of our wide line detector to noise should be considered further. Our

wide line detector is not based on derivatives of images and thus is robust against noise. We

will further demonstrate and analyze the robustness of our wide line detector to impulse

noise by comparing with two well-known line detection approaches [3,26].

The Chapter is accordingly organized as follows. Section 4.2 introduces the concepts of

performance evaluation which is used in the rest of this Chapter. Section 4.3 describes a

scheme to determine the optimal core function of the proposed wide line detector by

evaluating the performance of various formulae. Two types of circular mask radius and the

calculation of line orientation are discussed in Section 4.4 and Section 4.5, respectively.

Section 4.6 demonstrates the robustness of the proposed wide line detector to impulse noise.

Finally, we give conclusions in Section 4.7.

58

4.2 Background

In this section, we will introduce the two concepts: signal-to-noise ratio and ROC curve,

which will be used in the rest of this Chapter.

4.2.1 Signal-to-noise ratio

A good measure for a detection method is its output signal-to-noise ratio (S/N). In his

seminal work on computational edge detection, Canny [27] gave the definition of the output

signal-to-noise ratio of a detector for step edges as

∫

∫+

−

−=

W

W

W

dxxfn

dxxfA

)(

)(SNR

20

0

, (4-1)

where f is the response of the filter which is assumed to be zero outside of the region

],[ WW− , A is the amplitude of the step, and 20n is the mean-squared noise amplitude per

unit length.

The value of SNR is the output signal to noise ratio and should be as large as possible. The

signal-to-noise ratio is a measure of how the signal from the interested objects compares to

other background reflections (categorized as "noise"). Informally, signal-to-noise ratio refers

to the ratio of useful information to false or irrelevant data. In section 4.3, we will employ

the S/N measure to evaluate the performance of the proposed wide line detector based on

various core functions.

4.2.2 ROC curve

In signal detection theory, a receiver operating characteristic, or simply ROC curve [96], is a

graphical plot of the sensitivity vs. (1-specificity) for a binary classifier system as its

discrimination threshold is varied. The ROC curve can also be represented equivalently by

plotting the true positive rate (TPR) and against the false positive rate (FPR) for the different

possible cutpoints of a test. ROC analysis is related in a direct and natural way to cost/benefit

59

Fig. 4.1 The ROC space and plots of the four prediction examples. [97]

analysis of decision making. Widely used in medicine [98-100], radiology [101-102],

psychology [96] and other areas for many decades, it has been introduced relatively recently

in other areas like biometrics [50, 103], computer vision [104], and machine learning [105].

Figure 4.1 illustrate the ROC space which is defined by FPR and TPR as x- and y- axes,

respectively. In this space, an ROC curve demonstrates several things: (1) It depicts the

relative trade-offs between sensitivity (TPR) and specificity (1-FPR): any increase in

sensitivity will be accompanied by a decrease in specificity; (2) the closer the curve follows

the left-hand border and then the top border of the ROC space, the more accurate the test; (3)

the closer the curve comes to the 45-degree diagonal of the ROC space, the less accurate the

test. In section 4.3, we will employ the ROC curve to analyze the output signal-to-noise ratio

for the selection of optimal core function.

60

4.3 Core function

In the wide line detector, the form of the brightness similarity function is the heart of WMSB

determination, called core function. In this section, we compare the different formulae for the

core function by evaluating their performance to the synthetic image and show the power of

the hyperbolic secant function.

4.3.1 SECH v.s. EXP

The brightness similarity function should guarantee counting pixels that have similar

brightness to the center of the circular mask into the mass of WMSB and counting pixels

with dissimilar brightness out of the mass of WMSB:

⎩⎨⎧

>≤

=tyx-IyxIiftyx-IyxIif

tyxyxs),(),( ,0),(),( ,1

),,,,(00

00000 , (4-2)

where t is brightness contrast threshold. In the wide line detector presented in Chapter 3, a

hyperbolic secant function was used to measure the brightness similarity and is defined as

JS

tyxIyxI

htyxyxs ⎟⎠⎞

⎜⎝⎛ −

=),(),(

sec),,,,( 00001 , (4-3)

where 5=JS in WLD. An alternative to the hyperbolic secant function can be given by

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−=JE

tyxIyxItyxyxs ),(),(exp),,,,( 00

002 , (4-4)

where JE is an even number.

Two core functions defined by the formula 1s of the sech to 5th power and the formula

2s of the exp to 6th power are plotted in Fig. 4.2, as well as the 0-1 formula 0s . The

motivation for introducing a particular formula is to give the tradeoffs between the stability

and the sensibility of the core function of the wide line detector. That is, the formula should

give a smooth profile to avoid dramatic changes near the brightness contrast threshold.

61

Fig. 4.2 Brightness difference versus the similarity formulae defined in (4-2), (4-3), and

(4-4), respectively. Here the brightness contrast threshold t is set to 10, 5=JS for (4-3), and

6=JE for (4-4).

At the same time, the formula should guarantee the original requirement of the core function,

which is to take all pixels whose intensities are similar to that of the center.

Besides smoothness near the brightness contrast threshold, the formula used as the core

function of the WLD should introduce the minimum deviation from the 0-1 function (as

defined in (4-2)) rather than the minimum MSE (mean squared error) because the wide line

detector is based on the inverse of summation of the core functions. Table 4-1 lists the

similarities of the core functions 1s and 2s with different powers and the deviation of the two

core functions from 0-1 function 0s . The deviation reaches the minimum when the core

function is defined as in (4-3) with 5=JS . Therefore, the optimal core function for the

proposed wide line detector is the formula 1s which is employed for the proposed wide line

detection method described in Chapter 3.

62

Table 4.1 Look up table of core functions 1s and 2s with different powers and the

deviation of the two core functions from 0s .

EXP ( 2s ) SECH ( 1s ) JE/JS

0II − 4 6 8 4 5 6 0s

0 1 1 1 1 1 1 1

1 0.9999 1.0000 1 1 1 1 1

2 0.9984 0.9999 1.0000 1.0000 1.0000 1 1

3 0.9919 0.9993 0.9999 1.0000 1.0000 1.0000 1

4 0.9747 0.9959 0.9993 0.9997 0.9999 1.0000 1

5 0.9394 0.9845 0.9961 0.9981 0.9995 0.9999 1

6 0.8784 0.9544 0.9833 0.9917 0.9970 0.9989 1

7 0.7865 0.8890 0.9440 0.9719 0.9860 0.9931 1

8 0.6639 0.7694 0.8455 0.9216 0.9486 0.9666 1

9 0.5189 0.5878 0.6502 0.8176 0.8478 0.8737 1

10 0.3679 0.3679 0.3679 0.6481 0.6481 0.6481 1

11 0.2313 0.1701 0.1172 0.4391 0.3842 0.3306 0

12 0.1257 0.0505 0.0136 0.2476 0.1650 0.1007 0

13 0.0575 0.0080 0 0.1146 0.0488 0.0160 0

14 0.0215 0 0 0.0429 0.0092 0.0011 0

15 0.0063 0 0 0.0127 0.0010 0 0

16 0.0014 0 0 0.0028 0 0 0

17 0 0 0 0 0 0 0

18 0 0 0 0 0 0 0

19 0 0 0 0 0 0 0

20 0 0 0 0 0 0 0

02/1 ss − -2.8720 -2.4456 -2.1651 0.4173 0.0705 -0.1427

02/1 ss − 2.8720 2.4456 2.1651 0.4173 0.0705 0.1427

63

(a)

(b)

Fig. 4.3 (a) A test image including straight lines and curvilinear structures of different

widths. (b) The ROC curves of (a) for the 0-1 function, the exp to 6th power formula, and the

sech to 5th power formula.

64

4.3.2 The power of the hyperbolic secant function

Using the synthetic image in Chapter 3, we show the power of the hyperbolic secant function

by comparing S/N of the wide line detector using three formulae defined in (4-2), (4-3), and

(4-4), respectively. The 0-1 function 0s , as defined in (4-2), formulates the principle of our

method. The formula 1s of the sech to 5th power is the core function used in the proposed

wide line detector. The formula 2s of the exp to 6th power was used to detect edge and corner

in [49]. The signal-to-noise ratio is compared using the ROC curve [101]. The ROC curve

for the method was obtained thresholding the line-strength image at a series of values and

comparing the resulting binary images with the ground truth. Detected pixels were counted

as true positives if they coincided with the synthetic image, and false positives otherwise. We

used 100 threshold values to cover the true and false fraction ranges evenly. The resulting

ROC curves for the synthetic image (Fig. 4.3a) are shown in Fig. 4.3b. These results suggest

that the wide line detector using the sech of 5th power (SECH) produces the best

performance.

Fig. 4.4 is the ROC curves of the synthetic image (Fig. 4.3a) for the 0-1 function 0s and the

formula 1s of the sech to 5th power with two weightings defined in (3-5) and (3-6),

respectively. We can see the performance of the SECH based wide line detection method is

higher than that using the 0-1 function, no matter what kind of weighting method used.

Hence, the SECH formula is the optimal core function for the proposed wide line detector.

Fig. 4.5 gives an example to show the importance of introducing the SECH formula. Fig.

4.5a is a synthesized image which contains a bright line of 5 pixels wide. According to the

scheme of parameter selection described in Chapter 3, the brightness contrast threshold is 3

and the radius of circular mask is 7. Fig. 4.5b and Fig. 4.5c are line strength images by using

the 0-1 function and the SECH formula, respectively. We can see the 0-1 function fails to

detect the whole line whereas the SECH formula succeeds.

65

Fig. 4.4 The ROC curves of Fig. 4.3a for different functions and different weighting.

(a) (b) (c)

Fig. 4.5 (a) A synthesized image with a bright line of 5 pixels wide. The pixel values are

marked. (b) and (c) The line response images by using the 0-1 function and the SECH to 5th

power function, respectively. The line responses on the center pixel and at the most left pixel

are shown.

66

4.4 Radius of circular mask

The wide line detector is implemented using an isotropic nonlinear filter. In Chapter 3, we

analyzed the relationship between the radius of a circular mask, r, and the width of the line

detected, w×2 , and concluded wr 5.2≥ . In this section, we will firstly describe the

relationship between the real radius and operating radius and then illustrate the restriction on

the real radius, r. Finally, we will extend this restriction to the operating radius.

4.4.1 Operating radius v.s. real radius

The isotropic filter, also called circular mask, is approximated by square. We call the radius

decided by the area of circular mask (the number of mask pixels) real radius, i.e. the radius

of circular mask r as defined in (3-5). The radius of a square kernel is referred to operating

radius. Using operating radius, the circular mask can be redefined as

⎩⎨⎧ +≤−+−

=otherwise

dRyyxxifryxyx op

0)()(1),,,,(

2220

20

00ω , (4-5)

⎥⎦

⎥⎢⎣

⎢=

3opR

d , (4-6)

where d is a positive integer and opR is the operating radius. Figure 4.6 is an example of a

circular mask approximated by a square kernel of 1515× where the operating radius is 7

pixels and the real radius is 7.5 pixels. Table 4.2 gives operating radii of square kernels with

different sizes, as well as the corresponding real radii of circular masks.

67

Fig. 4.6 An example of circular mask approximated by a square kernel of 1515× .

Table 4.2 Square kernel and the corresponding operating radius and real radius. Here the

operating radius is half the number of pixels along x or y-direction excluding the center

pixel.

Mask size

Operating radius

Real radius

77× 3 3.43

99× 4 4.26

1111× 5 5.32

1313× 6 6.41

1515× 7 7.51

1717× 8 8.39

1919× 9 9.66

2121× 10 10.54

2323× 11 11.57

2525× 12 12.68

2727× 13 13.74

2929× 14 14.64

3131× 15 15.89

3333× 16 16.78

3535× 17 17.74

3737× 18 18.92

3939× 19 19.91

4141× 20 20.88

4343× 21 22.06

4545× 22 23.02

4747× 23 23.94

4949× 24 25.16

68

4.4.2 Relationship of mask radius and detected line width

In Section 3.4.1, analysis shows only 43.0≤= rwx , where r refers to the real radius, can

guarantee the complete detection of a line with w×2 pixels wide. Although any value of x

below 0.43 can satisfied the requirement of complete line detection, it is obvious there is a

balance between the time efficiency and detection ability of the wide line detector. Given the

line width, a smaller ratio means a slower the detection speed, while a larger ratio which

indicates a smaller mask will undermine line detection. Table 4.3 lists the values of x given

different widths and different radii. The complete detection of line L requires the subtraction

of the WMSB mass 0LW from

0BW gives a positive value, where 0LW is the maximum

WMSB mass of line pixels and0BW is the minimum WMSB mass of background pixels.

Table 4.3 indicates that this requirement will be satisfied when the value of x is equal to or

less than 0.4, no matter what the values of the width and radius. Hence, we set 4.00 =x and

thus get the relationship of the radius of circular mask and width of detected line, wr 5.2≥ .

However, this relationship is for real radius of a circular mask and not convenient in

practice where is usually expected to know the proper operating radius directly. According to

(4-5), (4-6), and (3-5), we have

22

2

3r

RR op

op =⎟⎟⎠

⎞⎜⎜⎝

⎛+ . (4-7)

Considering (3-25), we can get the relationship of the operating radius and the detected line

width

wRop 3.2≥ . (4-8)

Figure 4.7 shows the WMSB mass of wide lines with different widths. We call the

minimum interger satisfying equation (4-8) critical operating radius. In Fig. 4.7, the values

of critical operating radii are 6, 17, and 28 pixels for lines of 5, 15, and 25 pixels wide,

respectively.

69

Table 4.3 The values of x given different widths and different radii. Here the operating

radius is half the number of pixels along x or y direction excluding the center pixel. 0L is

the line pixel where WMSB mass of line pixels reaches the maximum, while 0B is the

background pixel where the WMSB mass of background pixels reaches the minimum.

Line width (pixel)

Operating Radius (pixel)

Real Radius (pixel)

0LW 0BW

00 LB WW − x

1 1.2616 0.60 0.80 0.20 0.3963 1

2 2.0342 0.38 0.77 0.38 0.2458

2 2.0342 0.62 0.69 0.07 0.4916

3 3.4318 0.38 0.68 0.30 0.2914 2

4 4.2595 0.32 0.72 0.40 0.2348

2 2.0342 0.85 0.69 -0.15 0.7374

3 3.4318 0.57 0.59 0.03 0.4371

4 4.2595 0.47 0.63 0.16 0.3522 3

5 5.3226 0.37 0.67 0.30 0.2818

3 3.4318 0.70 0.59 -0.11 0.5828

4 4.2595 0.60 0.58 -0.02 0.4695

5 5.3226 0.47 0.60 0.12 0.3758 4

6 6.4080 0.40 0.64 0.24 0.3121

4 4.2595 0.72 0.58 -0.14 0.5869

5 5.3226 0.57 0.56 -0.01 0.4697

6 6.4080 0.50 0.59 0.09 0.3901 5

7 7.5061 0.42 0.62 0.20 0.3331

5 5.3226 0.67 0.56 -0.11 0.5636

6 6.4080 0.59 0.55 -0.04 0.4682

7 7.5061 0.50 0.57 0.07 0.3997 6

8 8.3873 0.45 0.60 0.15 0.3577

6 6.4080 0.67 0.55 -0.12 0.5462

7 7.5061 0.57 0.54 -0.03 0.4663

8 8.3873 0.52 0.56 0.04 0.4173

9 9.6574 0.45 0.59 0.14 0.3624

7

10 10.5399 0.42 0.62 0.20 0.3321

70

(a)

(b)

71

(c)

Fig. 4.7 The plots of WMSB mass of lines with width of (a) 5 pixels, (b) 15 pixels, and (c)

25 pixels, respectively.

(a) (b) (c) (d)

Fig. 4.8 The line with orientation of (a) 15 degree, (b) 30 degree, (c) 60 degree, and (d) 75

degree, respectively.

72

4.5 Line orientation

As our wide line detector is based on an isotropic nonlinear filter, no line orientation is

required for line detection. However, the calculation of line orientation is necessary either for

post-processing or for application requirements. In Chapter 3, we give the way to calculate

the orientation of a line pixel, φ . According to the definition of (3-12), the calculation of φ

is correct only for lines either parallel to one of the coordinate axes or at an angle of 4/π

to a coordinate axis. In this section, we will illustrate although the error of the calculation of

φ will occur in other cases, such error is very small and thus can be ignored.

One pixel wide lines with different orientations are shown in Fig. 4.8. Figure 4.8a and

4.8b are more horizontal lines with orientation of 15 degree and 30 degree, respectively.

While Figure 4.8c and 4.8d are more vertical lines with orientation of 60 degree and 75

degree, respectively. Table 4.4, according to the definition (3-12), gives the calculated φ of

lines in Fig. 4.8 with different widths. Two masks are employed to calculate line orientations,

one is of 77× (the operating radius is 3) and the other is of 1313× (the operating radius

is 6). The brightness contrast threshold used here is 10. We can see that errors of φ due to

the definition of (3-12) are small. Moreover, the calculation of φ keeps the characteristic of

the line orientation. That is, the error of the calculation of φ from line orientation makes a

more horizontal line (as shown in Fig. 4.8a and Fig. 4.8b) more horizontal, while a more

vertical line (as shown in Fig. 4.8c and Fig. 4.8d) more vertical. Hence, the error of the

calculated φ can be ignored and the calculation of φ can satisfy the requirement of

post-processing and applications.

73

Table 4.4 The calculated φ . Here opR is the operating radius which is half the number of

pixels along x or y-direction excluding the center pixel.

Calculated Orientation (degree)Line Orientation

(degree)

Line Width (pixel)

3=opR 6=opR

Digital Orientation (degree)

1 8.1301 6.8924

2 14.9951 8.8999

3 --- 9.5644

4 --- 12.8451

5 --- 14.7746

15

6 --- ---

15.9453

1 23.1986 17.1027

2 28.9677 18.9528

3 --- 19.5607

4 --- 22.5304

5 --- 24.2539

30

6 --- ---

29.7449

1 66.8014 72.8973

2 61.0323 71.0472

3 --- 70.4393

4 --- 67.4696

5 --- 65.7461

60

6 --- ---

60.2551

1 81.8699 83.1076

2 75.0049 81.1001

3 --- 80.4356

4 --- 77.1549

5 --- 75.2254

75

6 --- ---

74.0546

74

Table 4.5 Comparisons of calculations per pixel for different line detection methods. The

size of the convolving kernel is NN × .

Line detection method Additions Multiplications

Koller’s approach 142 +N 82 +N

Steger’s approach* > 23N > 123 2 +N

Line Operator 142 −+ NN 2N

Wide Line Detector 32 2 −N 12 −N

* The calculations of convolving the image with the 2D Gaussian partial derivative kernels without considering the calculations introduced by computing eigenvector and eigenvalue of Hessian matrix.

4.6 Time complexity

In computational complexity theory, the time complexity of a problem is the number of steps

that it takes to solve an instance of the problem as a function of the size of the input. For a

given input image, the time complexity is related to the calculations per pixel, i.e., the

number of additions and multiplications for each pixel. Table 4.5 shows the time complexity

of the proposed wide line detector compared with there typical line detection methods,

Koller’s line finding approach, Steger’s line detection approach, and the Line Operator. In

terms of Big O notations, all the four line detection methods have the same polynomial time

complexity )( 2nO .

4.7 Robustness to impulse noise

Our proposed wide line detector applies an isotropic nonlinear filter to extract a line

completely without any derivative. Because the detection is not based on derivatives of

images, the wide line detector is robust against noise. In this section, a comparative study is

conducted to demonstrate the robustness of our method.

75

(a) (b)

(c) (d)

(e) (f)

Fig. 4.9 The test image (Fig. 4.3a) is added impulse noise with the noise density of (a) 0.01 and

(b) 0.1, respectively. Line strength images by using our wide line detector to (a) and (b) are

shown in (c) and (d), respectively. (e) and (f) are final results of line detection by performing

morphological operations to (c) and (d), respectively.

76

(a)

(b)

Fig. 4.10 Line detection results of the noisy image Figure 4.9a using (a) Koller’s edge-based

line finder [26] and (b) Steger’s ridge-based line detector [3].

The testing results are illustrated in Fig. 4.9. The test image is the synthetic image

employed in Chapter 3 (see Fig. 4.3a), which contains straight lines and curvilinear

structures of different widths with varying background. Fig. 4.9a and 4.9b are noisy images

by adding impulse noise to the test image with noise density of 0.01 and 0.1, respectively.

Applying our wide line detector to the two noisy images, we get line strength images Fig.

4.9c and 4.9d and then binarize them by proper thresholds. The threshold is the minimum

value which makes false negatives equal to zero. Here false negatives refer to true line pixels

not yet detected when thresholding line-strength image at a series of values. Fig. 4.9e and

4.9f demonstrate the final detection results after performing morphological operations (a

77

morphological opening operation followed by a removing spur operation) on binary images.

The final detection results show that line structures and widths of two noisy images are

preserved very well. Therefore, the robustness of our method against noise is not to remove

the impulse noise before detection but to prevent the impulse noise from deforming or

destroying the line structures and widths.

For comparison, Fig. 4.10 displays the line detection results of the noisy image Fig. 4.9a

using Koller’s edge-based line finder [26] and Steger’s ridge-based line detector [3]. Due to

derivatives employed to extract lines, both approaches are very sensitive to noise. In the line

detection results, line structures are destroyed where noise is present, as well as line widths.

Normally, before using a derivative-based detection method, a filter is employed to reject

noise and preserve image structures. However, it doesn’t always work well. The median

filter is regarded as an excellent rejector of impulse noise and is able to remove the noise and

replace the bad pixels with reasonable values [106]. Figure 4.11 displays the median filtering

results of the noised image Fig. 4.9b using three different neighborhoods: a 33× square,

a 31× horizontal line, and a 51× horizontal line. The one pixel wide line disappears in Fig.

4.11a using the median filter with a 33× square neighborhood and the filtering result image

is degraded. A median filter with a horizontal line neighborhood can keep the one pixel wide

line and yet much more noise, as shown in Fig. 4.11b and 4.11c. Also, directional distortion

occurs in the two filtering result images due to horizontal neighborhoods used. Therefore, no

matter what kind of neighborhoods used, the median filtering fails to offer the

derivative-based detection method a noise free and structure preserved image.

78

(a)

(b)

(c)

Fig. 4.11 Filter the noisy image Figure 4.9(a) using median filters with three different

neighbors: (a) a 33× square, (b) a 31× horizontal line, and (c) a 51× horizontal line.

79

4.8 Summary

In this Chapter, we have analyzed the proposed wide line detector further. The optimal core

function, the hyperbolic secant function of the 5th power, is determined by evaluating the

performance of various formulae. The relations between the real radius and the operating

radius are investigated to facilitate the parameter selection. The restriction on the real radius

is illustrated and is extended to the operating radius. The calculation of line orientation is

analyzed to show the reasonableness of the approximation results. The time complexity of

the proposed method is analyzed and shown that the wide line detector has the same time

complexity )( 2nO as the typical line detection methods. The robustness of our wide line

detector to impulse noise is also demonstrated by a comparative study.

80

Chapter 5

Palmprint Recognition by Using Line

Features

In this chapter, we address the first application of the wide line detector, a novel palm-line

feature extraction method for palmprint recognition, which is discussed in the introductory

chapter (cf. Fig. 1.1). This palm-line feature extraction method can detect line-like features

which convey both structure features and strength features of palm lines. An isotropic

nonlinear filter is employed to calculate the line strength of palmprint. Palm-line feature

images are obtained via binarilization of line strength images. A Gaussian smoothing filter

serves as post-processing for palm-line feature image denoise. A translation-invariant

similarity measure is introduced for palm-line feature matching. To determine the optimal

combination of parameters for the proposed palm-line feature extraction method, an

experimental scheme is designed. An extensive test is conducted on the PolyU Palmprint

Database [107]. Experimental results show that the performance of the proposed palm-line

feature extraction method is comparable with the state-of-the-art algorithm of palmprint

identification, which indicates that the palm-line feature is appropriate for palmprint

recognition.

5.1 Introduction

Biometrics, an important and powerful technique for personal recognition, is becoming more

and more popular in today’s information and networked society. The biometric

computing-based approach is concerned with identifying a person by his/her characteristics

[47,108]. These characteristics can be divided into two categories. One is physiological

characteristics including fingerprints [109-110], face [111-113], iris [72], hand geometry

81

[114], and palmprints [50]. The other is behavioral traits such as voice [115-116], signature

[117], and gait [118-119]. Based on the intrinsic features of a human being, biometric “keys”

or “passwords” are always available and reliable for automatically recognizing a person’s

identity.

Fingerprint identification [109-110] is the most well-known and widespread biometric

method. However, manual workers and elderly people may have great difficulty to provide

clear fingerprint for minutia extraction. Iris-based recognition has been successfully

developed [120], but it suffers from the inconvenience of iris picture capturing and even

breaks down due to unstable eyes. Thus, there is a demand for a new automatic personal

identification system.

Recently, there has been a great deal of attention devoted to the study of palmprint-based

personal identification [13,48,50-51,55,58-59]. Palmprint is one of the most reliable traits in

personal recognition due to its stability and uniqueness. Palmprint-based personal

verification is user-friendly and convenient. Moreover, palmprint-based identification can be

operated by a low cost and low resolution imaging device. In the palmprint identification

system developed by the Biometric Research Centre in the Hong Kong Polytechnic

University, a charge-coupled device (CCD) camera is used to capture low-resolution

(<100dpi) palmprint images. To limit the palm’s stretching, translation, and rotation, the

CCD-based palmprint capture device [50] is fitted with some pegs. These pegs separate the

fingers and thus form holes, one between the forefinger and the middle finger and the other

between the ring finger and the little finger. A typical palmprint image captured by this

system is shown in Fig. 5.1.

82

Fig. 5.1 The main patterns in a palmprint. [13]

5.1.1 Palm lines

The main patterns in a palmprint image, as illustrated in Fig. 5.1, can be generalized to

principal lines, wrinkles, and creases (also called ridges). Usually, there are three principal

lines in a palmprint: the heart line, the head line, and the life line. These lines vary little over

time, and their shapes and locations on the palm are the most important physiological

features for individual recognition. Most wrinkles are much thinner than the principal lines

and much more irregular. However, some wrinkles of some palms are as strong as the

principal lines and also stable and reliable for identification. Creases exist all over the palm

just like the ridges in a fingerprint and cannot be observed in low-resolution images.

Although some crease-based palmprint recognition methods [121] have been proposed, they

require rather high resolution imaging and consume a large amount of data. Generally

speaking, the principal lines and wrinkles, also called palm lines, are stable and reliable for

individual identification and can be exploited and derived from a low-resolution palmprint

image.

Palm lines have their own properties. Firstly, palm lines are negative lines (also called

dark lines) on which pixels’ intensities are lower than neighbours’. Secondly, palm lines,

Principal lines

Wrinkles

Creases

83

especially principal lines, consist of many short line segments and curves which form many

corners, junctions, branches, rings and chains. Finally, principal lines and some thick

wrinkles are very strong and look wider than other light palm lines. That is, palm lines have

different width which generally reflects strength information. The width feature of palm lines

is very important to describe a palmprint clearly especially when different palmprints have

similar line structures. Hence, not only structure features but also width information of palm

lines is necessary and important for palmprint recognition.

Although line features play an important role in palmprint identification, little work has

been done on line feature based palmprint recognition. In [50], Zhang et al pointed out that it

is difficult to obtain a high recognition rate using only principal lines because of their

similarity among different people. In this chapter, we will investigate on the ability of palm

lines to recognize palmprint images.

5.1.2 Review

Palm-line based palmprint identification schemes, such as interesting points, line segments

and line features, have been presented. In the offline palmprint verification, Zhang et al. [48]

approximated line features by using several straight-line segments. Duta et al. [51] extracted

a set of feature points along palm lines and the associated line orientation to represent line

features. You et al. [58] detected interesting points by applying the Plessey operator, a corner

detector, to achieve higher performance than edge points by eliminating the redundancy. Han

et al. [59] extracted the line-like features of a palmprint by using a morphological edge

detector.

In the past several years, more and more researchers have focused on the on-line palmprint

identification for the real-time application. You et al. [55] further extracted the “interest”

lines based on the interesting points by applying a fuzzy rule. Zhang and Zhang [13]

obtained a set of statistical features of palm lines to characterize a palmprint by employing

the overcomplete wavelet expansion. Wu et al. [60], for the first time, directly extracted palm

lines through morphological operations and trace each extracted line in a recursive process.

84

They further devised a set of directional line detectors to extract palm lines in different

directions and represented these irregular lines using chain codes [61]. However, none of

these offline and online palmprint recognition methods considers width features of palm

lines which indicate their strength characters.

In this Chapter, we focus on palmprint recognition by detecting wide lines which convey

palm-line structure and strength features. A palm-line feature extraction method based on the

wide line detector [62] is proposed to extract line-like features which contain width

information of palm lines. To give isotropic responses, circular masks of different radii are

digitally approximated via a constant weighting. By inverting the WMSB mass, the line

strength of palmprint is determined. Palm-line feature images are obtained via binarilization

of line strength images. A Gaussian smoothing filter serves as post-processing for palm-line

feature image denoise. For palm-line feature matching, a translation-invariant matching

method is introduced. An experimental scheme is developed to select the optimal

combination of parameters for the proposed palm-line feature extraction method.

The Chapter is organized as follows. Section 5.2 describes the proposed WLD-based

palm-line feature extraction method. The matching scheme for detected palm-line features is

provided in Section 5.3. Section 5.4 describes the palmprint database employed to test our

method and shows the experimental results of palm-line feature based palmprint verification

and identification. Finally, we make discussions and draw conclusions in Section 5.5.

5.2 Line-like feature extraction

In this section, we describe the palm-line feature extraction method based on the wide line

detector which is presented in Chapter 3. As palm lines are dark lines, according to the

equation (3-16), the core function of the wide line detector used to extract line-like features

is defined as

85

Fig. 5.2 Brightness difference versus the similarity defined in the core functions (5-1), (5-4),

and (5-5), respectively. Here the brightness contrast threshold t is set to 10.

⎪⎩

⎪⎨⎧

>⎟⎠

⎞⎜⎝

⎛ −×=

otherwise1

),(),( if),(),(

sec),,,,( 00

500

0001yxIyxI

tyxIyxI

htyxyxc ω , (5-1)

where t is the brightness contrast threshold and 0ω is the normalized circular mask which is

digitally approximated by a constant weighting

∑+≤≤−+≤≤−

=

ryyryrxxrx

ryxyx

0000 ,

000 ),,,,(ω

ωω , (5-2)

⎩⎨⎧ ≤−+−

=otherwise

ryyxxifryxyx

0)()(1

),,,,(22

02

000ω . (5-3)

where r is the radius of the circular mask. In [95], an alternative to the core function is

defined based on an exponential function

86

Fig. 5.3 A 3D plot of the WMSB mass given a test image with a 3 pixels wide line.

⎪⎩

⎪⎨

⎧>

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −

−×=

otherwise1

),(),( if),(),(

exp),,,,( 00

600

0002yxIyxI

tyxIyxI

tyxyxc ω (5-4)

Normally, the brightness contrast threshold t in (5-1) and (5-4) should be a positive integer.

However, when 0=t , both core functions will degrade to

⎩⎨⎧ >

×=otherwise1

),(),( if0),,,,( 00

0000

yxIyxItyxyxc ω . (5-5)

The core function 0c is plotted in Fig. 5.2, as well as 1c and 2c , where t is set to 10 for (5-1)

and (5-4).

The comparison measured by any core function is done for each pixel within a circular

mask. The sum of all comparisons in the circular mask is calculated as the WMSB mass of

the center (ref. Eq.3-9) and the palm-line strength can be obtained by inverting the WMSB

87

mass (ref. Eq.3-10). The principal of the WLD-based palm-line feature extraction method is

illustrated in Fig. 5.3, where a test image with a 3 pixels wide line has been processed to give

WMSB mass as output. All of WMSB mass can be divided into two groups: one is obtained

from pixels on the line and the other is from background. The complete extraction of the line

requires the local maximum of WMSB mass given by pixels on the line be less than the local

minimum from background. This can be realized by selecting proper parameters for the wide

line detector.

Fig. 5.4 The palmprint sub-images (the first row) with the size of 128128× , the

corresponding line-strength images (the second row) using the wide line detector, the

palm-line feature images (the third row) via thresholding the line-strength images, and the

post-processed palm-line feature images (the last row) with the size of 6464×

88

Due to the normalization of circular masks, the WMSB mass varies between 0 and 1 and

thus the palm-line strength between 0 and 0.5. The palm-line feature image can be obtained

by removing all pixels which line-strength is below a threshold. Some examples of palmprint

sub-images are shown in Fig. 5.4, as well as the corresponding line-strength images and

palm-line feature images. Here the brightness contrast threshold t and the circular mask

radius r are set to 8 and 12, respectively. The threshold to obtain the binary palm-line feature

image is set to 0.1. As shown in the third row of Fig. 5.4, not only the structure features but

the width characters of palm lines are derived from the palmprint sub-images by using the

proposed WLD-based palm-line feature extraction method. However, there exists some noise

in the detected palm-line feature images. For denoise, a Gaussian smoothing filter is

employed and then the smoothed palm-line feature image is resized to 6464× for matching,

as shown in the last row of Fig. 5.4, where the scale of the Gaussian smoothing filter is 1.

In the wide line detector, two parameters, the brightness contrast threshold t and the radius

of the circular mask r, are required for complete line extraction. Figure 5.5 shows the

influence of the two parameters on the palm-line feature extraction results. With the increase

of the brightness contrast threshold, detected palm lines become thinner and weak lines will

be missed. While with the increase of the mask size, detected palm lines become wider.

Notice that given the brightness contrast threshold, when the radius of the circular mask

changes from 12 to 20, the width of detected palm lines especially principal lines varies little.

The increase of the circular mask radius reduces the noise of the palm-line feature extraction

results and yet lowers the completeness of detected wrinkles. Therefore, the parameter

selection has a great influence on the palm-line feature extraction and consequently on the

palm-line feature based palmprint identification.

89

0=t 4=t 8=t 12=t

4=r

8=r

12=r

16=r

20=r

Fig. 5.5 Palm-line feature extraction results using the WLD-based palm-line feature extraction

method with different brightness contrast thresholds t and different radii of the circular mask r.

For 0=t , the core function defined in (5-5) is employed.

90

5.3 Palm-line feature matching

A matching algorithm is described in this section to measure the degree of similarity between

two palm-line feature images. Let P and Q denote two palm-line feature images, the

similarity between P and Q is defined as the proportion of matched bits to the total line bits

in P and Q, i.e.,

∑∑= =

∧+

=N

i

N

jQp

jiQjiPMM

M1 1

),(),(2 , (5-6)

where ∧ is the logical AND operation, NN × is the size of palm-line feature image, and

PM and QM are the number of line pixels in P and Q, respectively. Obviously, M is

between 0 and 1. For perfect matching, the matching score is 1. Because of imperfect

segmentation of ROI region of the palmprint image, there may still be little translation

between the palmprints captured from the same palm at different times. To overcome this

problem, we need to translate one of palm-line feature images vertically and horizontally and

then perform the matching again. The maximum of matching scores obtained at all translated

positions is taken as the final matching score.

To implement an effective matching, we encode each binary palm-line feature image to a

bitwise line vector. According to this bit representation of the palm-line feature image, a

more effective implementation of translation-invariant matching score can be defined as:

∑∑

∑ ∑

= =

−

−=

−

−=

≤≤+

++∩= N

i

N

jbb

sNN

si

sNN

sj bb

ssssjiQjiP

sjsiQjiPM

1 1

)1,min(

)11,1max(

)2,min(

)21,1max(

|2|,|1|max

),(),(

)2,1(),(2max , (5-7)

where bP ( bQ ) is the bitwise line vector of P(Q), ∩ is the AND operator detecting

agreement between any corresponding pair of bits, and s is the translation range in the

matching process. The bit representation of palm-line feature image is not only effective for

matching but also effective for storage. The size of a line vector is 512 bytes for a palm-line

feature image size of 6464× .

91

5.4 Experimental results

An extensive test has been conducted on a large-scale palmprint database. In this section, we

will first describe the large-scale palmprint database and parameters required in the proposed

line feature based palmprint recognition method and then will report and analyze the

experimental results.

5.4.1 Palmprint database

The proposed palm-line feature detector has been tested on the public palmprint database

[107] built by the Biometric Research Center at the Hong Kong Polytechnic University. This

database contains 7,752 grayscale palmprint images corresponding to 386 different palms.

Around twenty samples from each of these palms were collected in two sessions, where

around 10 samples were captured in the first session and the second session, respectively.

The average interval between the first and the second collection was two months. The size of

these images is 284384× . In our experiments, the region of interest (ROI) is the central

128128× part of the palmprint image which was cropped by using the preprocessing

technique described in Section 2.3.3. This central part represents the whole palmprint and is

used for palm-line feature extraction. In the stage of palm-line feature extraction, for (5-1)

and (5-4), a look up table is calculated for speed.

5.4.2 Parameters for the palm-line feature based palmprint

recognition

In the proposed WLD-based palm-line feature extraction method, there are three parameters,

two for the wide line detector, the brightness contrast threshold t and the radius of circular

mask r, and one for post-processing, the scale of Gaussian smoothing filterσ . In the

palm-line feature matching scheme, there is one parameter, the translation range s. Therefore,

there are four parameters for the palm-line feature based palmprint recognition. From Fig.

5.5, we can see that palm-line feature extraction results vary greatly with different parameter

92

combinations. Hence, our experiments aim at finding the optimal parameter combination for

the palm-line feature based palmprint recognition.

For line-like feature extraction, we used six brightness contrast threshold values,

{ }10,8,6,4,2,0∈t , and nine radii of circular masks, { }20,19,18,17,16,15,14,13,12∈r . In

the stage of post-processing, we employed six scales for Gaussian smoothing filter,

{ }00.2,75.1,50.1,25.1,00.1,75.0∈σ . For palm-line feature matching, we used six

translation range values, { }7,6,5,4,3,2∈s . This results in 1,944 parameter combinations for

palm-line feature based palmprint recognition. A natural way to determine the optimal

parameter combination is to find out the lowest equal error rates (EER) among all parameter

combinations. However, it is too time-consuming to obtain the EER of all parameter

combinations. Fortunately, the four parameters of our methods can be assumed independent.

Therefore, we can determine the optimal parameters one by one.

5.4.3 Palmprint matching and parameter selection

To determine the optimal parameter combination for the palm-line feature based palmprint

recognition, we test the performance of the proposed method for different parameter

selections on a training set. The training set contains 600 palmprint images from 100

different palms which randomly selected from the public palmprint database. In the training

set, each palmprint in the public database was matched with all of the others. A matching

was labeled correct if the matched palmprint was captured from the same palm, and incorrect

otherwise. A total of 179,700 )2/599600( × matchings have been performed on the

training set including 1,500 genuine matching attempts and 178,200 impostor matching

attempts. The performance of the proposed method for different parameter combinations is

measured by the equal error rates (EER) where the false match rate (FMR) is equal to the

false non match rate (FNMR). A lower EER means a higher performance.

93

Table 5.1 Equal error rates (%) for different brightness contrast thresholds (t) and

different radii of circular masks (r). Here the standard deviation of Gaussian smoothing filter

is 0.75 and the translation range is 2. For t larger than 0, the core function defined in (5-1) is

applied. For 0=t , the core function defined in (5-5) is applied.

r t 12 14 16 18 20

0 0.837 0.746 0.621 0.629 0.629

2 0.840 0.789 0.665 0.657 0.671

4 0.853 0.796 0.732 0.797 0.802

6 1.067 1.060 1.033 1.009 0.982

8 1.123 1.113 1.159 1.178 1.211

10 1.406 1.300 1.226 1.278 1.289

Fig. 5.6 EER (%) values for different combinations of brightness contrast threshold and

radius of circular mask. Here the standard deviation of Gaussian smoothing filter

is 75.0=σ and the translation range is 2=s .

94

Optimal brightness contrast threshold t

The PolyU’s palmprint database was built up under constant and uniform lighting conditions

[50]. We therefore firstly optimized the brightness contrast threshold t. Given the scale of

Gaussian smoothing filter and the translation range, we calculated the EER of different

combinations of brightness contrast thresholds and radii of circular masks. Table 5.1 shows

the results where the standard deviation of Gaussian smoothing filter is 0.75 and the

translation range is 2. All of brightness contrast thresholds given in Section 5.4.1 were used

and the radius of circular masks ranged from 12 to 20 with the step of 2. The core function

defined in (5-1) is employed for 0>t , while (5-5) is applied for 0=t .

Figure 5.6 plots the results grouped by the radius of circular mask. Obviously, for each

radius, EER takes the minimum value at 0=t . This means, with same post-processing and

matching, the brightness contrast threshold of zero always indicates the lowest EER, the best

performance, no matter what value of the radius of circular mask used. Therefore, the

optimal brightness contrast threshold is 0=t and consequently the core function defined in

(5-5) is optimal for the proposed palm-line feature extraction method.

Optimal translation range s

Translating the matched palm-line feature image is necessary for palm-line feature matching

due to the imperfect preprocessing. If the translation range is too small, the performance will

deteriorate. While if the translation range is too large, the matching of palm-line features will

become very time-consuming. So the translation range should guarantee the performance of

the palm-line feature based palmprint recognition and, at the same time, guarantee the time

effectiveness of palm-line feature matching.

95

Table 5.2 Equal error rates (%) for different translation ranges (s) and different radii of

circular masks (r). Here 0=t and the standard deviation of Gaussian smoothing filter takes

two values, 1 and 1.25.

14 16 18 r s 1=σ 25.1=σ 1=σ 25.1=σ 1=σ 25.1=σ

2 0.628 0.577 0.578 0.534 0.583 0.551

3 0.422 0.415 0.413 0.409 0.421 0.419

4 0.362 0.349 0.352 0.346 0.362 0.355

5 0.357 0.339 0.347 0.335 0.356 0.346

6 0.356 0.339 0.346 0.335 0.355 0.343

7 0.356 0.339 0.346 0.334 0.355 0.343

Given the optimal brightness contrast threshold 0=t , Table 5.2 shows the EER values for

different combinations of three other parameters: translation range s, circular mask radius r,

and Gaussian smoothing filter scaleσ . Here we used all translation ranges given in Section

5.4.2 and two scales of Gaussian smoothing filter, { }25.1,0.1∈σ . Three radii of circular

masks, { }18,16,14∈r , were employed because in Table 5.1 they gives the corresponding

minimum EER value (marked in bold) for each brightness contrast threshold.

The EER values in Table 5.2 are divided into two groups according to the two scales of

Gaussian smoothing filter and plotted in Figure 5.7(a) and 5.7(b), respectively. We can see

that, given the combination of r andσ , the EER values decrease with increasing the

translation range and reach the corresponding lowest value when { }7,6,5∈s . Considering

the balance between the verification performance and the time effectiveness, we select

5=s as the optimal translation range.

96

(a)

(b)

Fig. 5.7 EER (%) values for different parameter combinations of circular mask radius and

translation range given the standard deviation of Gaussian smoothing filter (a) 0.1=σ and

(b) 25.1=σ , respectively. Here the brightness contrast threshold is 0=t .

97

Table 5.3 Equal error rates (%) for different radii of circular masks (r) and different

scales of Gaussian smoothing filter with 0=t and 5=s . The core function defined in (5-5)

is used.

r σ 12 13 14 15 16

1.00 0.452 0.346 0.357 0.351 0.347 0.371

1.25 0.348 0.341 0.339 0.335 0.335 0.340

1.50 0.345 0.339 0.335 0.333 0.335 0.337

1.75 0.340 0.338 0.336 0.334 0.339 0.337

2.00 0.345 0.339 0.338 0.338 0.339 0.340

0.366 0.341 0.341 0.338 0.339

Optimal circular mask radius s and Gaussian smoothing filter scaleσ

Now that the optimal brightness contrast threshold and translation range have been

determined, we optimize the circular mask radius and Gaussian smoothing filter scale in this

subsection. The EER values of different radii of circular masks against different scales of

Gaussian smoothing filters are shown in Table 5.3 with the optimal combination of

brightness contrast threshold and translation range. Five radii values { }16,15,14,13,12∈r

and five scales { }0.2,75.1,5.1,25.1,0.1∈σ are employed in this table.

We calculated the average EER value for each σ which are listed in the last column and

also for each r which are listed in the last row. The average EER for Gaussian smoothing

filter scales reaches the minimum at 5.1=σ and for circular mask radii at 15=r . This

combination of the two parameters gives the lowest EER 0.333%, which is the best

verification performance we can get. Therefore, the optimal combination for parameters,

brightness contrast threshold t, circular mask radius r, Gaussian smoothing filter’s scaleσ ,

and translation range s, is )5,5.1,15,0(),,,( =srt σ .

98

Fig. 5.8 Genuine and impostor distributions for the optimal parameter combination.

5.4.4 Verification

Verification refers to one-to-one matching which seeks to answer the question “whether the

person is whom he or she claims to be” by examining his or her biometric traits. In palmprint

verification, a user indicates his or her identity and thus the input palmprint is matched only

against the corresponding stored template. To determine the verification accuracy of our

WLD-based palmprint recognition method, each palmprint was matched with all of the other

palmprints in the public database. All matching scores are thereby divided into two groups:

genuine matching scores and impostor matching scores. The probability distributions of

genuine and impostor for the optimal parameter combination )5,5.1,15,0(),,,( =srt σ , are

plotted in Fig. 5.8. To measure the separability of the distributions of genuine and impostor,

we introduced the decidability index 'd (d-prime) [120], which is defined as the separation

between the means of the two distributions, divided by the square-root of their average

variance. The decidability index of our WLD-based method with the optimal parameter

combination is listed in Table 5.4.

99

Table 5.4 Comparison of our method with four representative palmprint verification

methods on PolyU database.

Method 'd EER

PalmCode 4.973 0.647%

CompCode 4.839 0.409%

Ordinal code 5.418 0.400%

Wu’s method 6.335 0.413%

WLD 5.453 0.373%

Fig. 5.9 Verification performance comparison on PolyU Palmprint Database.

100

Table 5.4 compares the accuracy measure of our WLD-based method with three coding

approaches, PalmCode [50], Competitive Code [70] and Ordinal Code [71], and one

palm-line feature based approach, Wu’s method [61]. The verification performances of the

five methods are illustrated in Fig. 5.9 by the receiver operating characteristic (ROC) curves

which plots FNMR as a function of FMR [103]. We can see our WLD-based method gives

the lowest EER among the five methods and the largest decidability index except Wu’s

method. The experimental results indicate that width features of palm lines are useful and

helpful for palmprint recognition.

5.4.5 Identification

Identification, also called one-to-many (1-to-S) matching, involves answering the question

“who is this person?” In our experiments, two registration databases are setup with the same

scale 386=S , which is the total number of different palms in the public palmprint database.

The first registration database RegDB1 contains S templates and the second one RegDB2

contains S3 templates. To establish the identification accuracy of our method, all templates

in both registration databases are randomly selected from the palmprint images captured in

the first session and the identification database consists of all the palmprint images captured

in the second session. The two registration databases, RegDB1 and RegDB2, and the

identification database contain 386, 1158, and 3863 palmprint images, respectively. Each

sample in the identification database is compared with all templates in each registration

databases and the template giving the maximum matching score is labeled as the

identification result. Table 5.5 compares the recognition rates of our WLD-based method on

both registration databases with PalmCode, Competitive Code, Ordinal Code, and Wu’s

method. The number of mismatched samples of each method is also listed in Table 5.5. In

palmprint identification, the accuracy of our WLD-based method outperforms other four

methods on both registration databases.

101

Table 5.5 Comparison of identification accuracy on two registration databases.

RegDB1 RegDB2 Method

Recognition rate Incorrect # Recognition rate Incorrect #

PalmCode 97.98% 78 99.02% 38

CompCode 98.91% 42 99.74% 10

Ordinal code 98.99% 39 99.82% 7

Wu’s method 98.71% 50 99.43% 22

WLD 99.22% 30 99.84% 6

5.5 Conclusion and discussions

We have presented a WLD-based method to simultaneously extracting structure and width

features of palm lines for palmprint recognition. A palm-line feature extraction method based

on the wide line detector is proposed to extract line-like features which contain width

information of palm lines. In the post-processing stage, a Gaussian smooth filter is employed

for palm-line feature image denoise. An effective translation-invariant matching method is

described for palm-line feature matching. An experimental scheme is designed to determine

the optimal parameter combination, )5,5.1,15,0(),,,( =srt σ . An extensive test of the

proposed WLD-based method with the optimal parameter combination has been conducted

on PolyU Palmprint Database compared with four representative palmprint identification

methods. In palmprint verification, the proposed WLD-based method offers the lowest EER

0.373%. In palmprint identification, the proposed WLD-based method generates the least

number of incorrect matching (30 in 3863 on RegDB1 and 6 in 3863 on RegDB2) and

accordingly the highest recognition rate, 99.22% on RegDB1 and 99.84% on RegDB2,

respectively. The experimental results demonstrate that the performance of the proposed

WLD-based method is comparable with the state-of-the-art algorithms of palmprint

recognition and thereby palm-line features can be used to recognize palmprints.

102

Chapter 6

Automatic Extraction of Cracks on

Tongue Images

This chapter attempts to detect tongue cracks, one of pathological features in tongue

diagnosis. A framework for adaptive tongue crack detection is proposed. Based on the

presented wide line detector described in Chapter 3, an automatic tongue crack detection

scheme is derived to extract tongue cracks. The wide line detector extracts the whole of the

line by employing an isotropic nonlinear filter and describes the relationship between the

size of the isotropic filter, i.e. the scale of this detector, and the width of detected lines. Due

to the large range of widths of tongue cracks, the maximum widths of cracks vary greatly

with different tongue images and consequently the sizes of the isotropic filters are very

different. To implement the proposed scheme totally automatically, an adaptive algorithm of

line width estimation is designed. The proposed scheme has been tested on a set of typical

cracked tongue samples and our experimental results demonstrate its effectiveness.

6.1 Introduction

Tongue diagnosis [75,76] is one of the most important and valuable diagnostic methods in

traditional Chinese medicine (TCM) and has been widely used to clinical analyses and

applications for thousands of years. In TCM theory [122], the tongue is connected with a

number of viscera via the meridians and accordingly the essential of the viscera can ascend

to nourish the tongue and pathological processes are reflected on it. Whenever there is a

complex disorder full of contradictions, examination of the tongue can instantly clarify the

main pathological processes. Therefore, it is very valuable in both clinic applications and

self-diagnosis. Moreover, tongue diagnosis is a non-invasive technique that is in accord with

103

the most promising direction in the 21st century: no pain and no injury.

Some researchers recently have paid attention to computerized tongue diagnosis

[8,77-86,125] by developing a set of objective and quantitative features and measurements

based on the theories of tongue diagnosis. So far, most investigation has been focused on

extraction of chromatic features [8,78,80-82,84-86,125] and textural features

[8,77-79,82,84,86,125]. Actually, according to the theories of tongue diagnosis, some

features on tongue surfaces are pathological forms and thereby have clinical significance, for

example, cracks on the tongue surface.

Tongue crack is one kind of textural features and frequently seen in clinical practice.

Tongue cracks refer to the surface of the tongue covered with fissures or lines in deep or

shallow shape, which are induced by the fusion or separation of the ligular papillae [123].

Normally, the tongue’s surface should be smooth and soft and show no cracks. A cracked

tongue indicates exhaustion of blood: the fewer and more superficial the cracks, the miler the

disease; the deeper and more numerous the cracks, the more serious the disease [76]. The

clinical significance of cracks depends on the tongue body color, the location of the cracks

and their shape and depth.

In spite of the clinical significance of tongue cracks, there is by far no paper, to the best of

our knowledge, concerning extraction of cracks on the tongue surface. This is our motivation

to develop the research on tongue crack extraction. Now a question arises: what is tongue

crack? Although tongue cracks appear as curvilinear structures (also simply called lines) on

the tongue surface, not all lines on the tongue surface are cracks. In the theories of tongue

diagnosis, flat and short lines which are no deeper than 0.35mm and no longer than 0.55cm

on the tongue surface have little clinical significance [75,76]. However, in computerized

tongue diagnosis, since the captured tongue pictures are 2D images, the information of depth

has been lost. Fortunately, the depth of cracks is normally related to their widths. Generally

speaking, the deeper the cracks the wider they are, and vice verse. Therefore, based on the

investigation on a number of cracked tongue images and suggestions from expert, we give

104

the definition of tongue cracks in the sense of imaging: tongue crack is kind of lines on the

tongue surface not too short and not too narrow.

So far, many algorithms for line detection have been developed for different applications.

However, there exist some shortcomings make them unsuitable for tongue crack extraction.

Hough transform [15,92-93], which is a widely used line detection method, was initially

proposed to find analytically defined curvilinear structures (e.g., straight lines, circles,

ellipses etc.). Although the generalized Hough transform [17] can be used to detect arbitrary

curvilinear structures in theory, it requires the complete specification of the exact shape of

the curvilinear structure which is very difficult and even unfeasible for tongue cracks due to

their complex shapes. One powerful line detection approach is based on the derivative

operations [3,26,28,30-31,35,94]. Steger [3] proposed a ridge-based line detector using

two-dimensional Gaussian partial derivative kernels. This detector extracts the ridges as

points for which the intensities are maxima or minima in the main principal curvature

direction, i.e., the direction of the maximum eigenvalue of the Hessian matrix. Since

Gaussian kernels are used to estimate the derivatives of the image, the line detector can scale

to lines of arbitrary widths. However, this approach is sensitive to noise due to the use of

second order derivatives, which makes it unsuitable for tongue crack extraction because of

the rough surface of tongue and the reflection on the tongue surface. Another simple but

powerful line detection approach is the line operator [45] which is successfully used to detect

linear structures in mammographic images [4]. The line operator extracts linear features

based on the difference between the average gray level of the pixels lying on an orientated

local line passing through the target pixel and the average intensity of all the pixels in the

similarly orientated neighborhood. The line operator improves the line signal to background

noise ratio by averaging the grey levels. However, this approach tends to output results with

similar widths whatever the true width of the detected lines. This is a disadvantage to extract

tongue cracks which widths normally vary in a large range.

Recently, a wide line detector [62] is developed to extract a line completely. Unlike line

105

detectors which use directional derivatives, this method applies a nonlinear filter to extract

the whole of the line without any derivative, which makes this line detector insensitive to

noise. In the wide line detector, a definite relationship is given between the width of detected

lines and the size of an isotropic filter which is employed to obtain an isotropic response.

Due to no Gaussian kernel used to detect lines, even narrow lines can be extracted well as

long as the intensity contrast between the narrow lines and the background is large enough,

which indicates this wide line detector can keep the width of the detected line as what it is

and thereby can extract lines of different widths. Therefore, we employ the wide line detector

to extract tongue cracks.

Purpose of this chapter is to attempt to extract tongue cracks by applying and improving

the wide line detector based on tongue crack features. An automatic tongue crack detection

scheme has been developed by modifying the wide line detector according to the

characteristics of tongue cracks. The size of the isotropic filter which determines the widths

of detected lines is related to the maximum width of cracks expected to extract. The widths

of tongue cracks, however, change greatly and the maximum width of tongue cracks varies

with tongue images. To implement the proposed scheme automatically, we also design an

adaptive algorithm to estimate the maximum width of tongue cracks.

The chapter is organized as follows. Section 6.2 describes the automatic tongue crack

detection scheme. In Section 6.3, we present the adaptive line width estimation algorithm.

Section 6.4 describes the results of our experiments and gives the analyses. Section 6.5 offers

our conclusion.

6.2 Methodology of crack extraction

Fig. 6.1 provides an overview of the proposed framework which indicates the automatic

tongue crack detection scheme. Given a tongue image (see Fig. 6.3a), in the first step, we

extracts the tongue body and, at the same time, creates the tongue body mask. In the second

step, we first utilize the extracted gray-level tongue body image to calculate the two

106

parameters for the wide line detector (WLD): the brightness contrast threshold and the radius

of the circular mask which is obtained by estimating the maximum width of cracks in the

tongue body image. The WLD algorithm is then employed to give the crack response image.

Finally, the crack response image is post-processed to obtain the final results. The tongue

crack detection module represents a modified version of the wide line detector and the

adaptive estimation of the maximum width of cracks is our novel contribution. In this section,

we describe the methodology of tongue crack extraction except the adaptive algorithm of the

line width estimation which will be presented in Section 6.3.

Fig. 6.1 The diagram of tongue crack extraction procedure using the WLD.

Contour shrinking

Contour Tongue Image

Tongue Body Mask

Binarization

Initialization

Tongue body segmentation

Tongue

Crack

Extraction

(WLD)

Brightness contrast

thresholding

Radius of the circular

mask

Final result

Preprocessing Extracting Tongue Cracks i

Smoothing

Estimate maximum width of cracks

Post-processing

107

6.2.1 Preprocessing

The purpose of this subsection is to segment the region of interest, i.e. the tongue body, from

the captured tongue image which has a large background. We employ the segmentation

method described in [83] to obtain the contour of the tongue body and segment the captured

tongue image to the contour tongue image. The tongue contour is then shrunk so that the

influence of the uneven illumination caused by the deformation close to the boundary can be

eliminated. The shrunk distance should not be too large since some tongue cracks are very

near the boundary of the tongue body (see Fig. 6.2a). Therefore, each pixel of the tongue

contour is moved to the centroid of the tongue body with a certain distance (as shown in Fig.

6.2b) and the shrunk contour is calculated by

220)()( ncnc

nccs

yyxx

xxdxx

−+−

−−= , (6-1)

220)()( ncnc

nccs

yyxx

yydyy

−+−

−−= (6-2)

where ),( nn yx is the centroid of the tongue contour, ),( cc yx is the coordinate of the

tongue contour pixel, ),( ss yx is the coordinate of the shrunk contour pixel, and 0d is the

shrunk distance. The tongue body mask is created by binarizing the contour tongue image

according to the shrunk contour and the tongue body image is consequently obtained, as

shown in Fig. 6.2c and Fig. 6.2d, respectively.

6.2.2 Extracting tongue cracks

We modified the method proposed in [95] to detect the tongue crack. This method, also

called the wide line detector [62], extracts a line completely by using a nonlinear filter based

on the isotropic response via a Gaussian weighting mask. Here, we replaced the Gaussian

weighting mask G with an inverse-Gaussian profile

108

(a)

(b) (c)

(d)

Fig. 6.2 Preprocessing of tongue crack extraction. (a) Captured tongue image, (b) contour

tongue image with the centroid and corresponding contour, (c) tongue body mask, and (d)

extracted tongue body image.

109

(a)

(b) (c)

(d) (e)

Fig. 6.3 Tongue crack extraction. (a) The ground truth for Fig. 6.2d, (b) The line-strength

image using the wide line detector (WLD), (c) tongue crack image obtained by

postprocessing (b), and tongue crack extraction results using (d) the Line Operator (LO) and

(e) Steger’s method, respectively.

110

( ) ∑+≤≤−+≤≤−

−+−−

−+−−

−+

−=

ryyryrxxrx

ryyxx

ryyxx

er

eryxyxIG

0000

2

20

20

2

20

20

,

2)()(

2

2)()(

00

12

1),,,,( , (6-3)

where ),( 00 yx is the coordinate of the center, ),( yx is the coordinate of any other pixel

within the mask, and r is the radius of the circular mask. The equation (6-3) gives a

normalized version of the inverse-Gaussian profile.

The wide line detector first examines the intensity of the center of the mask and groups

pixels having similar intensities to the center into the weighted mask having similar

brightness (WMSB). Since tongue cracks are dark lines, this similarity in our method is

measured by:

⎪⎩

⎪⎨

⎧≥⎟

⎠

⎞⎜⎝

⎛ −•=

otherwise

),(),(if),(),(

sec),,,( 00

500

00IG

yxIyxIt

yxIyxIhIGyxyxwmsb , (6-4)

where xx eexh

−+=

2)(sec , ),( yxI is the brightness of the pixel ),( yx of the tongue

body image, t is the brightness contrast threshold and wmsb is the output of the weighting

comparison. This function gives a smooth profile and does not have too large an effect on

wmsb as a pixel’s brightness changes slightly, especially when it is near the threshold and

further, has proved to be optimal in Chapter 4. This function gives a trade-off between the

stability about the threshold and the requirement of the detector, which is to count pixels that

have similar intensity to the center into the mass of the circular mask.

This comparison is done for each pixel within the mask. The WMSB mass of the center

),( 00 yx is given by ∑ +≤≤−

+≤≤−=

ryyry

rxxrxyxyxcyxm 00

00),,,(),( 0000 .The line strength L is the

inverse WMSB mass obtained by using the following rule:

111

⎩⎨⎧ <−

=otherwise

gyxm ifyxmgyxL

),(0

),(),( 0000

00 . (6-5)

Here g is the geometric threshold and 2/maxmg = , where maxm is the maximum value

which m can take. As a normalized circular mask is used, maxm is not larger than but very

close to one and thereby the line strength ranges between zero and one. Fig. 6.3b shows the

line strength image of Fig. 6.2d.

The WLD requires two parameters – the brightness contrast threshold, t, and the radius of

the circular mask, r. In our method, the brightness contrast threshold is defined by

( ) 21

1

2),(),(

11

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛−

−= ∑

=

N

immii yxIyxI

Nt , (6-6)

where ∑=i

iimm yxIN

yxI ),(1),( and N is the number of non-zero pixels of the tongue

body image which is obtained through the preprocessing described in Section 6.2.1. The

brightness contrast threshold t is the standard deviation of the tongue body region.

In [62,95], the relationship between the width of lines detected and the size of Gaussian

weighting masks is given via analysis. In the same way, if a line of width w×2 is fully

detected by using an inverse-Gaussian weighting mask with radius r, it requires

⎟⎟⎠

⎞⎜⎜⎝

⎛−=−<−

−+

−+

−

∫∫∫∫ 211

211 2

1222 2

22

2

22

erdxdyedxdyeC

ryx

L

ryx

π , (6-7)

where C denotes the region of the circular mask and L the region of the line which passes

through the center of the circular mask. The relationship between the width of the detected

line and the radius of a circular mask with inverse-Gaussian profile is consequently

determined in terms of (6-7). Given the circular mask of radius r, the critical width of line

detected, cw×2 , is obtained when the left and right arguments of (6-7) are equal. As the

analytic form of the left function is not available, we only give the approximate results in

112

Table 6.1. We also show in Table 6.1 the relationship between the width of line detected and

the radii of circular masks with Gaussian profile ( )222 2/)(exp ryx +− and with constant

weighting, respectively. Comparing the results, we find out that the detection capacity of the

WLD using an inverse-Gaussian weighting mask is higher than that using the corresponding

circular mask with either constant weighting or Gaussian profiles. It means that, with the

same radius r, the circular mask of inverse-Gaussian profile can detect widest lines, while, in

order to detect lines of same width, the size of an inverse-Gaussian weighting mask needed

is smallest.

6.2.3 Post-processing

In the final stage, pixels of line strength below a threshold (=0.1) are removed firstly. Tongue

cracks are extracted by applying the technique of hysteresis thresholding to the line-strength

images, followed by some morphological operations. The hysteresis thresholding [126] uses

two thresholds: one is high and the other is low. Any pixel in the line-strength image that has

a value greater than the high threshold is presumed to be a line pixel. Then, any pixels that

are connected to any line pixel and that have a value greater than the low threshold are also

selected as line pixels. In the morphological operations, the crack will be discarded if (i) its

length, l, is very short (<20 pixels), (ii) its area, A, is too small (< 100 pixels), and (iii) its

eccentricity, e, is less than 0.9. The eccentricity is the ratio of the distance between the foci

of the ellipse and its major axis length. Here the major axis length of the ellipse is

approximated to l and the minor axis length of the ellipse is calculated by lAb = . So the

eccentricity e can be estimated by

4

21

lAe −= . (6-8)

Fig. 6.3c shows the tongue crack detection result of Fig. 6.2d

113

Table 6.1 Comparison of the relationship between radii of different profiles and

approximately critical widths of detected lines (ACWL).

Critical Width of Line Detected ( cw×2 )

Constant weighting Gaussian weighting Inverse-Gaussian weighting

Radius of Gaussian mask (r)

ACWL Digital ACWL ACWL Digital ACWL ACWL Digital ACWL

3 2.4 2 2.6 2 4.0 4

4 3.2 3 3.5 3 5.3 5

5 4.0 4 4.4 4 6.6 6

6 4.8 5 5.3 5 7.9 8

7 5.6 5 6.2 6 9.2 9

8 6.4 6 7.1 7 10.6 10

9 7.2 7 7.9 8 11.9 12

10 8.0 8 8.8 9 13.2 13

11 8.8 9 9.7 10 14.5 14

12 9.6 9 10.6 10 15.8 16

13 10.4 10 11.5 11 17.2 17

14 11.2 11 12.4 12 18.5 18

15 12.0 12 13.2 13 19.8 20

16 12.8 13 14.1 14 21.1 21

17 13.6 13 14.9 15 22.4 22

18 14.4 14 15.8 16 23.7 24

19 15.2 15 16.7 17 25.0 25

20 16.0 16 17.6 17 26.4 26

21 16.8 17 18.5 18 27.7 28

22 17.6 17 19.4 19 29.1 29

23 18.4 18 20.3 20 30.4 30

24 19.2 19 21.2 21 31.7 32

25 20.0 20 22.1 22 33.0 33

26 20.8 21 22.9 23 34.3 34

114

6.3 Adaptive line width estimation

In line detection the scale of the filter is one very important factor to detect lines of arbitrary

widths. An optimal scale of the filter should be big enough but not too big to detect all lines

in an image. Since the widths of tongue cracks may vary largely with tongue body images,

the optimal scale of the filter will be quite different from image to image. Consequently we

should select the corresponding optimal scale of the filter for each tongue body image rather

than use only one filter-scale for all tongue body images. In terms of WLD, the scale of the

filter, i.e. the radius of the circular mask, is related to the maximum width of tongue cracks

expected to detect in a given tongue body image. Therefore, the estimation of the maximum

width of cracks in a tongue body image is essential and necessary for applying the wide line

detector to extract tongue cracks correctly and completely. Normally, the estimation of line

widths is done by human being. Adaptively estimating widths of curvilinear structures with

various widths and various orientations still remains a big challenge in image analysis and

pattern recognition due to complicated scenes. For the purpose of fully automatic extraction

of tongue cracks, in this section, we attempt to realize the adaptive estimation of the

maximum width of tongue cracks by utilizing their properties.

Tongue cracks can be considered as dark lines with a bar-shaped profile

⎪⎩

⎪⎨

⎧

>−<≤≤−

=wxbwxa

wxwx

0)(l , (6-9)

where w×2 is the line width, 0>a , and 0>b . Ideally, lines would have the same

contrast on both sides, i.e., ba = , as shown in the first row of Fig. 6.4a. However, this

assumption is not always true for tongue cracks due to the tongue coating and

illumination.The first rows of Fig. 6.4b and 6.4c show the asymmetrical bar-shaped lines

where ba < and ba > , respectively.

115

(a) (b) (c)

Fig. 6.4 Illustration of the line width estimate. The first row is the three dark line models.

The second row shows the corresponding Gaussian smooth profiles. The last row is the

first-order derivatives of Gaussian (DoG) profiles shown in the second row. The line width

can be obtained by calculating the distance between the pair of minimum and maximum of

DoG filtered results along the line profile.

If the bar-shaped profiles )(xl are convolved with a Gaussian kernel

( ) ( )σπσσ 2/2/exp 22xg −= , a smooth profile )(xs is obtained in each case, as shown in

the second row of Fig. 6.4. Thus, a useful criterion for dark lines can be employed to

estimate the line width. The left edge of the dark line, i.e., the decreasing edge, has the

minimum of )(xs′ , while the right edge of the dark line, i.e., the increasing edge, has the

maximum of )(xs′ , as shown in the last row of Fig. 6.4. Mathematically, )(xs′ can be

obtained by convolving the bar-shaped profiles )(xl with the first-order derivative of

Gaussian kernel (DoG) which is defined as:

Tongue crack models

Gaussian smooth profiles

DoG profiles

116

2

2

232

)( σσσπ

x

exxDoG−−

= , (6-10)

whereσ is the scale of Gaussian kernel. Therefore, the line width can be estimated by

calculating the distance between the pair of minimum and maximum of the DoG filtered

response.

A line width estimation algorithm is designed based on multi-scale analyses to adaptively

estimate the maximum width of cracks for each input tongue images. This estimation

algorithm is specified in Fig. 6.5. Since tongue cracks are normally horizontal and vertical,

we sample some rows and columns for analyses (step 01). In order to eliminate the influence

of reflecting points, one-dimensional median filter is first applied to each sampled vector

(step 02). For each filtered vector v, a multi-scale analysis is developed in the scale space

∑ to calculate the normalized DoG filtered response

σσ σ dvdv norm ×=− , (6-11)

σσ DoGvdv ∗= , (6-12)

and then find the maximal vertical distance vdσ among all pairs of local minimum and local

maximum of normdv −σ on each scale ∑∈σ (step 05-06). The candidates of the maximum

width of cracks consist of the maximum width of each vector vw , where the vertical distance

reaches the maximum in the scale space (step 07). The maximum width of cracks w is

determined by the maximum value of candidates which vertical distance is larger than a

threshold vVvd dratioT ∈∪×= max (step 08). Here we define ratio=0.8.

117

Fig. 6.5 Line width estimation algorithm.

Table 6.2 The estimation results of maximum widths of cracks by applying the algorithm

described in Figure 6.5. The true widths of cracks are also listed for reference.

Image # Estimated Max-Width (pixel)

True max-width (pixel)

Fig. 6.2d 12 12

Fig. 6.6a 14 14

Fig. 6.7a 13 13

Fig. 6.8a 17 16

Fig. 6.8b 21 18

Input: tongue body image I

setΣ of scales

Output: maximum width w of tongue cracks in I

01 Sample a set of vectors 0V in tongue body image I along the horizontal and vertical

direction;

02 Obtain filtered vectors V by apply the one-dimensional median filter to vectors 0V ;

03 For each Vv∈

04 For each Σ∈σ

05 Obtain the normalized filtering response normdv −σ of vector v for scaleσ ;

06 Calculate the max-vertical distance vdσ of normdv −σ for scaleσ ;

EndFor

07 Determine the maximum width vw of vector v, where the corresponding vertical

distance vv dd σσ ∑∈∪= max ;

EndFor

08 ( )vVvd

vv dratioTdVvww ∈∪×=>∈= max,|max .

118

The estimation of max-width of cracks in Fig. 6.2d is listed in Table 6.2. In WLD, the filter

scale is the radius of the circular mask, which is determined by the maximum width of cracks.

The relationship between the radius of circular mask and the max-width of crack is given in

Table 1 and thus, according to the estimated max-width of cracks, the size of circular mask

used for Fig. 6.2d is 4141× with the radius of 20 pixels wide. The extraction result obtained

by WLD using the corresponding circular mask is shown in Fig. 6.3c.

Actually, the max-width of cracks can determine the filter scale not only for the WLD but

also for other line detection methods as long as the relationship is definite between the filter

scale and the line width. In [3], Steger gave the restriction on the scale of Gaussian kernel to

ensure that the salient lines can be detected. In [4], the principle of the line operator (LO)

requires that the filter scale, i.e., the size of the square neighborhood, should be larger than

the maximum line width to guarantee the complete extraction. Here, we employ the two

popular wide line detection methods to extract cracks in Fig. 6.2d under the corresponding

scales determined by the estimated max-width, which are shown in Fig. 6.3d and Fig. 6.3e,

respectively. Compared with the ground truth as shown in Fig. 6.3a, the extraction results of

the wide cracks by using the three methods show that the scales for three methods

determined by the estimated max-width of cracks are proper for the tongue cracks and

thereby indicate that the proposed estimation algorithm can work well.

6.4 Experimental results and analysis

We have conducted a test of the described scheme on a set of typical tongue crack samples

purposely chosen by the experts for diagnosis. To establish the effectiveness of the wide line

detector for the tongue crack extraction, we employed two popular line detection methods to

extract tongue cracks by replacing the WLD in the stage of extracting tongue cracks and

compared the performance of the three methods. In this section, we will firstly describe the

measure of performance evaluation of tongue crack extraction methods and then present and

discuss the experiment results.

119

6.4.1 Performance evaluation

Performance evaluation of medical image segmentation is a challenging job due to the

complexity and difficulty of medical image segmentation. Normally, a line detector

performance is evaluated with specified ground truth [127]. Once the ground truth is given,

quantitative evaluation can be readily carried out by comparing detected features with the

ground truth features. For each tongue crack sample used in our experiment, the ground truth

was drawn by hand, which is a binary map where tongue cracks are marked in white.

Let GTC and TDC denote the set of tongue crack pixels of the ground truth and tongue

cracks detected by an approach, and GTB and TDB the set of background pixels,

respectively. The set of correctly detected tongue crack pixels is true positives

( GTTD CCTP I= ). The set of falsely detected tongue crack pixels is false positives

( GTTD BCFP I= ). The set of correctly marked non-crack pixels is true negatives

( GTTD BBTN I= ). The true positive rate (TPR) is established by dividing the number of

true positives by the total number of crack pixels in GT. The false positive rate (FPR) is

computed by dividing the number false positives by the total number of non-crack pixels in

GT. A measurement of accuracy (Ac) can be defined by the sum of true positives and true

negatives divided by the image size.

We also define a performance measure of a tongue crack extraction method as:

)()()(

)(FNnumFPnumTPnum

TPnumPM++

= , (6-13)

where num(X) denotes the number of the set X and FN is the false negatives which the set of

the ground truth missed by the detection results. The performance measure PM ranges from

0 to 1. For perfect tongue cracks detection, PM=1. For all other cases, the performance

measure is smaller than one. The definition of PM guarantees that the performance measure

is closer to zero with more tongue crack pixels missed and/or falsely detected by a line

120

Table 6.3 Comparisons of performance evaluation between different methods used in

Fig. 6.3.

Method TPR FPR Ac PM

Steger 0.7844 0.0109 0.9863 0.4419 LO 0.7738 0.0084 0.9886 0.4840

WLD 0.8181 0.0019 0.9956 0.7196

detector. The performance measure is used to evaluate the effectiveness of tongue crack

extraction methods.

Table 6.3 shows the comparisons of performance evaluation between different methods

used in Fig. 6.3. The proposed WLD-based scheme gives the highest value of true positive

rate and the lowest value of false positive rate, which resulted in achieving the highest

accuracy score and the highest performance measure among all extraction methods. In the

following experiments, we will employ the true positive rate, false positive rate, accuracy,

and performance measure to evaluate the performance of different methods.

6.4.2 Experimental results

In this section, we will show the effectiveness of the WLD-based scheme by comparing with

two popular line detection approaches, the line operator (LO) and Steger’s unbiased detector.

In WLD, the two parameters are the brightness contrast threshold which is calculated by (6)

and the radius of inverse-Gaussian weighting mask which is determined by the max-width of

tongue cracks maxw as shown in Table 6.1. The parameter for Steger’s approach isσ , the

standard deviation of a 2-D Gaussian partial derivative kernel, which is restricted by

3/w≥σ (w is half of the line width) and the parameter for LO is l , the length of line,

which should be at least larger than the line width expected to detect. In our experiments, we

set max3.0 w=σ and max2w=l . The max-width of tongue cracks for each sample is

automatically estimated by applying the algorithm presented in Section 6.3. Table 6.2 lists

the estimated max-widths of tongue crack samples used in our experiments, as well as the

corresponding true max-widths.

121

(a)

(b) (c)

(d) (e)

Fig. 6.6 (a) The vertical cracks with (b) the ground truth and extraction results by using (c)

WLD, (d) LO, and (e) Steger’s method, respectively.

122

Table 6.4 Comparisons of performance evaluation between different methods used in

Fig. 6.6.

Method TPR FPR Ac PM

Steger 0.7588 0.0134 0.9846 0.3014

LO 0.8025 0.0092 0.9892 0.3943

WLD 0.8563 0.0016 0.9972 0.7279

The first example is illustrated in Fig. 6.6a, which contains a vertical crack on the rough

tongue surface. The line width of this tongue crack sample is calculated by the algorithm

described in Fig. 6.5. The estimated max-width of this crack is 14 pixels and accordingly the

radius of inverse-Gaussian weighting mask used in WLD is 11 pixels wide, referring to

Table 6.1. The extraction result of this tongue crack sample using WLD is shown in Fig. 6.6c

and the ground truth for this tongue crack sample in Fig. 6.6b. The results obtained by LO

and Steger’s method are shown in Fig. 6.6d and Fig. 6.6e, respectively. Table 6.4 shows the

values of true positive and false positive rates reported by different methods. The wide line

detector generates the highest value of true positive rate and the lowest value of false

positive rate, which results in the highest accuracy and highest PM value among three

methods. Compared with the ground truth, the wide line detector output the best extraction

results without any piece of falsely detected cracks, while both LO and Steger’s method

produce spurious cracks where the shadow occurs. The spurious cracks lead to very high

false positive rates for both LO and Steger’s method, 0.92% and 1.34%, respectively. The

reason for the failure of the two line detectors is that both of them extract lines based on the

derivative of kernels in nature, which is sensitive not only for the linear structures but also

for edges. In WLD, no derivative operation is directly used and consequently produces much

more stable and sensible extraction results.

123

(a)

(b) (c)

(d) (e)

Fig. 6.7 (a) The horizontal cracks with (b) the ground truth and extraction results by using

(c) WLD, (d) LO, and (e) Steger’s method, respectively.

124

Table 6.5 Comparisons of performance evaluation between different methods used in

Fig. 6.7.

Method TPR FPR Ac PM Steger 0.8423 0.0285 0.9686 0.3787

LO 0.8435 0.0276 0.9695 0.3859 WLD 0.8734 0.0081 0.9892 0.6471

Figure 6.7 illustrates the strong noise rejection of the wide line detector as compared with

the LO and Steger’s method. The example shown in Fig. 6.7a is a typical sample of

horizontal tongue cracks, which ground truth is given by expert, as shown in Fig. 6.7b. The

estimated max-width of this tongue crack sample is of 13 pixels and accordingly the radius

of circular mask used for WLD is 10 pixels wide. Figure 6.7c-e display the extraction results

by applying the WLD, LO, and Steger’s method, respectively. The performance evaluation

results of the three methods are listed in Table 6.5. Notice that both LO and Steger’s method

produce false positive rates much higher than that of WLD. Compared with the ground truth,

most of the spurious crack pixels detected by the line operator and Steger’s method are found

as the branches of horizontal cracks which are induced by the reflection on the tongue

surface. In contrast, the WLD produces very few reflection-caused spurious crack pixels due

to the use of equation (6-4) which is defined specially for dark line detection. Therefore, the

WLD has strong noise rejection ability for tongue crack extraction.

The last clinical example is presented in Fig. 6.8 and consists of two samples (as shown in

Fig. 6.8a and Fig. 6.8b), both of which are typical irregular cracks which demonstrate more

clinical significance than vertical and horizontal cracks. The two samples contain many

pieces of cracks with different widths and directions and thereby are more of challenge. The

ground truth for both samples is labeled by expert and shown in Fig. 6.8c and Fig. 6.8d,

respectively. The estimated max-width values are 17 pixels and 21 pixels for Fig. 6.8a and

Fig. 6.8b and accordingly the corresponding radii of circular masks are 13 pixels wide and

16 pixels wide, respectively. The crack extraction results of two samples by using the three

125

(a) (b)

GT (c) (d)

WLD (e) (f)

LO (g) (h)

126

Steger (i) (j)

Fig. 6.8 (a-b) Two irregular cracks with (c-d) the corresponding ground truth and extraction

results by using (e-f) WLD, (g-h) LO, and (i-j) Steger’s method, respectively.

line detection methods are displayed in Fig. 6.8e-j and the corresponding performance

evaluation results are listed in Table 6.6 and Table 6.7, respectively. Again, our WLD

produces the best results for both samples. Compared these extraction results of tongue

cracks by the WLD, LO, Steger’s method, it can be observed that the detected cracks by

using WLD have different widths which are close to the true widths of cracks in both

samples, while the widths of detected cracks in each sample by either LO or Steger’s method

seem to be very similar, which results in the highest true positive rate of the wide line

detector among different methods. This illustrates that, given the scale for a method, our

WLD can remain the width of the detected line as it is, whereas the LO and Steger’s method

have the tendency to produce detected lines with similar widths. In addition, for the two

samples, both LO and Steger’s method respond many week linear structures which are not

regarded as cracks by expert and thereby disappear in the ground truth. The unexpected

response of the two line detection methods leads to the high values of false positive rates for

the two samples. The reason that our WLD has no output of weak lines is that this method

detects lines based on the comparison of brightness in a neighborhood (referring to the

equation (6-4)) and accordingly weak lines will give a weak response which tends to be

discarded when thresholding (referring to the equation (6-5)).

127

Table 6.6 Comparisons of performance evaluation between different methods used in

Fig. 6.8a.

Method TPR FPR Ac PM Steger 0.6712 0.0258 0.9553 0.4833

LO 0.6310 0.0292 0.9496 0.4383 WLD 0.7787 0.0085 0.9782 0.6902

Table 6.7 Comparisons of performance evaluation between different methods used in

Fig. 6.8b.

Method TPR FPR Ac PM

Steger 0.5089 0.0299 0.9405 0.3544 LO 0.6355 0.0445 0.9350 0.3853

WLD 0.7505 0.0207 0.9646 0.5761

Notice that the detected cracks by using our WLD (as shown in Fig. 6.8f) seems to be

wider than the labeled cracks in the corresponding ground truth (as shown in Fig. 6.8d)

which results in the highest false positive rate among all extraction results obtained using our

WLD. This is because the over estimated max-width (21 pixels vs. 18 pixels) of tongue

cracks for the sample shown in Fig. 6.8b and accordingly a circular mask about 30% larger

than required is used to detect tongue cracks. This illustrates that the use of the proper size of

a circular mask, i.e. the proper scale of a filter, is very important in our WLD and thus the

estimation algorithm of max-width of cracks, which determines the scale of a filter, plays a

significant role for tongue crack extraction.

Table 6.8 shows the average values and variance of performance evaluation results of

different methods for all cracked tongue samples used in this manuscript. Table 6.9 reports

the paired t-test results of the hypothesis that two matched samples come from distributions

with equal means. It can be seen that performance evaluation results of the wide line detector

are significantly different from the results of both the line operator and Steger’s method.

128

Table 6.8 Comparisons of average performance evaluation between different methods.

Method TPR FPR Ac PM

Steger 1297.00.7131± 0089.00.0217 ± 0195.00.9671± 0718.00.3919 ±

LO 0981.00.7372 ± 0152.00.0238 ± 0239.00.9664 ± 0431.00.4176 ±

WLD 0515.08154.0 ± 0077.00.0082 ± 0136.00.9850 ± 0623.00.6722 ±

Table 6.9 Paired t-test results of different methods. The p values are calculated using the

paired t-test of the hypothesis that two matched samples in the two vectors come from

distributions with equal means. p<0.05 was considered statistically significant.

Method TPR FPR Ac PM

WLD-Steger 0.0555 0.0040 0.0037 0.0020

WLD-LO 0.0261 0.0119 0.0185 0.0004

LO-Steger 0.4512 0.5710 0.7616 0.3190

0

10

20

30

40

50

60

70

80

90

Steger LO WLD

Per

form

ance

Mea

sure

(%

)

Q1

min

median

max

Q3

Fig. 6.9 Box-and-whisker plots of the PM values of three methods for all test cracked

tongue images.

129

We have also conducted a test of proposed scheme on a total of 286 cracked tongue

images. Figure 6.9 shows comparative statistical box-and-whisker plots of PM values for all

test images. The plots reveal a much better performance of the WLD algorithm. Hence, our

WLD are proper for tongue crack extraction.

6.5 Conclusion and discussion

We for the first time attempted to detect cracks of tongue images. An automatic tongue crack

detection scheme using the wide line detector is described in this chapter. An adaptive

algorithm of line width estimation is designed to implement the wide line detector totally

automatically. The error generated by the maximum line width estimation algorithm is small

enough. The tongue crack extraction method works well for all test tongue images. Because

no derivative is directly used in the wide line detector, the tongue crack extraction method

gives strong noise rejection. The detection results obtained using our scheme keep line width

information well due to no Gaussian smooth kernel applied. Compared to the classic line

detection methods, our WLD has been successful in improving the performance by

increasing PM 71.5% compared to Steger’s method and 61.0% to the line operator,

respectively. Therefore, the wide line detector is definitely proper for tongue crack

extraction.

130

Chapter 7

Conclusion

We have presented a general method for wide line detection. In contrast with the previous

work which detects the wide line as parallel opposing edges, the proposed wide line detector

extracts the line entirely. The line detection method works very well for a range of images

containing different widths of linear and curvilinear structures, especially for those where the

width of lines varies greatly. This method also works well when the lines run close together

or cross each other due to no line direction required to estimate.

We have applied this proposed general method to solve two practical line detection

problems: palm-line feature based palmprint recognition and adaptive tongue crack detection.

Both have obtained promising results. The main contributions of this thesis are listed below.

7.1 Main contributions

A novel wide line detector using an isotropic nonlinear filter: In contrast with the

traditional directional-derivative-based edge and line extraction method, our wide

line detector is based on isotropic nonlinear filtering without any derivatives and

consequently is more robust to noise. Since no Gaussian kernel is required for our

wide line detector, even narrow lines can be extracted well, which indicates the

multi-scale inherence of our wide line detector.

Dynamic selection of parameters for the wide line detector: We introduced a scheme

to investigate the relationship between the size of circular masks and the width of

detected lines and defined the calculation of brightness contrast threshold so that the

wide line detector can automatically determine the two parameters for the input

image.

131

Analysis of the proposed wide line detector: We presented a scheme for selecting the

optimal core function for the wide line detector by evaluating the performance of

various formulae. We clarified the restriction on the radius of circular masks and the

calculation of the line orientation. We also conducted a comparative study to

demonstrate that the wide line detector is more robust against noise than the

traditional line detection methods.

A novel palm-line feature extraction method for palmprint recognition: As compared

to previous work on palm line extraction [60,61], our wide line detector-based

method extracts not only structure features but also strength features of palm lines for

personal identification. We described a translation-invariant approach for palm-line

feature matching. We also developed an experimental scheme to find out the optimal

combination of parameters for the proposed palm-line feature extraction method. The

experimental results demonstrate that the performance of the proposed WLD-based

method is comparable with the state-of-the-art algorithms of palmprint recognition

and thereby palm-line features can be used to recognize palmprints.

An automatic tongue crack extraction scheme: We for the first time attempted to

extract cracks from tongue images. We proposed a framework for automatic tongue

crack extraction. We derived a tongue crack detection scheme based on our wide line

detector. We also designed an adaptive algorithm for line width estimation to

determine the maximum width of tongue cracks in an input tongue image

automatically; the adaptive selection of maximum width of tongue cracks makes the

tongue crack extraction totally automatically. Compared to the typical line detection

methods, the automatic tongue crack extraction scheme improves the performance by

increasing PM 71.5% compared to Steger’s method and 61.0% to the line operator,

respectively. The experimental results show that the wide line detector is definitely

proper for tongue crack extraction.

132

7.2 Future Work

We now discuss a few directions along which we plan to continue our work.

Line width extraction: The proposed wide line detector can be extended to estimate

line width. We plan to design an algorithm to extract the thickness at each point and

then to validate that this thickness is reasonable at each point.

3-D line detection: The principle introduced in Chapter 3 can be used to detect lines

in 3-D. We would like to design a 3-D line detection algorithm to extract wide lines

and estimate the width and volume of lines.

Proper size of palm-line feature image for palm-line feature based palmprint

recognition: At the moment, the size of the palm-line feature image for palm-line

feature matching is fixed to 64x64. In Coding methods, the feature images for

matching is 32x32. We plan to investigate which size of palm-line feature image is

proper for the WLD-based palm-line feature extraction method.

Palm-line model: Although palmprint recognition has achieved a high performance, it

is needed to build the model of palm lines because it can reveal the nature of

palmprints and accordingly improve the performance further. We would like to study

the characteristics of palm lines further and build a model for palm lines.

Tongue crack description: The destination of tongue crack detection is for diagnosis.

According to the knowledge in TCM, we plan to describe tongue cracks in length,

width, depth, location and orientation to facilitate the tongue diagnosis.

Heuristic algorithm for tongue crack detection: We plan to develop a heuristic

algorithm to improve the performance of tongue crack detection. Such heuristic

algorithm will be based on the wide line detector and employ prior knowledge of

tongue diagnosis.

133

Retina vessel extraction: We would like to apply the proposed wide line detector and

the line width extraction method for retinal vessel extraction, which requires the

precise estimation of vessel width at each vessel point.

134

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