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(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 10, No. 3, March 2012
Image Classification in Transform Domain
Dr. H. B. Kekre Dr. Tanuja K. Sarode Jagruti K. Save
Professor, Associate Professor, Ph.D. Scholar, MPSTME,
Computer Engineering Computer Engineering, NMIMS University,
Mukesh Patel School of Technology Thadomal Shahani Engineering Associate Professor,
Management and Engineering, College, Fr. C. Rodrigues College of
NMIMS University, Vileparle(w) Bandra(W), Mumbai 400-050, India Engineering, Bandra(W), Mumbai
Mumbai 400–056, India tanuja_0123@yahoo.com 400-050, India
hbkekre@yahoo.com. jagrutik_save@yahoo.com
Abstract— Organizing images into meaningful categories using [11], Artificial Neural Network [12] [13], Genetic algorithm
low level or high level features is an important task in image [14] are used.
databases. Although image classification has been studied for
many years, it is still a challenging problem within multimedia
II. IMAGE TRANSFORMS
and computer vision. In this paper the generic image
classification approach using different transforms is proposed.
The two main steps in image classification are feature extraction A. Discrete Fourier Transform (DFT)
and classification algorithm. This paper proposes to generate The discrete Fourier transform (DFT) is one of the most
feature vector from image transform. The paper also investigates important transforms that is used in digital signal processing
the effectiveness of different transforms (Discrete Fourier and image processing [15]. Two dimensional discrete Fourier
Transform, Discrete Cosine Transform, Discrete Sine Transform, transform for an image f(x, y) of size N by N is given by
Hartley and Walsh Transform) in classification task. The size of equation 1.
feature vector also varied to see its impact on the result.
Classification is done using nearest neighbor classifier. Euclidean
and Manhattan distance is used to calculate the similarity
− j2π ux +
N −1 N −1 vy
N
measure. Images from the Wang database are used to carry out F(u, v) = ∑ ∑ f(x, y)e N
the experiments. The experimental results and detailed analysis x =0 y =0 (1)
are presented. for 0 ≤ u, v ≤ N − 1
Keywords- Image classification; Image Transform; Discrete
Fourier Transform (DFT); Discrete Sine Transform(DST); B. Discrete Cosine Transform (DCT)
Discrete Cosine Transform(DST); Hartley Transform; Walsh
Transform; Nearest neighbor Classifier.
The discrete cosine transform (DCT), introduced by
Ahmed, Natarajan and Rao [16], has been used in many
applications of digital signal processing, data compression,
I. INTRODUCTION information hiding and content based Image Retrieval
Though the image classification is usually not a very system(CBIR)[17]. The discrete cosine transform (DCT) is
difficult task for humans, it has been proven to be an extremely closely related to the discrete Fourier transform. It is a
complex task for machines. In the existing literatures, most of separable linear transformation; that is, the two-dimensional
the frameworks for image classification include two main transform is equivalent to a one-dimensional DCT performed
steps: feature extraction and classification algorithm. In the first along a single dimension followed by a one-dimensional DCT
step, some discriminative features are extracted to represent the in the other dimension. The two dimensional DCT can be
image content such as color [1] [2], shape [3] and texture [4]. written in terms of pixel values f(x, y) for x, y= 0, 1,…, N-1
There has been a lot of research work done in the area of and the frequency-domain transform coefficients F(u, v) as
feature extraction. Saliency map is used to extract features to shown in equation 2.
classify both the query image and database images into
attentive and non-attentive classes [5]. The image texture
feature is calculated based on gray-level co-occurrence matrix F(u, v) =
(GLCM) [6]. Color Co-occurrence method in which both the (2x + 1)uπ (2y + 1)vπ (2)
α(u) α(v) ∑ ∑ f(x, y) cos cos 2N
color and texture of an image are taken into account, is used to 2N
generate the features [7]. Transforms have been applied to gray for 0 ≤ u, v ≤ N − 1
scale image to generate feature vector [8]. In classification
algorithm step, various multi-class classifiers like k nearest Where
neighbor classifier [9], Support Vector Machine (SVM) [10]
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α (u ) = 1 / N for u = 0 • Wj takes on the values +1 and -1
2 • Wj[0] = 1 for all j
α (u ) = for 1 ≤ u ≤ N − 1
N
• Wj x [Wk]t=0, for j≠k and Wj x [Wk]t =N, for
α (v ) = 1 / N for v = 0 j=k.
2 • Wj has exactly j zero crossings, for j = 0, 1,..., N-1
α (v ) = for 1 ≤ v ≤ N − 1
N
Each row Wj is even (when j is even) and odd (when j is
C. Discrete Sine Transform (DST) odd) w.r.t. to its midpoint.
The discrete sine transform was introduced by A. K. Jain in
1974. The two dimensional sine transform is defined by an III. ROW MEAN VECTOR
equation 3. The row mean vector [25] [26] is the set of averages of the
intensity values of the respective rows as shown in equation 5.
2 (x + 1)(u + 1)π
F(u, v) = ∑∑ f(x, y)sin
N +1 N +1 Avg(Row 1)
(y + 1)(v + 1)π
sin (3) Avg(Row 2)
N +1 Row mean vecto r = : (5)
for 0 ≤ u, v ≤ N− 1
:
Avg(Row N)
Discrete Sine transform has been widely used in signal and
image Processing [18] [19]. IV. PROPOSED ALGORITHM
The image database is divided into a training set and a
D. Discrete Hartley Transform (DHT) testing set. The feature vector of each training/testing image is
The Hartley transform [20] is an integral transform closely calculated. Given an image to be classified from testing set, a
related to the Fourier transform. It has some advantages over nearest neighbor classifier compares it against the images of a
the Fourier transform in the analysis of real signals as it avoids training set, in order to identify the most similar image and
the use of complex arithmetic. consequently the correct class. Euclidean and Manhattan
distance is used as similarity measure.
A discrete Hartley transform (DHT) is a Fourier-related
transform of discrete, periodic data similar to the discrete
A. Generation of feature vector
Fourier transform (DFT), with analogous applications in signal
processing and related fields [21]. Its main distinction from the 1. For each color image f(x,y), generate its three color
DFT is that it transforms real inputs to real outputs, with no (R, G, and B) planes fR(x,y), fG(x,y) and fB(x,y)
intrinsic involvement of complex numbers. Just as the DFT is respectively.
the discrete analogue of the continuous Fourier transform, the 2. Apply transform T (DCT, DFT, DST, HARTLEY,
DHT is the discrete analogue of the continuous Hartley WALSH) on the columns of three image planes as
transform. The discrete two dimensional Hartley Transform for given in equation 6 to 8 to get column transformed
image of size N x N is defined as in equation 4. images.
F(u, v) = [T ]× [ f R ( x , y ) ] = F R ( x , v ) (6)
1 2π (ux + vy )
∑ ∑ f(x, y) cas
(4)
N N
where casθ = cos θ + sin θ [T ]× [ f G ( x , y ) ] = F G ( x , v ) (7)
E. Discrete Walsh Transform (DWT))
The Walsh Transform [22] has become quite useful in the [T ]× [ f B ( x , y ) ] = F B ( x , v ) (8)
applications of image processing [23] [24]. Walsh functions
were established as a set of normalized orthogonal functions, 3. Calculate row mean vector of each column
analogous to sine and cosine functions, but having uniform transformed image.
values ± 1 throughout their segments. The Walsh transform
matrix is defined as a set of N rows, denoted Wj, for j = 0, 1, ... 4. Make a feature vector of size 75 by fusing the row
, N - 1, which have the following properties: mean vectors of R, G, and B plane. Take first 25
values from R plane followed by first 25 values from
G plane followed by first 25 values from B plane.
Identify applicable sponsor/s here. (sponsors)
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5. Do the above process for training images to generate
the feature database.
The different values of feature vector size like 150 (50R +
50G + 50B), 225 (75R + 75G + 75B), 300 (100R + 100G +
100B), 450(150R + 150G + 150B), and 768 (256R + 256G +
256B) are also considered to generate feature vectors.
B. Classification
1. In this phase, for given testing images, their feature
vectors are generated.
2. Euclidean distance and Manhattan distance is
calculated between each testing image feature vector
and each training image feature vector.
3. Minimum distance indicates the most similar training
image for that testing image. Then the given testing
image is assigned to the corresponding class.
We have also considered another training set where each
feature vector is the average of feature vectors of all training Figure 2. Sample database of testing images
images of a particular class.
Each image is resized to 256 x 256. Table I and Table II shows
the number of correctly classified total images (out of 240) for
V. RESULTS different transforms over different vector sizes for two different
The implementation of the proposed technique is done in training sets. The correctness of classification is visually
MATLAB 7.0 using a computer with Intel Core 2 Duo checked.
Processor T8100 (2.1GHz) and 2 GB RAM. The proposed
technique is tested on the Wang image database. This database With average training set Walsh transform gives better
was created by the group of professor Wang from the performance compared to other transforms with Manhattan as
Pennsylvania State University [27]. The experiment is carried similarity measure. If Euclidean distance is used for
on 8 classes of Wang database. For testing, 30 images for each calculation then feature vector size of 768 gives the marginally
class were used and for training, 5 images of each class were better performance in all transforms. Considering the results as
used. Thus total testing images were 240 and total training shown in Table 1, best results are obtained for Manhattan
images were 40. Training set contains 40 feature vectors. The distance as similarity measure. DST Walsh and DFT gave
proposed method is also implemented using another training better performance in that order.
set that contain 8 feature vectors where each feature vector is
the average of feature vectors of all training images of same Now considering individual class classification performance
class. Fig. 1 shows the sample database of training images and using these two similarity measures is shown in Table III to
Fig. 2 shows the sample database of testing images. Table VI. For this purpose the vector size is selected based on
the performance. For Euclidean distance criterion, the number
of correctly classified images in each class for different
transforms over two training sets is shown in table III and table
IV with feature vector size 768. If a Manhattan distance
criterion is used, then there is a variation in the performance of
the transforms for different feature vector sizes. In most cases
vector size 225 gives better performance. So using this vector
size, the number of correctly classified images in each class for
different transforms over two training sets is shown in table V
and table VI.
Figure 1. Sample database of training images
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TABLE I. NUMBER OF CORRECTLY CLASSIFIED IMAGES (OUT OF 240) FOR DFT, DCT, DST, HARTLEY AND WALSH OVER DIFFERENT FEATURE VECTOR
SIZES USING EUCLIDEAN AND MANHATTAN DISTANCE., T RAINING SET: FEATURE VECTORS OF 5 IMAGES FROM EACH CLASS
Transform Distance Feature vector size
E-Euclidean
M-Manhattan
75 150 225 300 450 768
E 155 159 159 159 160 167
DFT
M 166 163 169 169 164 163
E 151 156 159 162 162 163
DCT
M 163 167 169 170 164 163
E 159 160 160 160 161 160
DST
M 164 173 176 174 168 161
E 148 150 151 151 152 158
HARTLEY
M 154 162 165 167 161 161
E 149 152 155 156 160 161
WALSH
M 160 162 166 170 171 170
TABLE II. NUMBER OF CORRECTLY CLASSIFIED IMAGES (OUT OF 240) FOR DFT, DCT, DST, HARTLEY AND WALSH OVER DIFFERENT FEATURE VECTOR
SIZES USING EUCLIDEAN AND MANHATTAN DISTANCE., T RAINING SET: AVERAGE OF FEATURE VECTORS OF 5 IMAGES FROM EACH CLASS
Transform Distance Feature vector size
E-Euclidean
M-Manhattan
75 150 225 300 450 768
E 155 160 162 162 161 166
DFT
M 175 173 171 169 164 156
E 156 158 157 159 160 160
DCT
M 171 172 169 168 163 156
E 161 160 160 159 161 161
DST
M 161 162 168 169 169 164
E 159 162 161 162 163 167
HARTLEY
M 169 168 172 171 168 164
E 155 157 158 158 158 159
WALSH
M 179 175 173 169 169 159
TABLE III. TOTAL CLASSIFIED IMAGES (OUT OF 30 IMAGES) IN EACH TABLE V. TOTAL CLASSIFIED IMAGES (OUT OF 30 IMAGES) IN EACH
CLASS FOR DIFFERENT TRANSFORMS, VECTOR SIZE: 768, DISTANCE CLASS FOR DIFFERENT TRANSFORMS, VECTOR SIZE: 225, DISTANCE
CRITERIA: EUCLIDEAN D ISTANCE, TRAINING: FEATURE VECTORS OF 5 CRITERIA: D ISTANCE CRITERIA: MANHATTAN D ISTANCE, TRAINING:
IMAGES FROM EACH CLASS FEATURE VECTORS OF 5 IMAGES FROM EACH CLASS
Classes DFT DCT DST HARTLEY WALSH Classes DFT DCT DST HARTLEY WALSH
Beach 15 14 11 14 11 Beach 23 21 19 24 23
Monument 10 13 7 9 8 Monument 9 11 9 11 8
Bus 24 21 27 22 25 Bus 25 20 27 22 24
Dinosaur 30 30 30 30 30 Dinosaur 30 30 30 30 30
Elephant 24 23 23 24 24 Elephant 22 23 20 22 21
Flower 27 25 26 27 25 Flower 30 28 30 30 25
Horse 26 28 26 25 28 Horse 22 23 24 19 25
Snow Mountain 11 9 10 7 10 Snow Mountain 8 13 17 7 10
TABLE IV. TOTAL CLASSIFIED IMAGES (OUT OF 30 IMAGES) IN EACH TABLE VI. TOTAL CLASSIFIED IMAGES (OUT OF 30 IMAGES) IN EACH
CLASS FOR DIFFERENT TRANSFORMS, VECTOR SIZE: 768, DISTANCE CLASS FOR DIFFERENT TRANSFORMS, VECTOR SIZE: 225, DISTANCE
CRITERIA: EUCLIDEAN D ISTANCE, TRAINING: AVERAGE OF FEATURE CRITERIA: MANHATTAN D ISTANCE, TRAINING SET: AVERAGE OF FEATURE
VECTORS OF 5 IMAGES FROM EACH CLASS VECTORS OF 5 IMAGES FROM EACH CLASS
Classes DFT DCT DST HARTLEY WALSH Classes DFT DCT DST HARTLEY WALSH
Beach 20 18 14 19 17 Beach 24 23 16 24 26
Monument 3 4 9 6 5 Monument 9 9 7 11 6
Bus 23 24 25 23 24 Bus 24 25 26 25 28
Dinosaur 30 30 30 30 30 Dinosaur 30 30 30 30 30
Elephant 25 22 24 25 24 Elephant 21 18 21 21 19
Flower 30 30 29 30 30 Flower 30 30 30 30 30
Horse 16 17 17 16 16 Horse 20 22 22 20 22
Snow Mountain 19 15 13 18 13 Snow
13 12 16 11 12
Mountain
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No. of correctly classified images
The comparisons of performances of different transforms
are shown in Fig. 3 to Fig. 6. Euclidean distance criterion
180
No. of correctly classified images 175
Euclidean distance criterion
170
180
165
175 160
170 155
165 150
160 145
155 140
150 75 150 225 300 450 768
Feature vector size
145 WALSH DCT DST
HARTLEY DFT
140
75 150 225 300 450 768
Feature vector size
WALSH DCT DST Figure 5. Performance of different transform (training set: Average of
HARTLEY DFT
feature vectors of 5 images from each class)
Figure 3. Performance of different transform (training set: Feature vectors No. of correctly classified images
of 5 images from each class)
Manhattan distance criterion
180
No. of correctly classified images
175
Manhattan distance criterion
170
180
165
175
160
170
155
165
150
160 145
155 140
150 75 150 225 300 450 768
145 Feture vector size
140 WALSH DCT DST HARTLEY DFT
75 150 225 300 450 768
Feature vector size
WALSH DCT DST HARTLEY DFT
Figure 6. Performance of different transform (training set: Average of
feature vectors of 5 images from each class)
Figure 4. Performance of different transform (training set: Feature vectors VI. CONCLUSIONS
of 5 images from each class)
This paper proposes to prepare the feature vector from an
image column transform and use it for image classification.
This gives considerable saving of computational time as
compared to full transform. The paper investigates the
performance of different transforms. The performance is
tested thoroughly using different criteria like distance
measure (Euclidean distance, Manhattan distance); size of
feature vector (75, 150, 225, 300, 450 and 768) and training
sets (feature vectors, average of feature vectors). Conclusion
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from the results of individual class classification is given in classification,” the IEEE Symposium on System Theory, SSST,
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Systems, Vol.: 4, pp. 180 – 183, Shanghai Dec 2009.
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Video Databases, in conjunction with ICCV’98, pp. 384-390, Jan AUTHORS PROFILE
2009.
[10] O. Chapelle, P. Haffner, and V. Vapnik, “Support vector machines Dr. H. B. Kekre has received B.E. (Hons.) in
for histogram- based image classification,” IEEE Transactions on Telecomm. Engineering. from Jabalpur University in
Neural Networks, vol. 10, pp. 1055-1064, 1999. 1958, M.Tech (Industrial Electronics) from IIT
[11] S. Agrawal, N. Verma, P. Tamrakar, and P. Sircar, “Content Based Bombay in 1960, M.S.Engg. (Electrical Engg.) from
Color Image Classification using SVM,” in Proc. of IEEE University of Ottawa in 1965 and Ph.D. (System
International Conference on Information Technology: New Identification) from IIT Bombay in 1970 He has
Generations (ITNG), pp. 1090 – 1094, Las Vegas, April 2011. worked as Faculty of Electrical Engineering and then
HOD Computer Science and Engg. at IIT Bombay.
[12] M. Lotfi1, A. Solimani, A. Dargazany, H. Afzal, and M. Bandarabadi, For 13 years he was working as a professor and head in the Department of
“Combining wavelet transforms and neural networks for image Computer Engg. at Thadomal Shahani Engineering. College, Mumbai.
96 http://sites.google.com/site/ijcsis/
ISSN 1947-5500
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Now he is Senior Professor at MPSTME, SVKM’s NMIMS University. He Dept. of Computer Engineering at Thadomal Shahani Engineering College,
has guided 17 Ph.Ds, more than 100 M.E./M.Tech and several B.E./ B.Tech Mumbai. She is life member of IETE, ISTE, member of International
projects. His areas of interest are Digital Signal processing, Image Association of Engineers (IAENG) and International Association of
Processing and Computer Networking. He has more than 450 papers in Computer Science and Information Technology (IACSIT), Singapore. Her
National /International Conferences and Journals to his credit. He was areas of interest are Image Processing, Signal Processing and Computer
Senior Member of IEEE. Presently He is Fellow of IETE and Life Member Graphics. She has more than 100 papers in National /International
of ISTE Recently twelve students working under his guidance have Conferences/journal to her credit.
received best paper awards and six research scholars have beenconferred
Ph. D. Degree by NMIMS University. Currently 7 research scholars are Jagruti K. Save has received B.E. (Computer Engg.)
pursuing Ph.D. program under his guidance.
from Mumbai University in 1996, M.E. (Computer
Engineering) from Mumbai University in 2004,
Tanuja K. Sarode has Received Bsc. (Mathematics) currently Pursuing Ph.D. from Mukesh Patel School of
from Mumbai University in 1996, Technology, Management and Engineering, SVKM’s
Bsc.Tech.(Computer Technology) from Mumbai NMIMS University, Vile-Parle (W), Mumbai, INDIA.
University in 1999, M.E. (Computer Engineering) She has more than 10 years of experience in teaching.
from Mumbai University in 2004, currently Pursuing Currently working as Associate Professor in Dept. of
Ph.D. from Mukesh Patel School of Technology, Computer Engineering at Fr. Conceicao Rodrigues College of Engg.,
Management and Engineering, SVKM’s NMIMS Bandra, Mumbai. Her areas of interest are Image Processing, Neural
University, Vile-Parle (W), Mumbai, INDIA. She has more than 10 years Networks, Fuzzy systems, Data base management and Computer Vision.
of experience in teaching. Currently working as Associate Professor in She has 6 papers in National /International Conferences/journal to her
credit.
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