enhanced gabor wavelet correlogram feature for image...

THEORETICAL ADVANCES

Enhanced Gabor wavelet correlogram feature for image indexingand retrieval

H. Abrishami Moghaddam • M. Nikzad Dehaji

Received: 8 July 2010 / Accepted: 15 June 2011 / Published online: 14 July 2011

� Springer-Verlag London Limited 2011

Abstract In this paper, a new feature scheme called

enhanced Gabor wavelet correlogram (EGWC) is proposed

for image indexing and retrieval. EGWC uses Gabor

wavelets to decompose the image into different scales and

orientations. The Gabor wavelet coefficients are then

quantized using optimized quantization thresholds. In the

next step, the autocorrelogram of the quantized wavelet

coefficients is computed in each wavelet scale and orien-

tation. Finally, the EGWC index vector simply consists of

the autocorrelogram coefficients. Due to non-orthogonality

of Gabor decomposition, the resulting wavelet coefficients

suffer from redundancy, which increases the computational

cost and reduces the effectiveness of EGWC. Here, we

present a solution to handle the redundancy problem using

non-maximum suppression and adjustment of autocorre-

logram distance parameters as a function of the wavelet

scale. The retrieval results obtained by applying EGWC to

index two image databases with 5,000 natural images and

1,792 texture images demonstrated its better performance

in terms of retrieval rates with respect to the state-of-the-art

content-based and multidirectional texture indexing

algorithms.

Keywords Content-based image indexing and retrieval �Wavelet correlogram � Enhanced Gabor wavelet

correlogram

1 Introduction

Digital image libraries and other multimedia databases

have been dramatically expanded in recent years. Storage

and retrieval of images in such libraries become a real

demand in industrial, medical and other applications [1, 2].

Content-based image indexing and retrieval (CBIR) is

considered as a solution. In such systems, in the indexing

algorithm, some features are extracted from every picture

and stored as an index vector [3]. Then, in the retrieval

algorithm, the index vector corresponding to the query

image is compared (using a similarity or dissimilarity cri-

terion) with all stored indices to find similar pictures [4].

Various indexing algorithms based on different image

features such as color [5, 6], texture [7] and shape [8] have

been developed. Color is frequently used as a signature for

indexing and retrieval of images and videos in multimedia

databases [9]. Color histogram [5] and its variations [10–

12] were the first algorithms introduced to the pixel

domain. Despite its efficiency and insensitivity to small

changes of view point, the color histogram is unable to

carry local spatial information of pixels. Therefore, in such

systems, retrieved images may have many inaccuracies,

especially in large image databases (imagebases). For these

reasons, three variations called image partitioning [13, 14]

histogram refinement [15] and color correlogram [6] were

proposed to improve the effectiveness of such systems. In

the histogram refinement approaches such as color coher-

ence vectors algorithm (CCV) introduced by Pass et al.

[15], each histogram bar is divided into two or more parts

H. Abrishami Moghaddam (&)

Biomedical Engineering Group,

Faculty of Electrical Engineering,

K.N. Toosi University of Technology,

16315-1355 Tehran, Iran

e-mail: [email protected]

M. Nikzad Dehaji

Department of Computer Engineering,

Islamic Azad University, Science and Research Branch,

1415-775 Tehran, Iran

e-mail: [email protected]

123

Pattern Anal Applic (2013) 16:163–177

DOI 10.1007/s10044-011-0230-1

according to its spatial color distributions. On the other

hand, in the color correlogram technique introduced by

Huang et al. [6], the spatial color correlation of the image

pixels are computed. Recently, Teng and Lu [16] used

vector quantization for indexing and retrieval of com-

pressed color images.

Shape description techniques are widely used in shape-

based indexing algorithms [17–24]. The visual part of the

MPEG-7 standard adopted the curvature scale-space rep-

resentation (CSS) and the angular radial transform (ART)

as the contour-based and region-based shape descriptors,

respectively [25]. Apart from CSS [18] and ART [22],

many other valuable and interesting algorithms have been

developed for shape retrieval, which can be classified as

global [17, 20, 26] and local [19, 21, 23, 24] methods

according to whether the shape is represented as a whole or

by local shape features. In Ref. [17], two sets of shape

features were used to describe the global shape informa-

tion: a 72-bin histogram of the shape edge direction and

seven invariant moments. To tackle occluded or partially

visible object retrieval, researchers tuned to local shape-

based methods. In Ref. [21], shape contexts were used for

finding correspondence between shapes. Huet and Hancock

[23] extracted line segments from an image as primitives.

An N-nearest neighbor graph was used as the shape

representation.

In the above algorithms (except Ref. [22]), the feature

vectors are constructed using spatial domain information.

Another possibility is the use of transformed domain data

to extract some higher-level features [27]. Wavelet-based

methods, which provide space–frequency decomposition of

the image, have been used [28–30]. Daubechies’ wavelets

are the most frequently used in CBIR for their fast com-

putation and regularity. In Ref. [27], Daubechies’ wavelets

in three scales have been used to obtain the transformed

data. Then, histograms of the wavelet coefficients in each

sub-band have been computed and stored to construct the

feature vector. In SIMPLIcity [28, 31], the image is first

classified into different semantic classes using a kind of

texture classification algorithm. Then, Daubechies’ wave-

lets are used to extract feature vectors. Kokare et al. [32]

proposed a texture image indexing retrieval method using

two-dimensional rotated wavelet filters, which could

improve characterization of diagonally oriented textures. In

2005, a wavelet-based CBIR system called wavelet corre-

logram was introduced by Moghaddam et al. [29]. This

system will be briefly reviewed in Sect. 2.1. In a later work

[33], the authors presented an enhanced version of the

wavelet correlogram method (EWC) using optimal quan-

tization thresholds obtained by evolutionary group algo-

rithm (EGA).

Although common wavelet-based methods like SIM-

PLIcity [28, 31] or wavelet correlogram [29] allow for a

multiresolution decomposition, they have limited direc-

tional selectivity and are not able to capture arbitrary

directional information. To overcome this shortcoming,

other multiresolution multidirectional image decomposi-

tion techniques such as 2D Gabor transform [34, 35],

discrete contourlet transform [36], steerable pyramid [37],

ridgelet transform [38], curvelet transform [39] and com-

plex directional filter bank (CDFB [40]) have been pro-

posed to be used to form a feature vector [41–44]. The use

of curvelet transform was also proposed to detect and

characterize non-Gaussian signatures in the image data

[44]. However, due to non-orthogonality of decomposition,

the multidirectional wavelet coefficients are redundant,

which degrade the indexing retrieval performance. Among

these techniques, the 2D Gabor wavelet has been shown to

provide indexing features with comparable or better aver-

age retrieval performance with respect to other multidi-

rectional wavelet decompositions including contourlet,

steerable pyramid and CDFB [41]. In Ref. [41], the features

were generated using only the mean and variance of the

wavelet coefficients and no post-processing has been made

before using them in retrieval. Furthermore, a simple dis-

tance measure was used there for feature matching. Most of

the wavelet-based CBIR methods use first, second [41, 42]

or higher order [44] statistical parameters of the wavelet

coefficients in different scales and orientations to construct

their index vector. In this paper, we propose the use of

spatial correlation of quantized Gabor wavelet coefficients

by wavelet correlogram method [29] to construct a new

effective index vector. Moreover, we introduce an efficient

method for handling redundancy problem in computing the

autocorrelogram of 2D Gabor wavelet coefficients. In

addition, current multidirectional wavelet-based indexing

methods do not present any solution for optimizing

indexing parameters. Here, we propose the use of a new

optimization method called evolutionary group algorithm

(EGA) to optimize quantization thresholds of Gabor

wavelet correlogram indexing features.

This paper is organized as follows. The wavelet corre-

logram method is briefly reviewed in Sect. 2. Section 3

presents the theoretical basis of the new image indexing

algorithm and explains some technical points including

redundancy problem handling, quantization threshold opti-

mization, feature construction and retrieval performance

improvement. Experimental results using two frequently

used texture and natural image datasets are given in Sect. 4.

Finally, Sect. 5 is devoted to the concluding remarks.

2 Wavelet correlogram

Wavelet correlogram applies the color correlogram method

[6] to the wavelet coefficients of an image. Therefore, it

164 Pattern Anal Applic (2013) 16:163–177

123

inherits the multiscale multiresolution properties from

wavelet transform and translation invariancy from color

correlogram. Color pictures in the database are first trans-

formed to a unified gray-level format. For this purpose, the

RGB values are first converted to NTSC coordinates and,

after setting the hue and saturation components to zero, the

values are converted back to RGB color space.

2.1 Wavelet correlogram indexing algorithm

Wavelet correlogram indexing algorithm consists of three

steps [29, 45]. First, the discrete wavelet transform of the

input image is computed using Daubechies’ wavelets for

their regularity, separability and compact support proper-

ties. In practice, a limited number of scales are sufficient

for wavelet decomposition. According to our experiments,

applying wavelet transform in three scales gives a good

compromise between efficiency and effectiveness of the

algorithm [29]. Then, the wavelet coefficients are quan-

tized into a small number of levels. Augmenting the

number of bins may improve the indexing effectiveness;

however, the computational cost and memory requirements

will be increased as well. Finally, horizontal and vertical

autocorrelogram of quantized coefficients are computed for

LH and HL submatrices in each scale, respectively. The

wavelet coefficients corresponding to HH filters have no

significant spatial correlation. Therefore, there will be no

need to obtain the autocorrelogram of these coefficients

[45].

Quantization thresholds corresponding to each wavelet

scale are illustrated as values under the axes in Fig. 1. As

shown, [-nm,1 nm,1] is considered as noise margin in the

mth scale, and the wavelet coefficients inside it are dis-

carded. The image noise can be originated by different

sources such as quantal or electronic noise. In general, it is

considered as zero mean Gaussian white noise. In this case,

the noise margin using each scale can be computed in

corresponding LH and HL matrices based on BayesShrink

method [46]. This method uses the noise variance in an

image, which can be estimated by Donoho’s method [47,

48]. According to [47–49], the noise standard deviation of

an image (rn) can be estimated using the median absolute

deviation (MAD) of the diagonal wavelet coefficients at the

first level of decomposition as:

rn ¼MedianðjYijjÞ

0:6745Yij 2 HH ð1Þ

This value can be also considered as the standard

deviation of noise in LH and HL matrices in the first level.

In the same way, if we consider the LL image in the mth

scale as a new image, the same method can be used to

estimate the variance of the noise in LH and HL images in

the mth scale. To take into consideration the dynamic range

of wavelet coefficients, different quantized levels in each

wavelet scale (-nm,2, nm,2) are used. These quantization

levels were obtained experimentally, by dividing the

dynamic range into a small number of bins, each bin

representing a percentage of the wavelet coefficient

population. In Fig. 1, the values above the axes show the

percentiles of wavelet coefficients’ population

corresponding to each quantized level.

Horizontal autocorrelogram of discretized LH coeffi-

cients matrix with distances k [ {1,2,3,4} is defined as

follows:

where ci-s are quantization levels and |{.}| represents the

cardinality of a set. Indeed, aH(i,k) is the probability of

finding two pixels with quantization level ci at the same

row of LH in a distance k of each other. Vertical auto-

correlogram aV(i,k) is computed in the same manner using

HL coefficients.

The wavelet correlogram index vector is simply con-

structed by using autocorrelogram coefficients computed

for LH and HL wavelet matrices in each scale. Each matrix

gives 16 coefficients resulting in a total of U = 96 words

per index [45].

2.2 Wavelet correlogram retrieval algorithm

In the retrieval phase of the wavelet correlogram, after

computing the index vector of the input image, all the

index vectors corresponding to the images in the database

are sorted according to a matching criterion. Then, N

images corresponding to the best-matched index vectors

are retrieved and shown to the user. Several matching

criteria including (a) geometric measures such as L1 or L2

distance, (b) information theoretic distances such as Kull-

back–Leibler or Jeffery divergence and (c) statistic mea-

sures such as Mahalanobis, Chi-squared or Kolmogorov–

Smirnov distance can be used [50]. A comparative study

aHði; kÞ ¼ðx; yÞ LHðx; yÞ ¼ ci; LHðx; yþ kÞ ¼ ci or LHðx; y� kÞ ¼ cijf gj j

2� jfðx; yÞjLHðx; yÞ ¼ cigji ¼ 1; . . .; 4k ¼ 1; . . .; 4

ð2Þ

Pattern Anal Applic (2013) 16:163–177 165

123

demonstrated that most of the dissimilarity measures from

the geometric category have better performance than the

other two categories [51]. Moreover, our main objective is

being focused on indexing performance evaluation; in this

paper we have used a modified version of L1 distance

measure, since it is commonly used when comparing two

index vectors [6].

3 Gabor wavelet correlogram

Wavelet correlogram was originally developed using

Daubechies wavelets for their regularity, separability and

compactness [45]. Other commonly used wavelets such as

9/7 biorthogonal could be used particularly for image

indexing in compressed domain. However, they have dem-

onstrated lower performance with respect to Haar and

Daubechies wavelet in retrieving nine classes of JPEG and

JPEG2000 compressed images [52]. In spite of their

advantages, these wavelets suffer from poor directional

selectivity; since they are computed in only horizontal,

vertical and diagonal directions. Moreover, as we explained

in the previous section, the wavelet correlogram uses only

horizontal and vertical wavelet coefficients. To alleviate this

problem, multiresolution multidirectional image decompo-

sition techniques such as steerable pyramid [37], 2D Gabor

transform [35], ridgelet [43], curvelet [39], discrete con-

tourlet transform [36] and CDFB [40] can be used. In a

recent study, Vo et al. [41] compared the texture retrieval

performance of feature vectors produced by the Gabor

wavelet, steerable pyramid, contourlet and CDFB. The

results of their study demonstrated that the Gabor wavelet

feature has a higher or comparable retrieval performance

with respect to the features obtained by other wavelets. On

the other hand, the features provided by ridgelet have shown

superior retrieval performance with respect to the features

provided by other multidirectional transforms. However, the

ridgelet features are relatively larger and proportional to the

image size. The use of curvelet transform was recently

proposed to detect and characterize non-Gaussian signatures

in the image data [44].

The use of Gabor filters in extracting textured image

features is further motivated by various factors [53]. The

Gabor representation has been shown to be optimal in the

sense of minimizing the joint two-dimensional uncertainty

in space and frequency [54]. These filters can be considered

as orientation and scale tunable edge and line (bar)

detectors, and the statistics of these micro features in a

given region are useful to characterize the underlying

texture information. Regarding the advantages of Gabor

wavelets in image representation, in this paper we propose

a new algorithm for constructing an enhanced Gabor

wavelet correlogram indexing feature. This new algorithm

handles the data redundancy caused by non-orthogonality

of the Gabor wavelet using non-maximum suppression and

an adaptive distance for computing the Gabor wavelet

correlogram.

3.1 Construction of the Gabor wavelets

A 2D Gabor function is a Gaussian modulated by a com-

plex sinusoid [35]:

wðx; yÞ ¼ 1

2prxryexp � 1

2

x2

r2x

þ y2

r2y

!þ 2pjxx

" #ð3Þ

The Gabor wavelets are obtained by dilation and

rotation of the generating function w(x,y) as follows:

wm;nðx; yÞ ¼ a�mwða�mðx cos hþ y sin hÞ;a�mð�x cos hþ y sin hÞÞ ð4Þ

Fig. 1 Wavelet correlogram

quantization. Values above and

under the axes are percentiles of

wavelet coefficient population

and quantization thresholds,

respectively


123

where h = np/K; m [ {0,…, S - 1} and n [ {0,…, K -

1} represent scale and orientation, respectively; and K and

S are the number of desired orientations and scales,

respectively. Equation 3 can be written in the frequency

domain as follows:

Wðu; vÞ ¼ 1

2prurvexp � 1

2

ðu� xÞ2

r2u

þ v2

r2v

!" #ð5Þ

where ru = 1/2prx and rv = 1/2pry. Gabor functions do

not result in an orthogonal decomposition, which means

that a wavelet transform based upon the Gabor wavelet is

redundant [35]. Manjunath and Ma [54] proposed a design

strategy to project the filters so as to ensure that the half-

peak magnitude supports of the filter responses in the

frequency spectrum touch one another. By doing this, it can

be ensured that the filters will capture the maximum

information with minimum redundancy. Hence, the

parameters a, ru and rv are computed by (6–8),

respectively:

a ¼ ðUh=UlÞð1=S�1Þ ð6Þ

ru ¼ða� 1ÞUh

ðaþ 1Þffiffiffiffiffiffiffiffiffi2ln2p ð7Þ

rv ¼ tanp

2K

� �Uh �

r2u

Uh

� �2 ln 2

� �, ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2 ln 2� ð2ln2Þ2r2

u

U2h

s

ð8Þ

where Ul and Uh are the upper and lower bound of the

designing frequency band, respectively. The resultant real-

valued even symmetric Gabor filters, which are oriented

over a range of 180�, are more appropriate for image

indexing purposes [54]. Examples of such Gabor filters in

the frequency domain are shown in Fig. 2.

3.2 Proposed indexing algorithm

The block diagram of GWC is shown in Fig. 3. According

to this figure, GWC computes first the wavelet coefficients

using Gabor wavelets in three different scales. In each

scale, the non-maximum suppression block is aimed to

reduce the data redundancy as will be explained in the

following subsection. Then, the coefficients are discretized

using three sets of quantization thresholds as indicated in

Fig. 4. In Ref. [34], these coefficients were selected

experimentally for achieving good retrieval performance.

However, as will be explained in Sect. 3.6, we propose the

use of recently introduced EGA [33] to optimize the

quantization thresholds. The final stage in the block dia-

gram of Fig. 3 is the computation of wavelet autocorrelo-

gram in each scale.

As illustrated in Fig. 4, small coefficients are considered

as noise and discarded. The distribution of noise in Gabor

wavelet coefficients depends on its distribution in the ori-

ginal image. If we consider that the noise distribution in the

Input Image

ψ0,0

ψ0,1

ψ0,2

ψ0,3

ψ1,0

ψ1,1

ψ1,2

ψ1,3

ψ2,0

ψ2,1

ψ2,2

ψ2,3

Non-M

aximum

Suppression

Non-M

aximum

Suppression

Non-M

aximum

Suppression

Quantization of 1

st Wavelet

Scale

Quantization of 2

nd Wavelet

Scale

Quantization of 3

rd Wavelet

Scale

Auto-

correlogram

(Distance Set 1)

Auto-

correlogram

(Distance Set 2)

Auto-

correlogram

(Distance Set 3)

EG

WC

Feature Vector

Fig. 3 Block diagram of GWC

Fig. 2 Examples of Gabor filter

in the frequency domain. Each

ellipse represents the range of

the corresponding filter

response from 0.5 to 1.0 in

squared magnitude. The plots

(a) and (b) illustrate two

different ways for sampling the

frequency spectrum by

changing the Ul, Uh, S and

K parameters of the Gabor

presentation. a Ul = 0.03,

Uh = 0.4, S = 3, K = 2,

b Ul = 0.05, Uh = 0.4, S = 3

and K = 4


123

original image is Gaussian, then its distribution in Gabor

wavelet coefficients will be also Gaussian with different

parameters due to linearity of the transform. It is worth-

while to note that in most of denoising algorithms for

image databases including objects, (natural or man-made)

scenes or objects in scenes, the noise distribution has been

considered as normal [46, 47, 55–57]. Therefore, the var-

iance of noise in an image can be estimated by Donoho’s

algorithm [47] and the noise margin can be estimated using

soft thresholding [47] or BayesShrink method [46].

The negative coefficients are truncated since they have

significant correlation with the positive coefficients. These

negative coefficients are mainly produced by undesirable

oscillations resulted from the Gabor wavelets especially in

higher scales, since for small m, Gabor wavelets are not well

localized in the spatial domain and do not die out quickly

away from their central point (Fig. 7). Finally, the auto-

correlogram of the quantized coefficients is computed along

the direction normal to the Gabor wavelet orientation:

am;nði; kÞ ¼ðx; yÞ

Wm;nðx; yÞ ¼ ci;

Wm;nðxkm; ykmÞ ¼ ci or Wm;nðx�km

; y�kmÞ ¼ ci

�

2� jfðx; yÞjWm;nðx; yÞ ¼ cigj

i ¼ 1; . . .Kq

k ¼ 1; . . .Kd

ð9Þ

where Kq is the number of quantization levels in each

wavelet scale, Kd is the number of distances, Wm,n is the

matrix of the quantized wavelet coefficients computed by

wm,n, km indicates the distance parameter of

autocorrelogram, and xkmand ykm

are given by:

xkm

ykm

� �¼ x

y

� �þ km sin h

km cos h

� �� ð10Þ

where the function bae rounds a 2 R to the nearest integer.

3.3 Handling the redundancy problem

Gabor wavelet coefficients are redundant because of non-

orthogonal decomposition. From wavelet correlogram

point of view, there are two types of redundancy in Gabor

wavelet coefficients, (a) the redundancy in the direction of

high-pass filtering and (b) the redundancy in the direction

of low-pass filtering. These redundancies may abnormally

increase the value of the correlogram coefficients and the

computational cost.

Gabor wavelet coefficients along the radial direction

are not expected to be correlated; because the Gabor

radial direction represents the direction of high-pass fil-

tering. However, due to the redundancy of transform,

Fig. 5 Suppressing non-maximum Gabor wavelet coefficients along the direction of high-pass filtering: a The query image, b Gabor wavelet

coefficients with m = 2 and n = 2 and c non-maximum suppressed Gabor wavelet coefficients along the vertical direction

Fig. 4 GWC quantization

thresholds. Values under the

axes are quantization thresholds


123

particularly in large scales, Gabor wavelet coefficients

along the radial direction show some correlation. This

phenomenon is clearly visible in Fig. 5b. In this figure,

Gabor wavelets have been computed in the third scale

(m = 2) and vertical direction (n = 2 or h = p/2). As can

be observed, Gabor wavelet coefficients are correlated in

the vertical direction, while this direction corresponds to

the direction of high-pass filtering. It is worthwhile to

note that correlation of wavelet coefficients in the direc-

tion of high-pass filtering is not informative. This is the

reason why Gabor wavelet correlogram is computed only

in the direction of low-pass filtering. Let us explain this

observation differently. As illustrated in Fig. 5b, the

Gabor wavelet coefficients represent horizontal edges in

the image, and Gabor wavelet correlogram looks for

correlation only along the edges. Therefore, it is reason-

able to suppress non-maximum coefficients along the

radial direction to reduce the redundancy of wave-

let coefficients and improve the efficiency of the

algorithm.

Furthermore, the redundancy in the direction of low-

pass filtering is avoided by adapting the distance parameter

km in (9) according to the wavelet scale as follows:

km 2 fsm � a a ¼ 1; . . .;Kdj g ð11Þ

where s indicates the scaling coefficient of the filter bank,

which is set to 2 for the Gabor wavelet filters used in this

article. In more details, let us consider that the original

image is low-pass filtered in the y direction using a

Gaussian kernel with standard deviation of ry. If the pixels

in the original image are supposed to be uncorrelated, it can

be easily shown that the autocorrelation function of the

filtered image in the y direction in the mth scale will be a

Gaussian function with the standard deviation equal toffiffiffi2p

rysm [58]:

RðkmÞ ¼1

2ffiffiffipp

rysme�1

2kmffiffi

2p

rysm

� �2

ð12Þ

where km is the distance between coefficients as a function

of scaling coefficient s and wavelet scale m. Therefore,

each sm adjacent wavelet coefficients is significantly

dependent in the mth wavelet scale due to the redundancy.

However, we should distinguish between inherent corre-

lation of pixels in the original image and the correlation

due to low-pass filtering by a Gaussian kernel. Obviously,

Gabor wavelet correlogram should not take into account

the correlations caused by low-pass filtering and it should

reflect only the inherent correlation of coefficients. This is

the reason why we propose the use of a scale-dependent

distance for the computation of autocorrelogram in the

direction of low-pass filtering.

3.4 GWC index vector

The index vector of GWC simply consists of the autocor-

relogram coefficients computed for all Gabor wavelets:

F ¼ ½am;0ði; kmÞ; am;1ði; kmÞ; . . .; am;K�1ði; kmÞ�;m ¼ 0; 1; . . .; S� 1; i ¼ 1; 2. . .;Kq ð13Þ

Therefore, GWC index vector includes U = S 9

K 9 Kq 9 Kd words. In this paper, we selected S = 3,

K = 4, Kq = 4 (Fig. 4), and Kd = 4 (Eq. 9) and hence,

U = 192. It should be noted here that the proposed feature

vector contains no color and macro-structure shape

information. As will be seen in Sect. 4 (Experimental

Results), this feature vector gives an effective and efficient

representation of the image for CBIR.

3.5 Retrieval algorithm

Different types of distances to compare color and texture

have been proposed and discussed in literature. SIMPLIcity

[28] uses a complex image similarity measure called

integrated region matching (IRM), which measures the

overall similarity between images by integrating the

properties of all the segmented region. Vo et al. [41] and

Manjunath et al. [42] used a special normalized L1

distance.

In this paper, for the feature vectors F and F0 (obtained

from the images I and I0, respectively), the distance mea-

sure d1 is defined as follows:

d1ðF;F0Þ ¼XCj¼1

Fj � F0j1þ Fj þ F0j

ð14Þ

where Fj indicates the jth component of the feature vector

F (the 1 in the denominator prevents division by zero [59]).

It can be easily shown that the use of d1 provides better

performance with respect to L1 [6].

3.6 Optimizing quantization thresholds

The quantization thresholds illustrated in Fig. 4 should be

optimally determined to achieve a good retrieval perfor-

mance of the resulted Gabor wavelet features. Optimization

of CBIR algorithms is a complicated and time-consuming

task since, each time a parameter of the indexing algorithm

is changed, all images in the database should be indexed

again. Therefore, classical optimization methods like

genetic algorithms (GA) cannot be used for this purpose,

since in each generation they need to index all the images

in the database using all chromosomes in the population

and compute the retrieval performance of each chromo-

some as fitness value. In this paper, we use EGA [33] that

has been shown to be particularly efficient for optimizing


123

the parameters of CBIR methods. In EGA, the evolution

process is made faster compared to GA by partitioning the

reference imagebase into several smaller subsets and the

whole database is used only once. Each subset is used by an

updating process as training patterns for each chromosome

during evolution. Therefore, in EGA, the evolution pro-

ceeds during indexing the image subsets of the reference

imagebase. This will reduce significantly the computational

cost of EGA compared to GA. Here, each chromosome

includes (a) an age gene that implies the progress of the

updating process, (b) some evolutionary genes that par-

ticipate in evolution, (c) a number of history genes for

saving the previous chromosome updating process states

and (d) finally some evaluation genes that indicate the

evaluation function value. Furthermore, a new fitness

function is defined, which evaluates the fitness of the

chromosomes of the current population with different ages

in each generation. This fitness value will be valid if the

chromosome’s age is larger than a threshold (mature

chromosome); otherwise, it will be set to zero for immature

chromosomes.

The EGA flowchart is shown in Fig. 6. This evolutionary

algorithm initially generates a random population. The

chromosomes of the current population are then updated by

a chromosome updating process (CUP) and the process is

repeated until there are at least two mature chromosomes. In

the next stage, based on the fitness of chromosomes, two

mature individuals are selected from the current population

as parents by a selection operator. Two offspring are then

generated by the parents using the crossover and mutation

operators. Finally, the new population is generated by

replacing two chromosomes that have the smallest fitness by

the new offspring. The above procedure is repeated until a

stop criterion is satisfied. Since in each generation, the elite

chromosomes are kept in the population, according to the

Rudolph theory [60], the proposed evolutionary group

converges eventually to the global optimum after a sufficient

number of generations. In EGA, the selection, crossover, and

mutation operators, stop criterion and other parameters can

be determined according to the application requirements.

In [33], six quantization thresholds were optimized

using a population size of M = 150 chromosomes. In this

application of EGA, the number of evolutionary genes

(quantization thresholds) is 12. Therefore, as a compromise

between population diversity and computational cost, the

population size was set to M = 200. In both applications,

the number of mature chromosomes in CUP was set to

SCUP = 0.2 9 M. Moreover, we used the tournament

selection operator [61] in which the tournament size was

set to M/7, one-point mathematical crossover operator [62]

and typical mutation operator in which the mutation

probability was set to Pm = 0.01 [63]. For EGA evolution,

we used the databases C5000 and Brodatz texture sepa-

rately (see Sect. 4.1). Table 1 indicates the resultant

quantization thresholds (illustrated in Fig. 4) for enhanced

GWC (EGWC), which correspond to the evolutionary

genes of the best chromosome in the final population after

800 generations for each dataset.

3.7 Computational complexity

Taking into account all Gabor wavelet scales (S), directions

(K), distances (Kd), and quantization levels (Kq), the

computational complexity of GWC and EGWC is

Fig. 6 EGA flowchart


123

OðSKM2KdKqÞ for an M 9 M image (see Eq. 9). In prac-

tice, S and K are fairly small (B4). Our experiments using

small values for S and K demonstrated a good overall

performance of the indexing retrieval algorithm. Because

of multiscale property of GWC and also adjusting distances

as a function of the wavelet scale, Kd is generally smaller

than the maximum number of distances used by the color

correlogram indexing algorithm [6]. The number of quan-

tization levels (Kq) is, in general, considerably less than the

number of image gray levels (L). Obviously, augmenting

L will require increasing Kq. However, the ratio

(Kq/L) remains considerably small, which justifies the

reasonable computational cost of GWC. Our algorithm has

been implemented in MATLAB on a PC with an Intel Core

2 Duo 2.67 GHz CPU and 3.24 GB of RAM. The com-

putation of the index vector for each image takes less than

2 s.

On the other hand, optimization of quantization thresh-

olds by EGA requires indexing and retrieval of the images

in the local database of each chromosome. Since, the

computational cost of indexing and retrieval of the images

in a database changes linearly with the number of quanti-

zation levels (Kq), it seems that EGA computational cost is

a linear function of Kq. However, it is worthwhile to note

that increasing the number of quantization levels increases

the complexity of the search space for EGA. In other

words, if the number of quantization levels increases, the

number of chromosomes in the initial population (or the

number of generations) will be increased.

4 Experimental results

A number of criteria influence the choice of K and

S. Bianconi and Fernandez [64] conducted an extensive

experimental campaign to investigate the effects of Gabor

filter parameters on texture classification. The outcomes of

the experimental activity demonstrate a poor correlation

between the number of frequencies and orientations used to

define a filter bank and the percentage of correct classifi-

cation. Greenspan and Perona [65] showed numerically

that taking complex filters in four directions is enough to

represent most (97%) of the image energy. Still, six

directions are usually used [42]. Using a larger number of

directions (K [ 4) may improve the feature effectiveness;

however, it increases the index size (memory requirement)

and computational cost. The number of scales (number of

considered filter frequency bands) is usually three or four

[41–43]. A larger number of scales have been used by some

authors [44]; however, a post-processing of the resulted

features has been performed to select the most important

components. In this paper, in order to obtain a feature

vector with reasonable dimensionality (without any post-

processing of the resulted features), we used Gabor

wavelets in four directions (K = 4) and three scales

(S = 3) as illustrated in Fig. 7.

The parameters Ul and Uh are chosen according to the

lowest and highest frequencies of interest in the image

[66]. Uh is usually chosen to maintain the filter response

inside the region delimited by the Nyquist frequency (0.5).

Bianconi and Fernandez [64] tested different values of

smoothing parameters rx and ry and showed that the per-

centage of correct classification decreases as the level of

the two parameters increases. They computed indirectly Uh

given the value of rx using:

Uh ¼rx

2 rx þffiffiffiffiffiffiffiffiffilog2p

=pð Þ ð15Þ

and showed that increasing Uh from 0.35 ðffiffiffi2p

=4Þ to 0.45

results in decreasing classification accuracy. For the natural

texture images, it can be seen that the directional structures

appear at finer scales, which are governed by higher fre-

quencies. Therefore, the lowest center frequency can be

placed at a fairly high value, Ul = 0.10 [66]. Manjunath

et al. [54] used a wide range of the frequency spectrum for

texture images (Ul = 0.05 and Uh = 0.40). In this work,

the parameters Ul and Uh are chosen experimentally as 0.05

and 0.49, respectively. A similar statistical strategy as in

[64] may be adopted to evaluate the effect of Ul and Uh and

other Gabor filter parameters on images retrieval accuracy.

However, this requires the design of experiments and

analysis of the results by applying different Gabor filter

bank over different groups of images and is subject to

ongoing work.

Table 1 Optimal values obtained for the quantization thresholds illustrated in Fig. 5 for C5000 and texture Brodatz datasets

Quantization thresholds in scale i

ni;1 ni;2 ni;3 ni;4

C5000 Brodatz C5000 Brodatz C5000 Brodatz C5000 Brodatz

Scale 1 132.92 85.3 150 128.2 410 292.4 983.13 579.4

Scale 2 207.82 118.01 274.76 282.2 343.46 338.5 945.29 908.04

Scale 3 316.10 209.3 365.46 342.1 751.14 508.5 1503.86 1042.8


123

In Fig. 7, it is worthwhile to note that an important

problem appears in the first scale (m = 0) where the fre-

quency response of the filter has significant amplitude

above the Nyquist frequency. Cutting off abruptly the filter

response above the Nyquist frequency strongly distorts the

filter shape in the spatial domain (this causes the appear-

ance of side lobes or ringing). Since the horizontal and

vertical filters are defined by central symmetry, they are

continuous across the periodicities of the Fourier domain;

therefore, they are well localized and without extra side

lobes in the space domain. The oblique filters (i.e., filters

which are neither vertical nor horizontal) are also defined

by central symmetry. But this is not sufficient to maintain

the Fourier domain continuously (across periods) and to

keep a good localization in the space domain. To alleviate

this problem, a solution has been proposed in [67].

The parameters used for the development of EGWC

(such as Ul, Uh, K and S) have already been used for

indexing and retrieval of image databases including objects

(natural or man-made), scenes, objects in natural scenes

and textures. Therefore, we studied the performance of the

proposed algorithm using two different datasets: COREL

and Brodatz texture databases [28, 68].

4.1 Image databases

To demonstrate the performance of the new algorithm on a

CBIR system, one subset of COREL imagebase [28] with

Fig. 7 Illustrations of the

applied Gabor wavelets in the

spatial (left images) and

frequency (right images)

domains

Table 2 The names of 50 categories in C5000

No. Category No. Category No. Category No. Category No. Category

1 Vultures 11 Dinosaurs 21 Card game 31 Snow board 41 Road signs

2 Decoys 12 Clouds 22 Easter egg 32 Fireworks 42 Troops parade

3 Lions 13 Dawn 23 Gun 33 Body building 43 Fashion

4 Elephants 14 Mountains 24 Flag 34 Kong Fu 44 Tran

5 Tigers 15 Caves 25 Dolls 35 Surfing 45 Airplane

6 Horses 16 Trees 26 Tools 36 Sailing ship 46 Food

7 Dolphins 17 Waves 27 Mineral texture 37 Cars 47 Ballet

8 Panthers 18 Flowers 28 Granular texture 38 Doors 48 Marble

9 Cats 19 Japanese trees 29 Precious-stones 39 Interior design 49 Bus

10 Shells 20 Antiques 30 Molecules 40 Historical building 50 Medicine


123

5,000 (C5000) images in 50 categories and with 100 ima-

ges in each category were utilized. The categories’ names

of C5000 are given in Table 2. In addition, a popular

texture database is used in our experiments: the Brodatz

texture database, consisting of 112 different types of tex-

ture images. Each original image with a size of 512 9 512

is evenly divided into 16 of 128 9 128 non-overlapping

sub-images, thus creating a database of 112 9 16 = 1,792

Brodatz texture images. If anyone of them is imposed as

the query image, the 16 texture images divided from the

same original image are viewed as the images from the

same class and targeted to be retrieved as the ground truth.

4.2 Evaluation measures

In this paper, the standard performance measurement pre-

cision-recall pair is used for the evaluation of retrieval

performance. Precision P is defined as the ratio of the

number of retrieved relevant images r to the total number

of retrieved images n, i.e., P = r/n. Precision P measures

the accuracy of the retrieval. Recall R is defined as the ratio

of the number of retrieved relevant images r to the total

number m of relevant images in the whole database, i.e.,

R = r/m. Recall that R measures the robustness of the

retrieval.

P ¼ r

n¼ No of relevant images retrieved

Total no of images retrieved

R ¼ r

m¼ No of relevant images retrieved

Total no of relevant images in DB

ð16Þ

4.3 Performance using 5,000 image database

The first experiment was performed to compare the pro-

posed algorithms with a number of counterpart methods

Fig. 9 A query results on C5000 obtained using GWC with d1. The top left image in each series is the query image and the following 11 images

are retrieval results

Fig. 8 Average retrieval result of 5,000 queries using GWC,

SIMPLIcity and EGWC


123

using the imagebase C5000. Figure 8 compares the per-

formance of EGWC, GWC and SIMPLIcity [28].

As can be seen from the figure, the retrieval perfor-

mance of EGWC feature is significantly higher than that of

SIMPLIcity and GWC feature. It is worthwhile to note that

EGWC uses a simple relative distance measure for feature

matching, while SIMPLIcity uses a complex integrated

region matching measure of image similarity, which works

based on region segmentation of images. Obviously, using

more complex distance measures or classifiers with EGWC

features may improve its retrieval performance. In addi-

tion, SIMPLIcity uses both color and shape features in

contrast to EGWC, which uses only micro-structure shape

information. Figures 9 and 10 illustrate the results of GWC

and EGWC, respectively, for two query images from

C5000.

4.4 Performance using Brodatz texture image database

The second experiment was aimed to study the perfor-

mance of the EGWC with the other multiresolution mul-

tidirectional image decomposition techniques such as

conventional 2D Gabor transform [35], discrete contourlet

transform [36], steerable pyramid [37] and CDFB [38] on

texture retrieval [41]. Figure 11 shows the overall perfor-

mances for the case of n (total number of retrieved images)

from 16 to 65. As shown in Fig. 11, EGWC performed

Fig. 10 A query results on C5000 obtained using EGWC with d1. The top left image in each series is the query image and the following 11

images are retrieval results

Fig. 11 Average retrieval rate of Brodatz database according to the

number of top images considered using directional filter banks

(conventional Gabor, district contourlet, steerable pyramid, CDFB

[40] and EGWC)


123

meaningfully better performance than other multiresolution

multidirectional counterpart techniques. As can be seen,

due to the nature of the Gabor transform, its conventional

feature structure [41] even has better or comparable per-

formance among its three counterparts (contourlet, steer-

able pyramid and CDFB transforms). Clearly, in EGWC,

the correlogram technique has promoted the quality of the

Gabor indexing features significantly. Figure 12 illustrates

the results of EGWC, respectively, for a query images from

Brodatz dataset.

5 Conclusion

In this paper, a new feature called enhanced Gabor

wavelet correlogram was proposed for image indexing

and retrieval. EGWC uses Gabor decomposition which

has been shown to be optimal in the sense of minimizing

the joint two-dimensional uncertainty in space and fre-

quency. It takes also advantage of Gabor wavelet direc-

tional selectivity to extract effectively shape features.

EGWC also proposes an appropriate solution to reduce

the data redundancy caused by Gabor decomposition. For

this purpose, it uses non-maximum suppression in the

direction of high-pass filtering. It proposes also the use

of a scale-dependent distance for the computation of

wavelet autocorrelogram. In addition, EGWC uses

quantization thresholds optimized by an evolutionary

algorithm particularly designed for optimizing CBIR

parameters.

Comprehensive experiments were performed with two

different datasets including 5,000 natural and 1,792 texture

images, respectively. EGWC provided better performance

with respect to a number of frequently used CBIR algo-

rithms including SIMPLIcity and directional filter bank

methods such as Gabor wavelets, discrete contourlet

transform, steerable pyramid and CDFB.

EGWC uses only micro-structure shape information for

constructing index vector. Obviously, enriching this feature

vector with color and macro-structure image information

may provide significant improvement in retrieval

performance.

Acknowledgments The authors would like to thank Pr. J.Z. Wang

for his invaluable comments and providing a subset of COREL

database and executable version of SIMPLIcity software with which

we could obtain retrieval results on C5000. We would also like to

thank Dr. M. Saadatmand-Tarzjan and Mrs. N. Nematzadeh for their

contribution and help.

Fig. 12 A query result on Brodatz texture database obtained using EGWC with d1. The top left image in each series is the query image and the

following 11 images are retrieval results


123

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