Brain Blood Vessel Map Extraction

Based on Fusion of Angiography Frames

and

Aneurysm Extraction

By

Saba Momeni

Department of Electronic Engineering

Najafabad University

2013

ii

Abstract

Recently, due to the development of facilities in imaging area, image processing can be effective in diagnosis,

prevention, and treatment of many diseases .Angiography images are one of the most useful categories in medical

image area. For example, some most common applications are Aneurysm and Arteriovenous Malformations (AVM)

detection, tumor evaluation and dissection. Angiography operation is done based on medicine reasons. It can be

operated with using x-ray, catheter and contrast material in 2-dimention or in 3-dimention with magnetic resonance.

Vessel map extraction can be a very helpful guidance for diagnosis and treatment of diseases. Moreover, merging of

information from all valuable frames from an angiography video can be introduced as a main process of vessel map

extraction based on contrast material motion.

In the first part of this thesis, for the first time, vessel map extraction is done based on the fusion of curvelet transform

coefficients automatically. Firstly, registration operation is done. Then, valuable frames are found based on our

proposed scheme. Moreover, background estimation and elimination are done based on counting average of valuable

frames and subtraction operation. In the next step, illumination smoothing is done by using homomorphic filter.

Finally our multi temporal fuzzy fusion algorithm is proposed based on feature of curvelet coefficients and fuzzy logic

rules.

In the second part, fusion images which represented aneurysm problem are applied to proposed aneurysm extraction

algorithm. This algorithm is performed based on morphology operation, nonlinear diffusion filtering, Hough

transform, and proposed region growing algorithm. As the best application, radius of each aneurysm is calculated and

presented based on doctor demand.

Finally the two proposed algorithms are evaluated based on objective evaluation criterion which is defined. In

comparison with other works proposed fusion algorithm is superior, which means it represented lower error and high

noise reduction. Moreover accuracy for aneurysm extraction algorithm is obtained around 80 percentages which is

acceptable for doctors.

Keywords: Brain vessel map, Coefficient merging, Fuzzy rules, Morphology operation, Nonlinear diffusion filter,

Region growing algorithm, Aneurysm extraction.

iii

List of Tables

Chapter I

Table.1 represents if-then fuzzy rules. 15

Table 2: The evaluation objective measures of fusion results. 19

Table 3: Fusion results for Caudal 6 (LAO)86 with different algorithms. 20

Table 4: Fusion results for Cranial 3 (LAO) 88 with different algorithms. 21

Table 5: Fusion results for Caudal 3 Left Anterior Oblique (LAO) 86 with different algorithms. 22

Table 6: Fusion results for AP Cranial 33 Right Anterior Oblique (RAO) 3 with different algorithms. 23

Table 7: Comparison our proposed fusion algorithm with presented work in [17]. 26

Table 8: Comparison our proposed fusion algorithm with presented work in [18]. 26

Chapter II

Table 1: Radius measurement 39

Table 2: Accuracy measurement 40

iv

List of Figures

Chapter I

Fig. 1: Block diagram of proposed DSA image fusion algorithm 4

Fig. 2: Valuable frame selection for fusion processing based on the average and variance values. (a)

Smoothed average values, (b) Smoothed variance values, (c) Difference of consecutive variances. 6

Fig. 3: Pre-processing results, (a) Registered frame, (b) Background elimination result, (c) Illumination

smoothing result. 8

Fig. 4 Coefficient grouping from all decomposed valuable frames for one sub-band. 9

Fig. 5: Block diagram of proposed fusion scheme based on WSGCT coefficients. 10

Fig. 6: Angiography serial images from two different views. (a) Cranial 3 Left Anterior Oblique (LAO)

88 . (b) Caudal 6 Left Anterior Oblique (LAO) 86 . 17

Fig. 7: Fusion results for Caudal 6 Left Anterior Oblique (LAO) 86 view. (a) AV method. (b) SML

method. (c) SEOG method. (d) LV method. (e) SC&SEOG&LE method. (f) SC&SML&LE method. 20

Fig. 8: Fusion results for Cranial 3 Left Anterior Oblique (LAO) 88 . (a) AV method, (b) SML method (c)

SEOG method (d) LV method (e) SC&SEOG&LE method. (f) SC&SML&LE method. 21

Fig. 9: Fusion results for Caudal 3 Left Anterior Oblique (LAO) 86 . (a) AV method. (b) SML method. (c)

SEOG method. (d) LV method. (e) SC&SEOG&LE method. (f) SC&SML&LE method. 22

Fig. 10: Fusion results for AP Cranial 33 Right Anterior Oblique (RAO) 3 view (a) AV method. (b) SML

method. (c) EOG method. (d) LV method. (e) SC&SEOG&LE method. (f) SC&SML&LE method. 23

Chapter II

Fig. 1: Fused DSA images for four different views. Blue circle shows aneurysm and red circles show vessels

overlap and cross section vessels. 33

Fig. 2: Removing vessel structure with multi directional morphological operation for four sample fused DSA

images. 36

Fig. 3: Red circles are wrong candidates and blue one is aneurysm 36

Fig.4 removing vessel structure with nonlinear filtering operation 37

Fig. 5: Aneurysm candidates from Houph transform. 38

Fig. 6: Region growing procedure result. 38

Fig. 7: Final results. 39

v

Contents

Abstract ii

List of Tables iii

List of Figures iv

1. An Automatic Fuzzy-based Multi-temporal Brain Digital Subtraction Angiography Image Fusion Algorithm Using Curvelet Transform and Content Selection Strategy

1

Abstract 1

1.1. Introduction 1

1.2. Our Proposed Automatic Fuzzy-based Multi-temporal Fusion Algorithm 4

1.2.1. Pre-processing 5

1.2.1.1. Registration 5

1.2.1.2. Valuable Frame Selection for Fusion Process 5

1.2.1.3. Background Subtraction and Illumination Smoothing 8

1.3. Fundamental Fusion Steps 9

1.3.1. Curvelet Transform 9

1.4. Proposed Fusion Scheme 10

1.4.1. Proposed Fusion Scheme for High Frequency Contents 11

1.4.1.1. Proposed Fuzzy-Based Fusion Scheme for High Frequency 13

1.5. Fuzzy Inference System 14

1.5.1. Fuzzy-based Fusion Method 15

1.6. Proposed Fusion Scheme for Low Frequency Coefficients 16

1.7. Experimental Results 16

1.7.1. Database 16

1.7.2. Preprocessing 17

1.7.3. Fuzzy-based Fusion Scheme for High Frequency 18

1.7.4. Evaluation Criteria 18

1.7.5. Analysis of Fusion Results and Discussion 19

1.8. Comparison with Other Works 25

1.9. Conclusion 27

References 28

vi

2. Aneurysm Extraction 31

Abstract 31

2.1. Introduction 31

2.2. Proposed Automatic Aneurysm Extraction Algorithm 32

2.2.1. Preprocessing 33

2.2.1.1. Morphological processing 33

2.2.1.2. Nonlinear Diffusion filtering 34

2.3. Extraction Procedure 34

2.4. Postproccessing 35

2.5. Experimental results 35

2.5.1. Data set 35

2.5.2. Preprocessing 35

2.5.2.1. Morphological operation 35

2.5.2.2. Nonliner Diffusion Filtering 36

2.5.3. Extraction Procedure 37

2.5.3.1. Houph Transform 37

2.5.3.2. Region growing Algorithm 38

2.5.4. Postproccessing 39

2.6. Evaluation of proposed algorithm 40

2.7. Comparison with other works 40

2.8. Discussion 41

References 42

3. Discussion 43

1

Chapter I

An Automatic Fuzzy-based Multi-temporal Brain Digital Subtraction Angiography

Image Fusion Algorithm Using Curvelet Transform and Content Selection Strategy

Abstract

Recently image fusion has prominent role in medical image processing and is useful to diagnose and treat many

diseases. Digital Subtraction Angiography (DSA) is one of the most applicable imaging to diagnose brain vascular

diseases and radio-surgery of brain. This thesis proposes an automatic fuzzy-based multi-temporal fusion algorithm

for 2-D DSA images. In our algorithm, for blood vessel map extraction, the valuable frames of brain angiography

video are automatically determined to form the DSA images based on a novel definition of vessel dispersion generated

by injected contrast material. Also, to overcome to defects of wavelet transform (WT) and first generation of curvelet

transform (FGCT), our proposed fusion scheme contains different fusion methods for high and low frequency domains

based on the coefficient characteristic of wrapping second generation of curvelet transform (WSGCT) and our

proposed content selection strategy. Our proposed content selection strategy is defined based on sample correlation of

the coefficient of WSGCT. In our proposed fuzzy-based fusion scheme, the selection of curvelet coefficients are

optimized by applying weighted averaging and maximum selection rules based on defined fuzzy logic rules for the

high frequency domain. For low frequency coefficients, the maximum selection rule based on local energy criterion is

applied to better visual perception. Our proposed fusion algorithm is evaluated on a perfect brain angiography image

dataset consisting of hundred 2-D internal carotid rotational angiography videos. The obtained results demonstrate the

effectiveness and efficiency our proposed fusion algorithm in comparison with common and basic fusion algorithm.

Keywords: Digital subtraction angiography, multi-temporal image fusion, curvelet transform, fuzzy logic.

1.1. Introduction:

Image fusion involves the combination of different images to form one image. The aim of fusion is to extract

perceptually important features from all the original images and create a high informative and comprehensive image

2

which is more useful for human visual perception or computer vision tasks. The principal motivation for image fusion

is to reduce uncertainty and minimize redundancy in the output while maximizing relevant information for a particular

application or task. The image fusion algorithms can be divided into low (pixel), mid (feature), and high levels [1].

The pixel-level algorithm can be performed by simple arithmetic operations such as: addition, subtraction, division,

multiplication or more complicated operators which are defined by a function [2]. Multiresolution analysis tools such

as discrete wavelet transform (DWT) [3,4], curvelet transform (CT) [5], contourlet transform [6], are prominent

transforms which are used in the pixel-level fusion algorithms. Less work has been done at the feature-level and high-

level image fusion. The feature-based image fusion algorithms typically segment the images into regions and fuse the

regions using their various properties and they are usually less sensitive to signal-to-noise level [7]. The high-level

fusion algorithms combine image descriptions, for instance, in the form of relational graphs [9].

The image fusion algorithms can be classified based on the data entering such as: (1) Multi-view: fusion of images

from the same modality which are taken at the same time but from different viewpoints. (2) Multi-modal: the fusion of

images coming from different sensors (for example, visible and infrared, CT and MRI). (3) Multi-temporal: the fusion

of images taken at different times from one view with same modality. (4) Multi-focus: the fusion of images of a 3D

scene taken repeatedly with various focal lengths. (5) Fusion for image restoration.

The image fusion has been widely used in many applications such as remote sensing and astronomy (pan-sharpening)

[8], target tracking system [10], surveillance systems (multiple camera surveillance systems) [11], and medical

diagnosis [12,13,14,7].

Along with the development of the medical image technology, medical image fusion becomes increasingly important

in analysis and diagnosis [12]. Different medical imaging techniques such as computed tomography (CT), magnetic

resonance imaging (MRI), and single photon emission computed tomography (SPECT) provide different perspectives

and information on the human body which are essential in the diagnosis of diseases or physical disorders. CTA, MRA

and DSA are three different types of angiography operations with special roles in radio-surgery and diagnosis of

vascular diseases [15]. Common applications of DSA, CTA and MRA are: Aneurysm and Arteriovenous

Malformations (AVM) detection, tumor evaluation and dissection. 2-D angiography is an invasive diagnostic test which

uses X-rays energy. For this operation at first a long flexible catheter is inserted through the blood stream to deliver dye (contrast

agent) into the arteries and making them visible then images will be taken with rotational angiography system from

different views such as lateral, anteroposterior (AP) and oblique view. An image without contrast material will be

defined as mask and after injecting contrast material into an artery or vein, actual angiographic image is captured.

3

Then mask and contrast image will be registered and DSA image will be obtained by subtraction operation. Due to the

dissolving and disappearing of contrast material as time goes, the DSA serial images present different parts of blood

vessel. Thus, by fusing these serial images into one image, vessel map for surgical operation and aneurysms or arterial

stenosis detection will be produced.

To benefit from properties of all modalities, multimodality image fusion in medical applications has important role. In

[16], multimodality image fusion for radio-surgery localization of large AVMs has been presented which combines 3D

MRA and 2D DSA vasculature information with 3D MR/CT anatomical information. At first the MRA and MR/CT

volumes are fused then 3D target localization and delineation within the fused volumes are performed. Next section,

(DSA target localization) determines the target position and the projection geometry. At last the correlation of the

MRA and DSA data is done. In [17, 18], the authors used DSA serial images which follow DICOM standard. In [17],

firstly DSA images are decomposed by Harr DWT (HDWT). Then by using a membership function based on dynamic

fuzzy data model (DFDM), coefficient selection is optimized in order to combine all series of DSA images in different

levels. In [18], the authors decomposed DSA images by CT to obtain information of different levels. Then, by using

entropy of different levels of DSA images and a membership function based on dynamic fuzzy logic, a set of weights

for image sub-band coefficients are assigned. At last, an inverse CT is applied to reconstruct the fusion result. Based

on our opinion, third major common disadvantages of fusion algorithm in [17,18] are seen. Firstly, the presented

fusion algorithm in [17, 18] are not automatically based on valuable frames for all of optional views and experimental

results have been obtained based on one view. Secondly, appropriate multiresolution transform is not used to present

salient features in different directions. For example, in [17], 2D HDWT is used to decompose the DSA images but due

to lack of shift invariance and inability to represent multi-scale and directional geometrical structures such as smooth

contours and edges in images, this transform is not appropriate. Moreover, in [18], the authors used first generation of

curvelet transform (FGCT) [19], which analyzes an image with different block sizes by a single transform. Moreover,

this transform decomposes the image into a set of wavelet bands, and then analyzes each band by a local ridgelet

transform. The utilized FGCT in [19] is more effective and applicable than WT to represent the image details but it

suffers from some drawbacks. Thirdly, from performance measurements, it is obvious that presented algorithms are

not successful in noise reduction.

4

Fig. 1: Block diagram of proposed DSA image fusion algorithm

In this thesis, we propose an automatic fuzzy-based multi-temporal fusion algorithm based on wrapping second

generation of curvelet transform (WSGCT) and fuzzy logic rules for the brain DSA images. In our algorithm, to

overcome to disadvantages of the fusion algorithms in [17, 18], such as not being automatically based on finding

valuable frames for all of views, lack of using proper multiresolution transform, and poor noise improvement,

alternative ways are proposed. At first, we carry out the fusion process automatically on valuable frames of brain

angiography video. Then, to overcome to defects of WT and FGCT, our proposed fusion scheme contains different

fusion methods for high and low frequency domains based on the coefficient characteristic of WSGCT. In our

proposed fuzzy-based fusion scheme, the selection of curvelet coefficients are optimized by applying weighted

averaging and maximum selection rules based on defined fuzzy logic rules for the high frequency domain. For low

frequency coefficients, maximum selection rule based on local energy criterion is used for better visual perception. At

last, to evaluate our proposed fusion algorithm, some famous objective evaluation criteria are applied.

The rest of this chapter is organized as follows. Section 2 explains principles of our proposed fuzzy-based multi-

temporal fusion algorithm. In section 3, experimental results and comparison with other works are presented and

discussed. Finally, our conclusions are presented in section 4.

1.2. Our Proposed Automatic Fuzzy-based Multi-temporal Fusion Algorithm

Figure 1 shows block diagram of our proposed fuzzy-based multi-temporal fusion algorithm for the brain DSA

images. At first for each view, the registration operation on all frames is performed. Then, by finding the valuable

frames, the fusion process is carried out automatically. To remove undesired background of frames, each frame is

subtracted from the estimated background. Then, illumination smoothing is performed by a homomorfic filter. To

represent the DSA images in different levels of frequencies, we decompose the images by using WSGCT. Then, we

Video Sequences

(Frame 1 ton)

Finding Valuable

Frames for Fusion

Process

Registration

Proposed Fusion

Scheme

Image Decomposition

Using Curvelet

Transform

Reconstruction

of Fused Image

Fused Image

Background Subtraction

and Illumination

Smoothing

5

apply different strategies to fuse low and high frequency coefficients. Finally, the fused image is formed by

reconstruction of the fused coefficients. In following, we describe the details of our proposed algorithm.

1.2.1. Pre-processing

1.2.1.1. Registration

Image registration operation attempts to align two images geometrically [20-21]. Registration is a crucial operation in

image fusion and its accuracy is a major factor in determining the quality of the output image. In this thesis, to

enhance the quality of DSA images, patient motion during image acquisition is improved by a registration procedure

before subtraction operation. So, all frames are registered on the first frame. Initial control points are specified in the

first frame by using canny edge detector, then for finding corresponding control points the entropy of the histogram of

differences between template from the first frame and sub-image pixel values in other frame is used as similarity

measure [22]. At last, by performing affine transform registration is accomplished.

1.2.1.2. Valuable Frame Selection for Fusion Process

All of frames in the brain angiography video have not valuable information and are not necessary to use. Therefore, to

select the valuable frames in the fusion process, we apply two measures that have been defined based on the change of

grayscale values generated by contrast material movement. For this purpose, for finding the valuable frames from a

sample view, after registration by subtraction operation, differences of consecutive frames are obtained as follows:

1zdif z zf f f , {2,3,..., }z n (1)

where z is the set of all frame numbers, f is the registered frame and zdiff is zth subtracted frame. In each view, dye

(contrast material) starts and disappears from bottom part of the frames. So, the bottom part of each subtracted image

is considered. Variance and average values for this sub-image are calculated as,

6

(a)

(b)

(c)

Fig. 2: Valuable frame selection for fusion processing based on the average and variance values. (a) Smoothed average values, (b)

Smoothed variance values, (c) Difference of consecutive variances.

1 1

1( , )

z

N M

z dif

y x

a f x yMN

{2,3,..., }z n (2)

where za is the average value of sub-image with size M N from zth frame.

2

1 1

1( ( , ) )

z

N M

z dif z

y x

v f x y aMN

{2,3,..., }z n (3)

7

where zv is the variance value of sub-image with size M N from zth frame. As a result, we have two sets of

average and variance values which are named A and V as,

{ | 2,3,.., }iA a i n , { | 2,3,.., }iV v i n (4)

To obtain real numbers of valuable frames, smoothing of small fluctuations in the average and variance diagram is

necessary. In this thesis, one dimension nonlinear diffusion filtering is used as a smoothing method [23]. The graph of

smoothed average and variance values is plotted in Fig. 2(a) and (b), respectively. In the rest of the thesis, variance

and average values are considered as the results of smoothing operation. The number of the last valuable frames is

specified based on this fact that when dye starts disappearing, sub-image pixel values are being increased and when it

disappears completely there is no more change. Based on the maximum average value and minimum variance value

this number is obtained as follows:

min([ rg max( ), rg min( )])i i

q a A a V (5)

where q is the number of last valuable frame. For finding the number of the first valuable frame, after obtaining set

of variance values for sub-image pixels, the difference of variances are calculated. Fig. 2(c) shows the difference of

consecutive variance (DOCV) values.

Two main points are considered in Fig. 2(c). When dye starts to flow, the point which has positive DOCV value for

the first time is defined as the first main point. Also, the point which has the first maximum difference value and after

that for two frames, this value has been decreased is considered as the second main point. Expressions are defined as

follows:

1zdif z zv v v , {2,3,..., }z n (6)

where difference of each two consecutive variance values is zdifv , and z is the index of frames.

2 3{ , ,... }

ndif dif dif difV v v v (7)

where difV is the set that includes all DOCV values.

2

i jn np

(8)

where [.] is a function that returns integer value, p is the number of the first valuable frame, in and jn are the frame

numbers which are located on the first and second main points, respectively. Regarding the last valuable frame

number, the rest of valuable frames is specified as follows:

8

p < 1 2, ,...m m < q if q is the maximum value of average values (9)

Where 1 2, ,...m m are the numbers of valuable frames which are located on the local maximum points in Fig. 2(a).

p < 1 2, ,...m m < q if q is the minimum value of variance values

(10)Where 1 2, ,...m m are the numbers of valuable frames which are located on the local maximum points in Fig. 2(b).

1.2.1.3. Background Subtraction and Illumination Smoothing

Removing undesired background for angiography image is an essential process which eliminates bone and soft tissues

and also makes blood vessels more clear. In this thesis, averaging method and subtraction operation on valuable

frames are considered as the estimation and elimination operations, respectively. Moreover, Since Curvelet Transform

(CT) is very sensitive to illumination changes, we employ homomorphic filter [24] to compensate the uneven

illumination and low contrast images. This filter is defined as:

22( , )/0

)( , ) ( 1

u v Dc D

H L LH u v e

(11)

where constant c has been introduced to control the steepness of the slope, 0D is the cut-off frequency, D(u,v) is the

distance between coordinates (u,v) and the centre of frequency at (0,0), H is the high frequency gain, L is the low

frequency gain. Fig .3 (b) and Fig. 3(c) shows result of background elimination and applying homomorphic filter

respectively.

(a) (b) (c)

Fig. 3: Pre-processing results, (a) Registered frame, (b) Background elimination result, (c) Illumination smoothing result.

9

Fig. 4 Coefficient grouping from all decomposed valuable frames for one sub-band.

1.3. Fundamental Fusion Steps

Fusion algorithms based on the multiresolution transform coefficients can be summarized in three steps such as

coefficient grouping, activity-level measurement (ALM) and coefficient merging [3]. The coefficient grouping for

three set samples of corresponding coefficients for one sub-band matrix is shown in Fig. 4. The coefficient-based and

window-based are two methods which we use to calculate activity-levels.

1.3.1. Curvelet Transform

Basis elements of CT [5] are highly anisotropic and have high directional sensitivity. This transform can be used as

highly efficient instrument for salient feature detection and extraction in image processing. The curvelet transform

coefficients are defined as:

( , ) ,

2

1( , , ) ( ) ( )

(2 )

j lk

l

i x

jc j l k f U R e d

(12)

where f is the Fourier transform of the signal and jU is the frequency window applied in the frequency domain. l

R

is rotation by l radian and is defined as:

cos( ) sin( )

sin( )cos( )R

(13)

10

So, ( , , )c j l k is achieved in the scale j , direction l , with the transition parameter k . x and are the variables of the

spatial and frequency domains, respectively. This transform is divided by employing two methods, i.e., the USFFT

transform and the wrapping transform. Both of them have the same output, but the wrapping algorithm gives a more

intuitive algorithm and faster computation time. We use WSGCT to decompose the DSA images into high and low

frequency coefficients.

Fig. 5: Block diagram of proposed fusion scheme based on WSGCT coefficients.

1.4. Proposed Fusion Scheme

One of the main purposes of our proposed fusion algorithm is reduction of noise and background artifacts to integrated

accurate detail information of the blood vessels. To achieve this aim, for low frequency domain, local energy (LE) and

maximum selection are proposed as an activity criterion and fusion rule. Moreover, for high frequency coefficients,

we propose a fusion map which specifies the fuzzy fusion scheme for each corresponding coefficient set as follows:

Illumination Smoothed

Valuable Frames from (1 to n)

Decomposition with

Curvelet Transform

Corresponding

Coefficients

Grouping

Corresponding

Coefficients

Grouping

Local

Variance

Maximum

Selection

Weighted

Averaging

Intersection

Operation

Fuzzy-Logic

Rules

Bound

ed

Range

of

Maximum

Selection

Counting

Variance value

for each set

High Frequency Low Frequency

Proposed

Fuzzy-based

fusion scheme

Yes No

Fused

Image

Fused

Image

11

Weighted averaging based on fuzzy logic rules Bounded range of varianceFuzzy-based fusion scheme=

Maximum intersection selection Unbounded range of variance

(14)

In this map, the weighted averaging based on fuzzy logic rules is considered for optimizing coefficient selection which

obtains more reliable and accurate vessel information. Also the maximum intersection selection is used to eliminate

noise and background artifacts. The bounded range of variance evaluates the variance value of each corresponding

coefficient group which we introduce it as matching degree (MD). The higher variance indicates the higher dispersal

of coefficient values and results the lower matching degree. The bounded range of variance is defined based on

Gaussian model of corresponding coefficient set variance. Therefore, for this Gaussian model, the average ( ave) and

variance ( var ) values are calculated and two thresholds of the bounded range of variance are defined as

var1 aveT and var2 aveT respectively. In Fig. 5 block diagram of our proposed fusion scheme is

illustrated.

1.4.1. Proposed Fusion Scheme for High Frequency Contents

The high frequency bands reflect mutation characteristics of image and describe the detailed information such as

salient features of image. Each sub-band of high frequency domain describes image information from special

directions. In this thesis, the blood vessels are considered as edge information and activity criteria are introduced

based on the edge characteristics such as large absolute value and high changes in grayscale values. In the rest of the

thesis, , ( , )j lic x y is the curvelet coefficient at point ( , )x y , in the scale j and direction l and i ( 1 2, , ,...i p m m q ) is the

set of valuable frame numbers. , ( , )j lfc x y is the fused coefficient at point ( , )x y , for scale j and direction l and

,( , )

j ldc x y is the coefficient which has maximum value of defined ALM at point ( , )x y , in scale j and direction l , from

frame d ( 1 2{ , , ,... }d p m m q ).

We consider maximum selection rule based on four main activity criteria as a basic fusion algorithm. Absolute

values, sum- modified Laplacian, sum energy of gradient, and local variance are the four applicable activity criteria

which defined as follow:

A. Absolute Value (AV)

The high frequency coefficients with large absolute values are considered as large changes or salient features in the

corresponding source image.

12

B. Sum-Modified Laplacian (SML)

Modified Laplacian (ML) [25], which takes the absolute values of the second derivatives in the Laplacian, can show

information changes in the high frequency coefficient. The higher ML value means higher detail information and more

salient image features. The modified Laplacian and SML for coefficient , ( , )j lic x y is obtained as follows:

2 , , , , , , ,( , ) 2 ( , ) ( 1, ) ( 1, ) | | 2 ( , ) ( , 1) ( , 1) |j l j l j i j l j l j l j lML i i i i i i ic x y c x y c x y c x y c x y c x y c x y (15)

Where 2 , ( , )j lML ic x y is ML.

In this thesis, “step” always equals to 1. SML, in a window around the centered coefficient , ( , )j lic x y is defined as:

, 2 ,( , ) ( , )

f y Nh x Nj l j li ML i

h x N f y N

SML x y c h f

1 2, , ,...i p m m q (16)

where , ( , )j liSML x y is the sum-modified Laplasian value and N is set to 5.

C. Sum Energy of Gradient (SEOG)

The gradient can well reflect the changes of the high frequency information. The higher gradient value means higher

detail information [26]. Energy of gradient (EOG) and SEOG for the coefficient , ( , )j lic x y are defined as follows:

, , , 2 , , 2( , ) ( ( , ) ( 1, )) ( ( , ) ( , 1))j l j l j l j l j li i i i iEOG x y c x y c x y c x y c x y , 1 2, , ,...i p m m q (17)

, ,( , ) ( , )

h y N f x Nj l j l

i i

h y N f x N

SEOG x y EOG f h

, 1 2, , ,...i p m m q (18)

where , ( , )j liEOG x y and , ( , )j l

iSEOG x y are the energy of gradient and sum energy of gradient values, respectively and N

is set to 5.

D. Local Variance

The bigger variance of coefficients reflect the bigger dispersive and more edge information [27]. The change in the

grayscale values is one of the edge characteristics which are available in the local variation of coefficients. The local

variance for coefficient , ( , )j lic x y is expressed as follows:

13

21 12 ( , ) ,

0 0

1( ) ( , ) ( , )

M Nj l j l

i i

x y

x y c x y mMN

, 1 2, , ,...i p m m q (19)

where 2 ( , )( ) ( , )j li x y is the local variance, m is the mean value of coefficients in the local window with size of M N

that 5M N is considered.

1.4.1.1. Proposed Fuzzy-Based Fusion Scheme for High Frequency

Recently fuzzy logic approaches are very applicable in the image fusion application [29-30]. In this thesis as

illustrated in Fig. 4, the coefficient grouping is applied on each sub-band matrix and also theirs variance values are

calculated so that the corresponding fuzzy fusion method is determined based on fuzzy-based fusion scheme (Eq.

(14)). In our application, while both SEOG and SML are effective and appropriate for edge extraction, the proposed

membership functions and fuzzy rules are the same, only SEOG and SML values are used instead of each other.

SEOG membership function is defined for the coefficient , ( , )j lic x y as follows:

,,

,

( , )( , )

( ( , ))i

j lj l i

d j li

SEOG x yx y

MAX SEOG x y , 1 2, , ,...i p m m q (20)

where ,( , )

i

j l

dx y and , ( , )j l

iSEOG x y are membership degree and the SEOG for coefficient , ( , )j lic x y , respectively.

Since detection of feature area from noise area based on distribution model and variance is not reliable, Sample

correlation [28] is another criterion which we use in our content selection strategy. Based on the SC criterion, the

feature areas have the large sample correlation at least in one direction whereas in the noise areas, the sample

correlation has not significant values. By considering the rearrangement of pixel values for the window patch

according to a specific orientation, estimation of the sample correlation in one or more directions are performed.

Suppose that NijM is an N × N sliding sample window centered at ijX over the each sub-band matrix. Let

21 2{ , ,... }N

U u u u , where 1 2{ , ,... }n is obtained from N

ijM by rearranging the pixel in NijM according to the

specific orientation . In this thesis, N=5 and n=4 and {0 ,45 ,90 ,135 } is considered. Fig. 6 shows rearranging

data in a window with size of 5 5 for four directions. To facilitate the sample correlation in the specific orientation

, the feature vector is defined as:

21 2{ , ,... }N

Z z z z (21)

14

where 1k k kZ u u for =1, 2... n; k = 2, 3,..., 2N

Note that the values of kz are small and similar when the calculated sample correlations are in the specific orientation

, and relatively have different values when the calculated sample correlation are in different orientations. Therefore,

if there is an image detail in the specific orientation , the variation of Z is smaller than Z for any other

( )where . Consequently, if the variance of Z (i.e., ) is the same in all orientations then NijM will be

composed of pure random noise. Unlike, if the variance of Z is not equal at least for two orientations, then NijM

contains an image feature (or detail).

To obtain SC for centered coefficient , ( , )j lic x y , the feature vectors are extracted for four orientations (

{0 ,45 ,90 ,135 } ). Then, for each feature vector ( Z ) in four orientations, the variance ( ) is calculated as,

= 2

1

1( )

K

k m

k

z zK

, 0 ,45 ,90 ,135 (22)

where kz is thk element, mz and are mean and variance values for the feature vector Z and K is number of the

vector elements. In the following, we define a membership function for coefficient , ( , )j lic x y as follows:

, 1( , )

1

j li v

x ye

(23)

where , ( , )j li x y is the membership degree for the coefficient , ( , )j l

ic x y and is defined as,

min( )

max( )v

, 0 ,45 ,90 ,135 (24)

This membership function shows that for lower v , the variance values for four orientations have more diversity.

Therefore, probability of the feature existence in the local window is more than noise existence, consequently

, ( , )j lic x y gets the higher membership degree.

1.5. Fuzzy Inference System

Two different membership functions were introduced based on SEOG and SC values in the previous section. The

membership degree of each coefficient based on SEOG and SC values is defined as the first and second inputs. In this

thesis, the membership degrees are rated into three levels Low (L), Medium (M) and High (H) and the output degrees

are rated into five levels Very Low (VL), Low (L), Medium (M), High (H) and Very high (VH). In experiments, for

15

the first input, we utilized polynominal-Z, G-Bell and sigmoid-right membership functions for L, M and H levels,

respectively. For the second input, the polynominal-Z, Sigmoid and G-Bell membership functions for L, M and H

levels are considered. For the output, the G-Bell and sigmoid-right membership functions are used for VL, L, M levels

and for H and VH levels, respectively. In this thesis, we specify the membership degree (weight) for each coefficient

based on Mamdani-type inference. These if-then fuzzy rules have been provided in Table 1.

Table.1 represents if-then fuzzy rules.

Membership Degree

Input 1 H H H M L M L M L

Input2 H M L H H M M L L

Output VH H VL H M M M L VL

1.5.1. Fuzzy-based Fusion Method

A. Weighted Averaging

In the fuzzy-based fusion scheme (Eq. (14)), we use the weighted averaging to obtain the fused coefficients in the

bounded range of variance of each corresponding coefficient group. The weighted averaging is defined as,

1 1

, , , .( , ) ( , ) ( , ) ... ( , )j l j l j l j lf p p m m q qc x y c x y c x y c x y (25)

where i is membership degree of coefficient , ( , )j lic x y for 1 2, , ,...i p m m q .

B. Maximum Intersection Selection

In the fuzzy-based fusion scheme (Eq. (14)), we use the maximum intersection selection to obtain the fused

coefficients in the unbounded range of variance of each corresponding coefficient group. In this scheme, for each

coefficient in the corresponding coefficient set, the intersection operation between two membership degrees which are

calculated based on Eq. (20) and Eq. (23) is performed then the coefficient which has maximum intersection value is

known as the fused coefficient as follows:

, , ,( , ) min[ ( , ), ( , )]

i i i

j l j l j l

b e dx y x y x y , 1 2, , ,...i p m m q (26)

where ,( , )

i

j l

bx y is intersection of two membership degrees for coefficient , ( , )j l

ic x y and ,( , )

j ldc x y is the coefficient

which has maximum intersection value from frame d ( 1 2{ , , ,... }d p m m q ) that is defined as

, ,( , ) ( , )j l j l

fdc x y c x y (27)

16

where , ( , )j lfc x y is fused coefficient. In the following, the maximum intersection degree is defined as,

max (i ,( , )

j lb x y ) , 1 2, , ,...i p m m q (28)

1.6. Proposed Fusion Scheme for Low Frequency Coefficients

The low-frequency sub-band reflects the approximate of image and concentrates the image energy. Choosing

appropriate fusion method for low frequency coefficients plays an important role to improve the visual effect of fusion

results. In this essay, local energy (LE) is used as an activity criterion. After coefficient grouping based on the section

(2.2), for each coefficient in the corresponding coefficient set, the local energy [31] is calculated in a local window

with size3 3 as follows:

,

(0)2( , ) ( , ). ( , )

i M j N

LE x y R x i y j g x i y j

(29)

where R is the local filtering operator. M and N are the size of local window ( ), (0)( , )g x y are low frequency

coefficients.

2 2 2

1

(0) (0) (0)( , ) * ( , ) * ( , ) ... * ( , )1 2p m qiLE x y E g x y E g x y E g x yK , 1 2, , ,...i p m m q (30)

where ( , )i

LE x y is local energy of each low frequency coefficient ( , )ig x y which centered at point ( , )x y . 1E , 2E … 1kE

and kE are the filter operators in K different directions. In this thesis, we use three directional filtering operators as

follows:

1

1 1 1

2 2 2

1 1 1

E

2

1 2 1

1 2 1

1 2 1

E

3

1 0 1

0 4 0

1 0 1

E

(31)

At last for each corresponding coefficient group, the coefficient which has maximum LE value is selected as the fused

coefficient.

1.7. EXPERIMENTAL RESULTS

1.7.1. Database

To test our algorithm, we gathered hundred 2-D internal carotid rotational angiography videos from Chamran hospital

which are acquired from different angiography views and follow DICOM standard. Twenty of videos show

intracranial aneurysm problem and rest of them are normal cases. Digital subtraction process was not operated on the

17

frames. X-ray exposures were obtained at 7.5 frames per second, and images were displayed on a 960 960 matrix.

Field of view was 20 to 25 cm for anteroposterior and lateral projections, and 17cm for oblique views. Two samples of

angiography serial images from our data which focus on the same scene at three different times are shown in Fig. 6.

(a)

(b)

Fig. 6: Angiography serial images from two different views. (a) Cranial 3 Left Anterior Oblique (LAO) 88 .(b) Caudal 6

Left Anterior Oblique (LAO) 86 .

1.7.2. Preprocessing

To find the valuable frames based on the change of gray scale values created by contrast material movement, the

variance and average values for bottom part of each subtracted image are calculated. In this thesis, based on results of

our experiments, our appropriate sub-image is extracted from each subtracted image from row 800 through row 900

and column 100 through 900. After counting variance and average values for the entire subtracted image by

performing one dimensional nonlinear filter, the average and variance graphs are smoothed. In the nonlinear filtering,

the standard deviation of Gaussian is set to 0.02, contrast parameter is 0.01 and the speed of flux changes for a

variation in the gradient is 8. Based on Fig. 2(a), the 28th frame has the maximum average value and based on Fig.

2(b) the 63rd frame has the minimum variance value. The last valuable frame number is defined as the minimum value

of these two numbers i.e., 28. The first valuable frame number is specified based on the DOCV values which are

shown in Fig 2(c). In our experiment, we consider the numbers which are higher than 3 and lower than 15. This idea is

followed for all the angiography videos. Based on the Fig. 2(c) and section (2.1.2) the numbers 4 and 9 are the first

and second main points, respectively. The average value of these two points obtained 6.5 then by performing bracket

18

function which returns greatest integer less than or equal to average value, the first valuable frame number is set to 6.

According to the last valuable frame number and based on Eq. (9) and Eq. (10), the rest of valuable frame numbers are

found in the smoothed average diagram. In Fig. 2(a) the numbers 6, 11 and 19 contain the local maximum values.

Consequently, the numbers 6, 11, 19 and 28 are considered as valuable frame numbers for the fusion processing. In

section (2.1.3), the illumination smoothing was performed with homomorfic filter. As defined in Eq. (11), we

considered 090, 400, 3, .45H Lc D for all of our dataset which result good contrast without vessel rupture.

1.7.3. Fuzzy-based Fusion Scheme for High Frequency

In section (2.3), our proposed fuzzy-based fusion scheme for the high frequency coefficients was proposed. In this

scheme, we modeled distribution of the variance of corresponding coefficient sets as a Gaussian function and bounded

it with two thresholds 1T and 2T as var1 aveT and var2 aveT . Based on our experiments, is set to

100.

1.7.4. Evaluation Criteria

To evaluate the performance of our proposed algorithm and comparison with other algorithms, we used the most

reliable objective measures [32-34] such as correlation coefficient (CC), spatial frequency (SF), sharpness (SP), root

mean square error (RMSE), Peak Signal-to-Noise Ratio (PSNR), Signal to Noise Ratio (SNR). In this thesis, the

reference image (R) is the frame that has maximum entropy between the valuable frames and F is the fused image.

Table 2 obtains these objective measures.

19

Table 2: The evaluation objective measures of fusion results.

Evaluation

Criteria Calculation Description

CC

( ( , ) ( ))( ( , ) ( ))1 1

( )2 2

( ( , ) ( )) ( ( , ) ( ))1 1 1 1

M NF i j F R i j R

F i jCorr

M N M NR

F i j F R i j Ri j i j

( )F and ( )R are mean values of two

images (F and R). Higher CC reflects higher

extent correlation between the reference and

merged images.

SF

2 2( ) ( )SF RF CF ,

21( ( , ) ( , 1))

1 1

M NRF F i j F i j

i jMN

1 2( ( , ) ( 1, ))

1 1

M NCF F i j F i j

i jMN

SF measures the overall activity level in an

image. The higher SF value shows more

image salient information.

SP 1 2 2

( ( , ) ( , 1)) ( ( , ) ( 1, )) / 2,

SP F i j F i j F i j F i ji jMN

SP can reflect the small details of image. The

larger value of SP indicates that the fused

image has more sharpness.

RMSE 1 2

( ( , ) ( , ))1 1

M NRMSE F i j R i j

MN i j

The lower RMSE means the merged image

has the lower error and better quality.

PSNR

2255

10 log( )2

( ( , ) ( , ))1 1

MNPSNR

M NF i j R i j

i j

PSNR measures ratio between the maximum

possible signal and noise powers the higher

PSNR means fusion result is more qualify.

SNR 2 2

10 log[ ( ) / ( ) ]1 1 1 1

M N M NSNR R R R F

i j i j

This metric is used to measure quality of the

fused image. R is the mean value of the all

valuable frames. The higher value of the SNR

shows better noise suppression.

1.7.5. Analysis of Fusion Results and Discussion

In this thesis, to achieve informative blood vessel map, at first, we defined the maximum selection method based on

four activity criteria in section (2.4), as basic fusion algorithm (BFA). In these algorithms, the fusion of low frequency

coefficients has not been considered. After that we introduced our proposed fuzzy-based fusion scheme which is

obtained high visual perceptions with considerable improvement in the noise suppression. The fusion results of our

proposed fusion scheme and BFA for four different angiography views are shown in Fig. 7 through Fig. 10. In Tables

3 through 6 the objective evaluation measures for each view are presented. In these tables, our proposed fuzzy-based

fusion scheme based on SC and SEOG criteria for high frequency, LE criterion for low frequency is called and

abbreviated as SC&SEOG&LE and the scheme that is used with SML measurement is called as SC&SML&LE.

20

(a) (b) (c)

(d) (c) (f)

Fig. 7: Fusion results for Caudal 6 Left Anterior Oblique (LAO) 86 view. (a) AV method. (b) SML method. (c) SEOG method.

(d) LV method. (e) SC&SEOG&LE method. (f) SC&SML&LE method.

Table 3: Fusion results for Caudal 6 (LAO) 86 with different algorithms.

Algorithms Evaluation measurements

CC SF SP SNR PSNR RMSE

AV 0.8726 5.2342 2.7812 0.00067 48.1318 0.999

SML 0.8502 4.8690 2.5360 0.00067 48.1318 0.999

SEOG 0.8403 4.8701 2.5305 0.00067 48.1318 0.999 LV 0.8419 4.8798 2.5401 0.0006 48.1318 0.999

SC&SEOG&LE 0.8775 216.4176 8.9101 57.1009 105.2320 0.0014

SC&SML&LE 0.8633 205.3547 8.5276 56.3771 104.5082 0.0015

21

(a) (b) (c)

(d) (e) (f)

Fig. 8: Fusion results for Cranial 3 Left Anterior Oblique (LAO) 88 . (a) AV method, (b) SML method (c) SEOG method (d) LV

method (e) SC&SEOG&LE method. (f) SC&SML&LE method.

Table 4: Fusion results for Cranial 3 (LAO) 88 with different algorithms.

Algorithms Evaluation Measures

CC SF SP SNR PSNR RMSE

AV 0.9072 5.7966 3.1175 0.00047 48.1319 0.999 SML 0.9115 5.3583 2.8093 0.00047 48.1319 0.999

SEOG 0.9027 5.4471 3.8177 0.00047 48.1319 0.999

LV 0.9038 5.4892 2.887 0.00047 48.1319 0.999 SC&SEOG&LE 0.8962 217.8535 9.7865 56.2059 104.3373 0.0015

SC&SML&LE 0.8958 209.1748 9.4884 55.6576 103.7890 0.0016

22

(a) (b) (c)

(d) (e) (f)

Fig. 9: Fusion results for Caudal 3 Left Anterior Oblique (LAO) 86 . (a) AV method. (b) SML method. (c) SEOG method. (d)

LV method. (e) SC&SEOG&LE method. (f) SC&SML&LE method.

Table 5: Fusion results for Caudal 3 Left Anterior Oblique (LAO) 86 with different algorithms.

Algorithms Evaluation Measures

CC SF SP SNR PSNR RMSE

AV 0.8465 3.6230 1.8502 .00048 48.1320 0.999

SML 0.8343 3.3153 1.6223 .00048 48.1320 0.999

SEOG 0.8303 3.2552 1.5991 .00048 48.1320 0.999

LV 0.8307 3.2487 1.6030 .00048 48.1320 0.999

SC&SEOG&LE 0.8636 171.52227 7.3386 56.1132 104.2452 0.0016 SC&SML&LE 0.8464 166.0756 7.2237 55.4877 103.6193 0.0017

23

(a) (b) (c)

(d) (e) (f)

Fig. 10: Fusion results for AP Cranial 33 Right Anterior Oblique (RAO) 3 view (a) AV method. (b) SML method. (c) EOG

method. (d) LV method. (e) SC&SEOG&LE method. (f) SC&SML&LE method.

Table 6: Fusion results for AP Cranial 33 Right Anterior Oblique (RAO) 3 with different algorithms.

Algorithms Evaluation Measures

CC SF SP SNR PSNR RMSE

AV 0.8829 5.1807 2.7860 0.00058 48.1316 0.999

SML 0.8796 4.9497 2.5738 0.00058 48.1316 0.999 SEOG 0.8802 4.9605 3.5015 0.00058 48.1316 0.999

LV 0.8816 4.9861 2.6122 0.00058 48.1316 0.999

SC&SEOG&LE 0.8706 293.6596 11.5514 60.6778 108.8881 0.0009

SC&SML&LE 0.8619 291.0898 11.5209 60.2969 108.4279 0.0009

24

The effectiveness of our study is analyzed by considering performance measurements and simulation results which are

presented in Tables 3 through 6 and Figs. 7 through 10. Based on the aims which are followed in this thesis, we

analyze the evaluation measures for each view individually and then conclude that which fusion method provides the

best performance for all angiography views.

At first, we analyze the performance of the basic fusion algorithms. To evaluate the noise suppression performance

using SNR, PSNR, RMSE measures presented in Tables 3 to 6. It is clear that each one of BFA has the same effect in

the noise reduction. According to the values of SF measure, the fusion method based on AV criterion obtains more

sharp and clear result in all views. But, based on values of the CC and SP measures, we can not specify the better

algorithm. For example, in Table 6, the maximum SP value is resulted from SEOG method but in Table 5, it resulted

from AV method or for CC values, in Tables 3, 5 and 6, the AV method has the maximum correlation value but in

Table 4, the SML method provides the best result. From Figs. 7 through 10(a-d), it can be concluded that visual

perception and contrast for all BFA are approximately the same. But a few vessels are more evident in the AV fusion

method in all views.

In the following, we compare our proposed scheme (SC&SEOG&LE) and BFA for each view. Based on the CC

values from Tables 3 through 6, we conclude that the best fusion method based on CC measure for each view is

different. For exam in Table 3 and 4, SC&SEOG&LE and SML fusion method has highest value respectively. It is

necessary to consider that in each view, the difference of CC values is not prominent between the fusion algorithms.

According to the values of SF and SP measures in Tables 3 through 6, for each view SC&SEOG&LE, the fusion

results are better than in the image detail and sharpness.

To evaluate the noise suppression performance using SNR, PSNR, RMSE measures presented in Tables 3 to 6. We

can conclude that SC&SEOG&LE fusion scheme obtains the greatest improvement in performance values. The

proposed fusion scheme (SC&SEOG&LE) shows more effective noise suppression performance in the fusion results

in all views.

Since, the brain blood vessel map is produced based on physician request, it is necessary to compare the fusion results

visually. From Figs. 7 through 10(a-e), considerable noise suppression and artifact (bone shadows) reduction in

homogenous regions from SC&SEOG&LE fusion results (Figs. 7-10(e)) is observed. It is produced an informative

vessel map for clinical application. Consequently, we can conclude that SC&SEOG&LE fusion method which

provides the effective noise suppression and high visual perception for tiny vessel structures is more efficient among

BFA.

25

As mentioned previously, both SEOG and SML are prominent activity criteria for edge and detail extraction and

therefore comparison between them is useful. The two criteria (SEOG, SML) approximately have the same

computational complexity. Overall, in all views SC&SEOG&LE fusion method with small difference obtains the

better performance than SC&SML&MLE method (Table 3 through 6). Also from Figs. 7 through 10 (e-f), it is

observed that in each view there is no great visual perception difference between the fused images.

Finally based on the visual perception and objective evaluation measures which analyzed and discussed in above, we

claim that SC&SEOG&LE fusion scheme is superior to others methods in noise and bone shadows elimination, higher

visual perception with more detail in the vessel structures and acceptable correlation based on clinical applications.

1.8. Comparison with Other Works

In this thesis, to make fusion process automatic and produce the informative brain blood vessel map with high noise

suppression performance, at first the valuable frame numbers for fusion procedure were found and then our fusion

scheme was proposed based on the characteristics of WSGCT coefficients. For low frequency coefficients, LE

criterion was performed which causes more visual perception and contrast in the fusion result and for high frequency

coefficients; the fuzzy-based fusion scheme using two activity criteria were suggested. In our proposed fuzzy-based

fusion scheme, the fusion scheme for corresponding coefficient sets is categorized in two ways which eliminates the

noise and artifact in background of fusion results. Also, by performing fuzzy rules (introduced in Table 1), edge

information from all valuable frames are gathered to obtain informative and reliable vessel map.

The perfect comparison between our proposed algorithm and other presented algorithm is an impossible work due to

utilize different database with various view of imaging from brain. However, we compare our work with other

presented works in the literature. For example, in [17], firstly each of DSA images was decomposed by 2-D Harr

discrete wavelet transform (HDWT). Then by using a membership function based on dynamic fuzzy data model

(DFDM), the selection of wavelet coefficient was enhanced to combine all series of DSA images in different levels. In

[18], the DSA images were decomposed by FGCT to obtain information of different levels. Then, by using entropy of

different levels of DSA images and a membership function based on dynamic fuzzy logic, a set of weights for image

sub-band coefficients was assigned. At last, the fusion result was obtained by reconstruction of the fused coefficients.

In comparison with our proposed fusion algorithm, the introduced fusion procedures in [17, 18] are not automatically

while in our algorithm with specifying the number of valuable frame, we save time in the fusion process. In [17],

HDWT is used to decompose the DSA images but due to lack of shift invariance and inability to represent multi-scale

26

structures, this transform is not appropriate. The authors in [17] tried to compensate 2-D HDWT defections by using

DFDM. But due to low SNR and high RMSE, this algorithm does not have appropriate results. In [18], the authors

used FGCT to represent the image details. But, it suffers from some drawbacks such as high redundancy and

computational cost. In contrast, WSGCT which is used in our algorithm has lower redundancy and computational cost.

Due to feature differences between low and high frequency coefficients, it is deserved to have individual rules for each

domain. This theorem is applied in our algorithm but in [17, 18], the fusion rules for two categories are the same. In

[17, 18] and our proposed fusion algorithm, dynamic fuzzy logic and fuzzy logic rules are used which obtains more

informative and reliable fusion results. In [17, 18], the authors did not define condition of dataset which was used and

they presented fusion results for one undefined angiography view. They compared their presented algorithms with

Laplacian pyramid, weighted average and traditional DWT methods [35, 36]. Therefore, Table 7 and 8 present a

comparison between our proposed algorithm and other presented works [17,18], for similar view based on SNR and

RMSE evaluation measures, individually. This comparison implies that our proposed fusion scheme

(SC&SEOG&LE) results more informative blood vessel map.

Table 7: Comparison our proposed fusion algorithm with presented work in [17].

Algorithms RMSE SNR

Laplacian Pyramid 4.306 35.623

Weighted Average 4.446 35.450

Traditional DWT 4.055 35.970

Wavelet &Dynamic fuzzy data model[17] 3.818 36.493

Proposed algorithm (SC&SEOG&LE) .0009 60.5280

Table 8: Comparison our proposed fusion algorithm with presented work in [18]. Algorithms RMSE SNR

Laplacian Pyramid 4.403 35.734

Weighted Average 4.857 35.336

Traditional DWT 4.107 36.086

Curvlet Entropy & Dynamic fuzzy logic [18] 3.925 37.528

Proposed algorithm (SC&SEOG&LE) 0.0012 58.7321

27

1.9. CONCLUSION

Automatic fusion process and extraction of informative blood vessel map from each angiography’s view were two

main purposes of this thesis. In order to achieve the first aim, the valuable frame numbers were found. For the second

aim, the fusion scheme based on the WSGOCT coefficients and content selection strategy was proposed. In this

scheme, for high frequency domain, we introduced a fusion map which categorized the fuzzy-based fusion scheme in

two methods of maximum intersection selection and weighted averaging based on the fuzzy logic rules and

intersection operation. In this scheme, improvement of the noise and artifact suppression in the background image was

obtained and by performing fuzzy logic rules, vessel information from all valuable frame sub-bands was gathered. In

our content selection strategy, SC and SEOG are the most effective activity criteria which we used in the high

frequency domain. For the low frequency, LE was applied as the best criterion. Finally, experimental results

confirmed that our proposed fuzzy-based algorithm is more effective in comparison with other presented fusion

methods.

28

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31

Chapter II

Aneurysm Extraction

Abstract

Brain aneurysm is one of the most life threatening event, which is associated with a high rate of

mortality and disability. There are many factors, which specify the best treatment option for each

particular patient. This chapter introduces a new brain aneurysm extraction algorithm for fused digital

subtraction angiography (DSA) images. It is noteworthy to say that, extracting aneurysm geometric features

automatically has a valuable clinical application in case of patient treatment. So, representing secular aneurysm

radius is considered as aim of this chapter.

2.1. Introduction

The word aneurysm comes from the Latin word aneurysma, which means dilatation. An aneurysm is an abnormal

bulge in the wall of an artery due to weakness or injury, whose rupture can lead to catastrophic complications such

as hemorrhagic stroke. A saccular aneurysm is the most common type of aneurysm which causes subarachnoid

hemorrhage. Computerized tomography angiogram (CTA), magnetic resonance angiogram (MRA), and X-ray

angiography are the most recently operations which can be used to visually observing aneurysm in detail.

Nowadays, automatic computational geometrics features for evaluating risk of rupture and treatment planning is

essential. Especially, when large number of data sets are used and manual process of these data are very time

consuming. To address this issue, based on aneurysm characteristics such as shape, gradient, size, and energy

medical image processing can proposes applicable algorithms which represent geometric feature of aneurysm.

One of the main problem of these algorithms is aneurysm isolation or extraction from parent vessels. Due to

different types of medical images, there are various methods and challenges for aneurysm extraction procedure.

Removing vessel structure can be a fundamental preprocessing which its accuracy has great effect on result of

32

aneurysm extraction algorithm. Especially, when shape similarity between aneurysm and vessel overlap or vessel

cross section is seen. However, removing vessel structures is always accompanied with removing non-vessel

structures, some of which can be aneurysm. Thus, there is a tradeoff between accuracy of vessel structure

removing and aneurysm extraction algorithms. In this thesis, introducing automatic aneurysm extraction algorithm

from different views of 2-D DSA fused images is the main purpose. In this algorithm, morphological characterize

and size of aneurysm are considered. In addition, to tackle with poor gradient edge, a new image is introduced

which extraction procedure will be done based on new pixel values. It is necessary to know that in each view

shape, size, location, and some image properties such as contrast and measures of edge gradient for each aneurysm

is different from another one. Hence, these differences faced our algorithm with various challenges.

Consequently, to overcome all problems, our new algorithm is presented in three steps. Step one is the most

essential one, which removes vessel structure based on multi structural morphological operators and nonlinear

filtering. In step two, Hough transform and region growing algorithm are used for extraction procedure. In last

step, morphological operator is used as a post processing to improve accuracy result. Finally, radius of each

aneurysm is represented which help doctors to choose the best treatment option. In the following sections, we

introduce our new algorithm in more details. Next, experimental results and compare with other works will be

represented, and final section, discusses the importance of new algorithm.

2.2. Proposed Automatic Aneurysm Extraction Algorithm

The fact of the matter is that there are some issues to overcome. In Fig. 1 four different fused DSA images from

four various views are presented. Aneurysm is distinguished with blue circle, and red circles show some wrong

candidates. In general, our challenges are divided into general view and angle view. In general view, due to

intensity similarity, the edge which surrounded aneurysm is characterized by poor gradient. In other words, there

is no sharp edge to separate aneurysm. Therefore, gradient-based methods failed to show acceptable result.

Another main issue is shape similarity between aneurysm and vessels overlap or vessels cross section, which is

why our accuracy can be decreased. In addition, it is good to know that because of near range of gray level

between aneurysm and other candidates energy can not be a suitable criterion for our method. In angle view, there

are three main challenges. Firstly, size of aneurysms is different. Next, aneurysms are located in different situation

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for example in Fig. 1(c) it placed among some branches and artery, but in Fig. 1(a), (b), and (d), it presents more

individual. The last problem is histogram differences, which means each aneurysm has different rang of gray

scales from other one. Consequently, due to cope with existence challenges, our new algorithms are divided into

three steps which will be explained in the following.

(a) (b) (c) (d)

Fig.1 Fused DSA images for four different views. Blue circle shows aneurysm and red circles show vessels overlap and cross

section vessels.

2.2.1. Preprocessing

Since shape similarity between aneurysm and vessel cross section or vessel overlap is existed, vessel structure

removing is known as the essential and basic part of the extraction scheme. This step is divided into two steps based

on morphological operators and nonlinear filtering.

2.2.1.1. Morphological processing

Since brain blood vessel structure is complex and it is presented in different directions, multi directional morphology

operators [1] are used to remove vessels as follow:

(( ) )i i i

I F S S (1)

Where F is fused image, i

S is morphological structure for i and i

I is image result. Moreover, and

denotes erosion and dilation morphological operator respectively. In the following, for all of the directions, for each

pixel in the resulted images, minimum value will be accounted.

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2.2.1.2. Nonlinear Diffusion filtering

In this step, nonlinear diffusion filtering [2,3] is used to remove vessels structure and make aneurysm more prominent

and individual. In the other words, this step completes result of last step to remove vessel structure more completely.

2.3. Extraction Procedure

Due to circularity of aneurysm, circular Houph transform [4] is applied to result of nonlinear diffusion filtering which

offers aneurysm candidates. Then, aneurysm extraction procedure will be completed with proposed region growing

algorithm [5]. It is necessary to mention that in all of cases aneurysm has the biggest radius between other candidates.

Our algorithm is divided into four steps. Firstly, center of the biggest circle with 5 neighboring pixels is considered as

an initial region. In second step, histogram differences and existence of poor gradient edge are challenging which put

serious limitation on region growing process for each optional view. In order to overcome these problems, a new

image is proposed based on nonlinear diffusion filtering result and range of considered numbers as follow:

( , ) ( , ) ( ).

( , ) 0

diff diff

i

new

I x y if I x y q i m

I x y others

(2)

Where i

newI is the new image, diffI is result of nonlinear diffusion filtering, q is set of numbers and m is average

value of diffI . In third step, region growing algorithm stars to grow based on pixel values of new image and circularity

criterion [6]. In last step, for each numbers in set q , which presents one new image, one extracted aneurysm image is

obtained from region growing procedure. For all of obtained results circularity criterion will be accounted based on

Eq.3. Then the candidate with higher circularity measure is selected as the main aneurysm.

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perimeter

areacircle (3)

Where perimeter is the number of pixels along the margin of the extracted aneurysm and area is the number of

pixels within the contour of the island that represents the candidate.

35

2.4. Postproccessing

In each view, due to aneurysm is not located in the same situation, and in some cases it is surrounded with thick

branches and artery, postproccessing is necessary. In this step, Morphological opening operator [1] is used to improve

accuracy of our new algorithm as follow:

finalI F S (3)

Where F is image which has the most circularity measure, S is ball structure and finalI is final result.

2.5. Experimental results

2.5.1. Data set

To test our algorithm, we gathered thirty 2-D fused DSA images from different views of angiography operation [7].

Moreover, based on the doctor knowledge in each fused image aneurysm problem is seen, and doctor needs to know

measure of radius for each aneurysm. Images are displayed on 960*960 matrix.

2.5.2. Preprocessing

2.5.2.1. Morphological operation

Firstly, in order to remove vessels structure, multi directional morphological operation [1] is used. In this thesis 12

structure elements for 12 different angles {0 ,15 ,30 ,45 ,60 ,75 ,90 ,105 ,120 ,135 ,150 ,165 )i with

window size of 7 7 and angle accuracy of 15 are considered. Figure.2 shows the result of first preprocessing step.

36

(a) (b) (c) (d)

Fig. (2): Removing vessel structure with multi directional morphological operation for four sample fused DSA images.

As it is obvious, in each view, based on the vessel structure results are different. For exam in Fig. 2 (a), (b), (d) thin

branches are eliminated approximately, but in Fig. 2(c) they are presented strongly. However, in all views, some

points are seen as wrong candidates, and aneurysm is not presented individual yet. In Fig. 3 some wrong points are

illustrated with red circles.

(a) (b) (c) (d)

Fig. 3: Red circles are wrong candidates and blue one is aneurysm

2.5.2.2. Nonliner Diffusion Filtering

Du to remove vessel branches and make aneurysm more prominent, nonlinear diffusion filtering [2,3] operator is used

as second step of preprocessing. Diffusion function is defined as:

37

1( )

1 (( ) )alfa

D IJ

absK

(4)

Where 2alfa and 0.02k . Figure .4 shows the results which are derived from this step.

(a) (b) (c) (d)

Fig.4 removing vessel structure with nonlinear filtering operation

From image results which are presented we can concluded that in Fig. 4 (a), (b), (d) all thin branches are removed and

background is shown clear, so many wrong candidates are not presented any more. However, in Fig. 4 (c), because of

thick vessels existence, removing branches are not as same as other views. Totally, we can conclude that some wrong

candidates such as vessel overlap or vessel cross section are removed and aneurysm presented more individual.

2.5.3. Extraction Procedure

2.5.3.1. Houph Transform

In order to aneurysm extraction, since aneurysm’s shape is supposed circular, circular Hough transform [4] from

Matlab toolbox is considered where edge gradient threshold and sensitivity factor to detect circles is .1 and .89

respectively. In addition, range of candidate radius is defined from 10 to 30 pixels. In Fig.5 aneurysm candidates are

presented with green circles.

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(a) (b) (c) (d)

Fig. 5: Aneurysm candidates from Houph transform.

As it is obvious, because of limited range of radius which is considered, some false candidates such as small vessel

cross sections or small vessel over laps, especially for thin branches are eliminated. Moreover, in comparison with

original images, it can be concluded that removing vessels structure as a basic step, has a great effect to represent

aneurysm candidates, which causes less false candidates.

2.5.3.2. Region growing Algorithm

As mentioned in section (2.2.2), experimentally, a set of numbers ( q ) is considered to make a new image. In this

thesis, q is set to {0.95,0.98,1.01,1.04,1.07,1.11,1.13} . In addition, minimum circularity criterion for growing

initial candidate region is set to .3, which means aneurysm with various shape can be extracted and in general,

proposed algorithm is independent on how aneurysm shape is far from circularity.

Result of using proposed region growing algorithm is shown in Fig. 6.

(a) (b) (c) (d)

Fig. 6: Region growing procedure result.

39

As it is illustrated, in Fig.6 (a) and (b), aneurysm is extracted completely with acceptable accuracy, but in Fig.6 (c), (d)

aneurysm extraction is not completely successful, which means artery and surrounding branches are seen.

2.5.4. Postproccessing

In order to improve accuracy for each optional view, morphological opening operator [1] based on ball structure is

used, which remove all reminder vessel branches with high performance. In Fig.7. results are shown.

(a) (b) (c) (d)

Fig. 7: Final results.

As a clinical application, measure of radius for each aneurysm is represented as follow. At first, with canny operator

[8] aneurysm’s edge is detected. Then, distance of centered pixel from all of the edge pixels is calculated, and average

value of all distances is considered as radius measure. Table.1 represents radius measurement results.

Table.1 Radius measurement

Radius measure Image number

9 mm Fig.7 (a)

3 mm Fig.7 (b)

7 mm Fig.7 (c)

8 mm Fig.7 (d)

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2.6. Evaluation of proposed algorithm

To evaluate our algorithm, pixels around aneurysm, which are labeled manually based on doctor guidance, are

compare with pixels around aneurysm which are extracted from proposed algorithm. The algorithm performance is

evaluated by the validity rate of the overlap between these two sets. An overlapping criterion is defined to measure the

common area between true region T and extracted region D as [9]:

( )

( )

Area T DAccuracy

Area T D

(5)

In Table.2 accuracy rate of our proposed algorithm for each aneurysm based on Eq.(5) is presented.

Table.2 Accuracy measurement

Accuracy measure Image number

80.50 Fig.7 (a)

80.04 Fig.7 (b)

80.11 Fig. (c)

80.23 Fig. (d)

2.7. Comparison with other works

To compare our proposed algorithm, there is not any similar aneurysm extraction algorithm which works on 2-D fused

brain DSA images, but in [10] a method for 2-D fused DSA images which detect aneurysm based on human eyes’s

ability to recognize wide range of color was proposed. Aim of this thesis was to distinguish veins, arteries and

aneurismal vessel based on HSV color scheme. At first, they fused all DSA frames by considering minimum intensity

of each pixel in the 2-D digital video. Next , by introducing time to peak and time duration criterion, fused map was

visualized in color image where Hue set to TTP or TD, Saturation set to 1 and Value set to pixel intensity value. At

last , multiscale vessel enhancement filtering was applied to improve vessel structure. In [10], not only aneurysm was

not extracted from fused DSA images but also there is no clear color image from aneurysm, which means some

vessels structure are seen in background around aneurysm tissue. Moreover, in this essay any geometrical aneurysm

feature is not obtained for clinical usage.

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2.8. Discussion

In this thesis, automatic brain aneurysm extraction algorithm was proposed for 2-D fused DSA images. Firstly, Multi

directional morphological operators and nonlinear diffusion filtering were used for vessel structure removing as an

fundamental step. Then, Houph transform applied for aneurysm candidates representation, and then our new region

growing algorithm was proposed to extract aneurysm completely. Since aneurysm was not isolated accurately,

postproccessing step was done based on morphological operator which results accuracy rate of 80% approximately. At

last, based on doctor’s demand for each aneurysm measure of radius is calculated, which shows risk of aneurysm

rupture or surgical treatment.

42

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Chapter III

Discussion

In this thesis 2-D internal carotid rotational angiography videos are applied from different views. Moreover, two main

aims are pursued. Firstly, an automatic algorithm for representation of brain blood vessel map is proposed for each

optional views based on contrast material movement. Then, extracting aneurysm from 2-D angiography videos from

different views with various features is targeted, which shows risk of aneurysm rupture or surgical treatment.

In this thesis, for the first aim, an automatic multi-temporal fusion method is proposed for the first time. Generally

speaking, our fusion strategy is organized in preprocessing and processing steps. In preprocessing, registration,

background estimation, elimination, and smoothing are done. In the following step, to overcome different challenges,

a fuzzy-based fusion algorithm for high frequency Curvelet coefficients, and maximum local energy method for low

frequency Curvelet coefficients are proposed. There are some remarkable points behind this algorithm such as its

generalization for all of the angiography views, noise improvement in background and vessel structures, high visual

perception from thin vessels, and reducing redundant frames to present a high informative map from blood vessels. In

comparison with other works, in this scheme, improvement of the noise and artifact suppression in the background is

obtained and by performing fuzzy logic rules, vessel information from all valuable frame sub-bands is gathered. In our

content selection strategy, the sample correlation and sum energy of gradient are the most effective activity criteria

which we used in the high frequency content. For the low frequency, local energy is applied as the best criterion.

Finally, experimental results confirmed that our proposed fuzzy-based algorithm is more effective and informative.

In the second part of this thesis, an automatic aneurysm extraction algorithm is proposed for fused images resulted

from the previous algorithm. Generally, our method is divided into three main steps. In preprocessing, vessel

structures are eliminated and background smoothing is done with multi directional morphological operators and

nonlinear diffusion filtering. Then, aneurysm candidates are represented by applying Hough transform. In the next

step, a new region growing algorithm is proposed to extract main aneurysm from previous resulted image. At last for

promoting accuracy and our performance, morphological-based operation is done as a postprocessing step.

Additionally, in terms of clinical application, radius measure for each extracted aneurysm is calculated. In comparison

with other works, there is not any similar aneurysm extraction algorithm which works on 2-D fused brain DSA

images. In the case of performance, based on thirty aneurysm cases, we obtain accuracy rate of 80% approximately.