Sectorization of Haar and Kekre’s Wavelet for Feature Extraction of color images in Image Retrieval

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Sectorization of Haar and Kekre’s Wavelet for
Feature Extraction of color images in Image
Retrieval
H.B.Kekre Dhirendra Mishra
Sr. Professor Associate Professor & PhD Research Scholar
MPSTME, SVKM’s NMIMS (Deemed-to be-University) MPSTME, SVKM’s NMIMS (Deemed-to be-University)
Vile Parle West, Mumbai -56,INDIA Vile Parle West, Mumbai -56,INDIA
hbkekre@yahoo.com dhirendra.mishra@gmail.com

Abstract- This paper presents the Innovative idea of useful for real-world applications if aggressive attempts are
Sectorization of Haar Wavelet transformed images and made. For example, many commercial organizations are
Kekre’s Wavelet Transformed images to extract features working on image retrieval despite the fact that robust text
for image retrieval. Transformed images have been understanding is still an open problem. Of late, there is
sectored into 4,8,12 and 16 sectors. Each sector produces renewed interest in the media about potential real-world
the feature vector component in particular sector size. applications of CBIR and image analysis technologies,
Thus the feature vector size increases with the increase There are various approaches which have been
in the sector size. The experiment of augmenting the experimented to generate the efficient algorithm for CBIR
feature vectors with extra components performed .The like FFT, DCT, DST, WALSH sectors [8-14][21][22],
performance of proposed method of sectorization Transforms [16][17], Vector quantization[17], bit truncation
checked with respect to increase in sector sizes, effect of coding [18][19].
augmentation of extra components in both Haar and
Kekre’s Wavelet sectorization .The retrieval rate The problem of CBIR still needs lots of research to achieve
checked with crossover of average precision and recall. the better retrieval performance. It needs extensive
LIRS and LSRR are calculated for average of randomly experiments on all of its parameters i.e. Feature extraction,
selected 5 images of all 12 classes and compared with the similarity measures, retrieval performance measuring
overall average of LIRS/LSRR. The work experimented parameters.
over the image database of 1055 images and the
performance of image retrieval with respect to two In this paper we have introduced a novel concept of
similarity measures namely Euclidian distance (ED) and Sectorization of Haar Wavelet and Kekre’s Wavelet in both
sum of absolute difference (AD) are measured. column wise and row wise transformed color images for
Keywords- CBIR, Haar Wavelet, Kekre’s Wavelet feature extraction (FE).Two different similarity measures
Euclidian Distance, Sum of Absolute Difference, LIRS, namely sum of absolute difference and Euclidean distance
LSRR, Precision and Recall. are considered. Average precision, Recall, LIRS and LSRR
are used for performances study of these approaches.
I. INTRODUCTION
Digital world of the current era needs storage and II. HAAR WAVELET [5]
management of bulky digital images. It is the need of the
century to have better mechanism to store, manage and The Haar transform is derived from the Haar matrix. The
retrieve whenever needed digital images from the large Haar transform is separable and can be expressed in matrix
database. Content-based image retrieval (CBIR), [1-4] is any form
technology that in principle helps to achieve this motive by [F] = [H] [f] [H]T
their visual content. By this definition, anything ranging Where f is an NxN image, H is an NxN Haar transform
from an image similarity function to a robust image matrix and F is the resulting NxN transformed image. The
annotation engine falls under CBIR. This characterization of transformation H contains the Haar basis function hk(t)
CBIR as a field of study places it at a unique juncture within which are defined over the continuous closed interval
the scientific community. It is believed that the current state- t Є [0,1].
of-the-art in CBIR holds enough promise and maturity to be The Haar basis functions are

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When k=0, the Haar function is defined as a
constant
hk(t) = 1/√N
When k>0, the Haar Function is defined as

Figure 1: Computation of 4 Sectors

B. 8 Sectors Formation

III. KEKRE’S WAVELET [5] The transformed image sectored in 4 sectors is taken
into consideration for dividing it into 8 sectors. Each
Kekre’s Wavelet transform is derived from Kekre’s sector is of angle 45o. Coefficients of the transformed
transform. From NxN Kekre’s transform matrix, we can image lying in the particular sector checked for the
generate Kekre’s Wavelet transform matrices of size sectorization conditions as shown in the Figur2.
(2N)x(2N), (3N)x(3N),……, (N2)x(N2). For example, from
5x5.Kekre’s transform matrix, we can generate Kekre’s
Wavelet transform matrices of size 10x10, 15x15, 20x20
and 25x25. In general MxM Kekre’s Wavelet transform
matrix can be generated from NxN Kekre’s transform
matrix, such that M = N * P where P is any integer between
2 and N that is, 2 ≤ P ≤ N. Kekre’s Wavelet Transform
matrix satisfies [K][K]T = [D] Where D is the diagonal
matrix this property and hence it is orthogonal. The diagonal
matrix value of Kekre’s transform matrix of size NxN can be
computed as Figure 2:Computation of 8 Sectors

C. 12 Sector Formation.
Division each sector of 4 sectors into angle of 30 o
forms 12 sectors of the transformed image.
(2) Coefficients of the transformed image are divided into
various sectors based on the inequalities shown in the
Figure 3.

IV. SECTORIZATION OF TRANSFORMED
IMAGES [8-14]

A. 4 Sector Formation
Even and odd rows/columns of the transformed images
are checked for sign changes and the based on which
four sectors are formed as shown in the Figure 1
below:
Figure 3:Computation of 12 Sectors

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D. 16 Sector Formation:

Similarly we have done the calculation of inequalities
to form the 16 sectors of the transformed image. The
even/odd rows/ columns are assigned to particular
sectors for feature vector generation

V. EXPERIMENTAL RESULTS

We have used the augmented Wang image database [2] The
Image database consists of 1055 images of 12 different
classes such as Flower, Sunset, Barbie, Tribal, Cartoon,
Elephant, Dinosaur, Bus, Scenery, Monuments, Horses,
Beach. Class wise distribution of all images in the database
has been shown in the Figure 4.

Class

No. of
Images
45 59 51 100 100 Figure 6: First 20 Retrieved Images of Row wise Haar
wavelet (16 Sectors)
Class

No. of
Images
100 100 100 100 100

Class

No. of
Images
100 100

Figure 4: Class wise distribution of images in the Image
database

Figure5. Query Image

The query image of the class Horse has been shown in
Figure 5. For this query image the result of retrieval of both
Column wise and Row wise Haar and Kekre’s wevlet
transformed images for all sectors are checked. The Figure 6 Figure 7: First 20 Retrieved Images of Row wise Kekre’s
shows the first 20 retrieval for the query image with respect Wavelet Sectorization (16 Sectors).
to of Row wise Haar Wavelet Sectorization for its 16
Sectors with sum of absolute difference as similarity Once the feature vector is generated for all images in the
measure. It can be observed that the retrieval of first 20 database a feature database is created. 5 randomly chosen
images are of relevant class i.e. Horse; there are no query images of each class is produced to search the
irrelevant images till first 45 retrievals in both cases. The database. The image with exact match gives minimum
result of row wise Kekre’s Wavelet shown in Figure 7; the absolute difference and Euclidian distance. To check the
retrieval of first 20 images is same as Kekre’s Wavelet effectiveness of the work and its performance with respect to
except the order of retrieval of images changes. retrieval of the images we have calculated the overall

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average precision and recall as given in Equations (3) and
(4) below. Two new parameters i.e. LIRS and LSRR are
introduced as shown in Equations (5) and (6).

Figure 8: Overall Average Precision and Recall performance
of Sectorization of Row wise Haar Wavelet. Absolute
All these parameters lie between 0-1 hence they can be Difference(AD) and Euclidian Distance (ED) as similarity
expressed in terms of percentages. The newly introduced measures.
parameters give the better performance for higher value of
LIRS and Lower value of LSRR [8-13].The class wise
performance of the proposed algorithm with respect to
average precision and recall cross over points in all sectors
for both Haar Wavelet (Row wise and column wise) and
Kekre’s Wavelet (Row wise and column wise) with the
consideration of two similarity measures namely Euclidean
distance(ED) and sum of absolute difference (AD) has been
shown in Figure 8- Figure 11.The average value of each
method has been plotted as horizontal lines to compare the
individual class performances .It is seen that sectorization of
column wise performs better than row wise transformed
images in both HAAR and Kekre’s wavelet. The use sum of
absolute difference gives better retrieval for in all sectors
except 16 sectors compared to Euclidian distance for all
Figure 9: Overall Average Precision and Recall performance
classes of images. The retrieval performance for each
of Sectorization of Column wise Haar Wavelet. Absolute
classes vary as it is observed that Diana sour, flowers, sunset
Difference (AD) and Euclidian Distance (ED) as similarity
and horses have maximum of retrieval i.e. 80%, 70%,50%
measures
and 50% respectively.
The Figure 12 depicts the overall average performances of
Haar and Kekre’s wavelet. It shows that for sector sizes
4,8,12 Haar wavelet has retrieval performance than Kekre’s
wavelet. The sectorization of column wise transformed
images is far better i.e. on average 45% than row wise i.e. on
average 30%.The performance of the proposed algorithm is
checked with respect to two new parameters i.e. LIRS and
LSRR .The class wise performance of LIRS and LSRR
shown in Figure 13-Figure 20.The class having maximum
value of average precision and recall cross over point must
have maximum LIRS and Minimum LSRR. Taking the
example of Diana sour class which has cross over points as:
80% (Row wise and column wise Haar and Kekre’s
Wavelet), has maximum LIRS (see Figures 13,14,17 and
Figure 18) and Minimum LSRR (see Figures 15,16,19 and
20).Similarly these parameters can be easily checked for Figure 10: Overall Average Precision and Recall
other classes as well. Thus these parameters are very useful performance of Row wise Kekre’s Wavelet Sectorization
to check the performances of the retrieval in CBIR.

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with Absolute Difference (AD) and Euclidian Distance (ED)
as similarity measures

Figure 13: The LIRS Plot of Row wise Haar transformed
images . Overall Average LIRS performances (Shown with
Horizontal lines :0.068 (4 Sectors ED), 0.086 (4 Sectors
AD), 0.036(8 Sectors ED), 0.038(8 Sectors AD), 0.040(12
Sectors ED), 0.066(12 Sectors AD), 0.068(16 Sectors ED),
Figure 11 Overall Average Precision and Recall
0.088(16 Sectors AD) ).
performance of Column wise Kekre’s Wavelet Sectorization
with Absolute Difference (AD) and Euclidian Distance (ED)
as similarity measures

Figure 14: The LIRS Plot of Column wise Haar transformed
images . Overal Average LIRS performances (Shown with
Horizontal lines :0.060 (4 Sectors ED), 0.074 (4 Sectors
AD), 0.063(8 Sectors ED), 0.089(8 Sectors AD), 0.061(12
Figure 12: Comparison of Overall Precision and Recall Sectors ED), 0.078(12 Sectors AD), 0.029(16 Sectors ED),
cross over points of Kekre’s Wavelet and Haar Wavelet with 0.030(16 Sectors AD) ).
Absolute Difference (AD) and Euclidean Distance (ED) as
similarity measure.

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Figure 17: The LIRS Plot of Row wise KWT transformed
Figure 15: The LSRR Plot of Row wise Haar transformed images . Overall Average LIRS performances (Shown with
images . Overall Average LSRR performances (Shown with Horizontal lines :0.048 (4 Sectors ED), 0.059 (4 Sectors
Horizontal lines :0.83 (4 Sectors ED), 0.84 (4 Sectors AD), AD), 0.044(8 Sectors ED), 0.053(8 Sectors AD), 0.067(12
0.87(8 Sectors ED), 0.86(8 Sectors AD), 0.88(12 Sectors Sectors ED), 0.076(12 Sectors AD), 0.070(16 Sectors ED),
ED), 0.86(12 Sectors AD), 0.64(16 Sectors ED), 0.67(16 0.10(16 Sectors AD) ).
Sectors AD) ).

Figure 18: The LIRS Plot of Column wise KWT
Figure 16: The LSRR Plot of Column wise Haar transformed images . Overall Average LIRS performances
transformed images . Overall Average LSRR performances (Shown with Horizontal lines :0.061 (4 Sectors ED), 0.078
(Shown with Horizontal lines :0.63(4 Sectors ED), 0.65 (4 (4 Sectors AD), 0.064(8 Sectors ED), 0.091(8 Sectors AD),
Sectors AD), 0.639(8 Sectors ED), 0.638(8 Sectors AD), 0.066(12 Sectors ED), 0.090(12 Sectors AD), 0.030(16
0.639(12 Sectors ED), 0.633(12 Sectors AD), 0.94(16 Sectors ED), 0.048(16 Sectors AD) ).
Sectors ED), 0.84(16 Sectors AD) ).

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gives better performance as far as overall average precision
and recall cross over point s concerned as compared to
Kekre’s Wavelet transform as shown in the Figure 12. The
newly introduced parameter LIRS and LSRR gives good
platform for performance evaluation to judge how early all
relevant images is being retrieved (LSRR) and it also
provides judgement of how many relevant images are being
retrieved as part of first set of relevant retrieval (LIRS).The
sum of absolute difference as similarity measure is
recommended due to its lesser complexity and better
retrieval rate performance compared to Euclidian distance.

VII. REFERENCES

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and sector mean with zero-sal and highest-cal AUTHORS PROFILE
components in Walsh transform sectors as feature
vectors for image retrieval”, published in
H. B. Kekre has received B.E. (Hons.)
international journal of Computer scienece and
in Telecomm. Engg. from Jabalpur
information security (IJCSIS) Vol.8(4) 2010, ISSN
University in 1958, M.Tech (Industrial
1947-5500 available online
Electronics) from IIT Bombay in 1960,
http://sites.google.com/site/ijcsis/vol-8-no-4-jul-
M.S.Engg. (Electrical Engg.) from
2010
University of Ottawa in 1965 and
Ph.D.(System Identification) from IIT Bombay in 1970. He
[ 15 ] Arun Ross, Anil Jain, James Reisman, “A hybrid
has worked Over 35 years as Faculty and H.O.D. Computer
fingerprint matcher,” Int’l conference on Pattern
science and Engg. At IIT Bombay. From last 13 years
Recognition (ICPR), Aug 2002.

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working as a professor in Dept. of Computer Engg. at
Thadomal Shahani Engg. College, Mumbai. He is currently
senior Professor working with Mukesh Patel School of
Technology Management and Engineering, SVKM’s
NMIMS University vile parle west Mumbai. He has guided
17 PhD.s 150 M.E./M.Tech Projects and several
B.E./B.Tech Projects. His areas of interest are Digital signal
processing, Image Processing and computer networking. He
has more than 350 papers in National/International
Conferences/Journals to his credit. Recently ten students
working under his guidance have received the best paper
awards. Two research scholars working under his guidance
have been awarded Ph. D. degree by NMIMS University.
Currently he is guiding 10 PhD. Students. He is life member
of ISTE and Fellow of IETE.

Dhirendra Mishra has received his BE
(Computer Engg) degree from University
of Mumbai. He completed his M.E.
(Computer Engg) from Thadomal
shahani Engg. College, Mumbai,
University of Mumbai. He is PhD
Research Scholar and working as
Associate Professor in Computer Engineering department of
Mukesh Patel School of Technology Management and
Engineering, SVKM’s NMIMS University, Mumbai,
INDIA. He is life member of Indian Society of Technical
education (ISTE), Member of International association of
computer science and information technology (IACSIT),
Singapore, Member of International association of
Engineers (IAENG). His areas of interests are Image
Processing, Operating systems, Information Storage and
Management

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