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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 firstname.lastname@example.org 400-050, India email@example.com. firstname.lastname@example.org Abstract— Organizing images into meaningful categories using , Artificial Neural Network  , Genetic algorithm low level or high level features is an important task in image  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 . 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 , 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). 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  , shape  and texture . 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 . The image texture feature is calculated based on gray-level co-occurrence matrix F(u, v) = (GLCM) . 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 . Transforms have been applied to gray for 0 ≤ u, v ≤ N − 1 scale image to generate feature vector . In classification algorithm step, various multi-class classifiers like k nearest Where neighbor classifier , Support Vector Machine (SVM)  91 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 10, No. 3, March 2012 α (u ) = 1 / N for u = 0 • Wj takes on the values +1 and -1 2 • Wj = 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   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  . 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  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 . 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  has become quite useful in the [T ]× [ f B ( x , y ) ] = F B ( x , v ) (8) applications of image processing  . 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) 92 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 10, No. 3, March 2012 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 . 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 93 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 10, No. 3, March 2012 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 94 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 10, No. 3, March 2012 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 95 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 10, No. 3, March 2012 from the results of individual class classification is given in classification,” the IEEE Symposium on System Theory, SSST, Table VII. pp.44-48, Aug 2009.  S. Sadek, A. Hamadi, B. Michaelis,and U. Sayed, “Robust Image Classification Using Multi-level Neural Networks,” Proc. of the IEEE TABLE VII. BEST 3 CLASS PERFORMANCES FOR DIFFERENT CRITERIA International Conference on Intelligent Computing and Intelligent Systems, Vol.: 4, pp. 180 – 183, Shanghai Dec 2009. Training Set Similarity Best 3 performer classes  J. Z. Wang, J. Li and G. Wiederhold, “SIMPLIcity: semantic sensitive Measure integrated matching for picture libraries,” IEEE Transactions on Dinosaur (100%) Pattern Analysis and Machine Intelligence, 2001, vol.23, no.9, Euclidean Horse (88.66%) pp.947-963. Feature vectors of 5 Flower (86.66%) images from each  E. O. Brigham, R. E. Morrow, “The Fast Fourier Transform,” class Dinosaur (100%) Spectrum, IEEE, Dec. 1967, Vol. 4, Issue 12, pp. 63-70. Manhattan Flower (95.33%) Bus (78.66%)  N. Ahmed, T. Natarajan, and K. R. Rao, “Discrete Cosine Dinosaur (100%) Transform,” IEEE Transctions, Computers, 90-93, Jan 1974. Euclidean Flower (99.33%)  H. B.Kekre, T. K. Sarode, S. D. Thepade, “Color-Texture Feature Average of feature Elephant (80%) based Image Retrieval using DCT applied on Kekre’s Median vectors of 5 images Codebook”, International Journal on Imaging (IJI), Volume 2, from each class Dinosaur (100%) Manhattan Flower (100%) Number A09, Autumn 2009,pp. 55-65. Available online at Bus (85.33%) www.ceser.res.in/iji.html (ISSN: 0974-0627) .  S. A. Martucci, “Symmetric convolution and the discrete sine and cosine transforms,” IEEE Transactions on Signal Processing, Vol. 42, Results also show that the training set containing average Issue 5, pp. 1038-1051, 1994. of feature vectors, gives better results and since they are less  H. B.Kekre and D. Mishra, “Feature Extraction of Color Images using in numbers, the computation is fast. 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F. Siraj, M. Salahuddin, and S. Yusof, “Digital Image Classification  H. B.Kekre, Sudeep D. Thepade, Akshay Maloo “Performance for Malaysian Blooming Flower,” the IEEE Second International Comparison for Face Recognition using PCA, DCT Conference on Computational Intelligence, Modelling and &WalshTransform of Row Mean and Column Mean”, ICGST Simulation, (CIMSiM), pp. 33-38,Bali, Sept 2010. International Journal on Graphics, Vision and Image Processing  D. Bashish, M. Braik, and S. Bani-Ahmad, “A Framework for (GVIP), Volume 10, Issue II, pp.9-18, June 2010. Detection and classification of Plant Leaf and Stem Diseases,” Proc.  H.B.Kekre, Tanuja Sarode, Sudeep D. Thepade, “DCT Applied to of the IEEE International Conference on signal and image processing Row Mean and Column Vectors in Fingerprint Identification”, In (ICSIP), pp. 113-118, Chennai Dec 2010. Proceedings of Int. Conf. on Computer Networks and Security  H.B. Kekre, T. K. Sarode, M. S. Ugale, “Performance Comparison of (ICCNS), 27-28 Sept. 2008, VIT, Pune. Image Classifier Using DCT, Walsh, Haar and Kekre’s Transform,”  Wang, J. Z., Li, J., Wiederhold, G.: SIMPLIcity: Semantics-sensitive International Journal of Computer Science and Information Integrated Matching for Picture LIbraries, IEEE Trans. on Pattern ol Security,(IJCSIS), V ..9, No. 7, 2011 Analysis and Machine Intelligence, vol 23, no.9, pp. 947-963, (2001).  M. Szummer and R. W. Picard, “Indoor-Outdoor Classification,” IEEE International workshop Content based Acess of Image and Video Databases, in conjunction with ICCV’98, pp. 384-390, Jan AUTHORS PROFILE 2009.  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  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.  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 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 10, No. 3, March 2012 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. 97 http://sites.google.com/site/ijcsis/ ISSN 1947-5500
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