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(IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 7, October 2010 Sector Mean with Individual Cal and Sal Components in Walsh Transform Sectors as Feature Vectors for CBIR H. B. Kekre Dhirendra Mishra Senior Professor, Computer Engineering Associate Professor, Computer Engineering MPSTME,SVKM‟S NMIMS University, MPSTME, SVKM‟S NMIMS University, Mumbai, INDIA Mumbai, INDIA hbkekre@yahoo.com dhirendra.mishra@gmail.com Abstract- We have introduced a novel idea of conceiving much smaller in size than the original image, typically of the complex Walsh transform for sectorization of transformed order of hundreds of elements (rather than millions). The components. In this paper we have proposed two different second task is similarity measurement (SM), where a approaches for feature vector generation with consideration of distance between the query image and each image in the all sal components and all cal components separately. Both database using their signatures is computed so that the top these approaches are experimented with the extra components of zero-cal and highest-sal. Two similarity measures such as closest images can be retrieved.[7-9]. There are various sum of absolute difference and Euclidean distance are used and approaches which have been experimented to generate the results are compared. The cross over point performance of efficient algorithm for CBIR like FFT sectors [4-6], overall average of precision and recall for both approaches on Transforms [15][17], Vector quantization[12], bit truncation different sector sizes are compared. The individual sector mean coding [13][14]. In this paper we have introduced a novel of Walsh sectors in all three color planes are considered to concept of complex Walsh transform and its sectorization design the feature vector. The algorithm proposed here is for feature extraction (FE).Two different similarity measures worked over database of 1055 images spread over 12 different namely sum of absolute difference and Euclidean distance classes. Overall Average precision and recall is calculated for the performance evaluation and comparison of 4, 8, 12 & 16 are considered. The performances of these approaches are Walsh sectors. The use of Absolute difference as similarity compared. measure always gives lesser computational complexity and consideration of only all cal components with augmentation of zero-cal approach with sum of absolute difference as similarity II. WALSH TRANSFORM measure of feature vector has the best retrieval performance. Index Terms- CBIR, Walsh Transform, Euclidian Distance, Walsh transform [17] matrix is defined as a set of N rows, Absolute Difference, Precision, Recall denoted Wj, for j = 0, 1, .... , N - 1, which have the following properties: I. INTRODUCTION Wj takes on the values +1 and -1. With the huge growth of digital information the need of its Wj[0] = 1 for all j. management requires need of storage and utilization in Wj x WTk=0, for j ≠ k and Wj x WkT =N, for j=k. efficient manner. This has lead to approach like content Wj has exactly j zero crossings, for j = 0, 1, ., N-1. based image search and retrieval to be used. Content-based Each row Wj is either even or odd with respect to image retrieval into automatic retrieval of images from a its midpoint. database by color, texture and shape features. The term has been widely used to describe the process of retrieving Walsh transform matrix is generated using a Hadamard desired image on the basis of features (such as colors, matrix of order N. The Walsh transform matrix row is the texture and shape) that can be automatically extracted from row of the Hadamard matrix specified by the Walsh code the images themselves. The typical CBIR system [1-6] index, which must be an integer in the range [0, ..., N - 1]. performs two major tasks. The first one is feature extraction For the Walsh code index equal to an integer j, the (FE), where a set of features, called image signature or respective Hadamard output code has exactly j zero feature vector, is generated to accurately represent the crossings, for j = 0, 1, ... , N - 1. content of each image in the database. A feature vector is 156 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 7, October 2010 Kekre‟s Algorithm[10] to generate Walsh Transform from sectors are further divided into 8, 12 and 16 sectors. We Hadamard matrix [17] is illustrated for N=16.However the have proposed two different approaches for feature vector algorithm is general and can be used for any N = 2 k where k generation namely sector mean of only sal components and is an integer. only cal components value of all the vectors in each sector with augmentation of extra highest-sal, zero-cal components and without augmentation of extra highest-sal, zero-cal Step 1: components with sum of absolute difference and Euclidean Arrange the „N‟ numbers in a row and then split the row at distance [7-9] [11-14] as similarity measures. Performances „N/2‟, the other part is written below the upper row but in of all these approaches are compared using both similarity reverse order as follows: measures. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 A.Four Walsh Transform Sectors: 15 14 13 12 11 10 9 8 To get the angle in the range of 0-360 degrees, the steps as Step 2: given in Table 1 are followed to separate these points into four quadrants of the complex plane. The Walsh transform We get two rows, each of this row is again split in „N/4‟ and of the color image is calculated in all three R, G and B other part is written in reverse order below the upper rows as planes. The complex rows representing sal components of shown below. the image and the real rows representing cal components 0 1 2 3 are checked for positive and negative signs. The sal and cal 15 14 13 12 Walsh values are assigned to each quadrant. as follows: 7 6 5 4 TABLE I. FOUR WALSH SECTOR FORMATION 8 9 10 11 Sign of Sal Sign of Quadrant Assigned This step is repeated until we get a single column which Cal gives the ordering of the Hadamard rows according to sequency as given below: + + I (0 – 90 Degrees) 0 ,15, 7, 8, 3,12,4,11,1,14,6,9,2,13,5,10 + - II ( 90 – 180 Degrees) Step 3: - - III( 180- 270 Degrees) According to this sequence the Hadamard rows are arranged - + IV(270–360 Degrees) to get Walsh transform matrix. Now a product of Walsh matrix and the image matrix is calculated. This matrix contains Walsh transform of all the columns of the given The equation (1) is used to generate individual components image. to generate the feature vector of dimension 12 considering three R, G and B Planes in the sal and cal density Since Walsh matrix has the entries either +1 or -1 there is distribution approach. However, it is observed that the no multiplication involved in computing this matrix. Since density variation in 4 quadrants is very small for all the only additions are involved computational complexity is images. Thus the feature vectors have poor discretionary very low. power and hence higher number of sectors such as 8, 12 and 16 were tried. In the case of second approach of feature III. FEATURE VECTOR GENERATION vector generation i.e. individual sector mean has better discretionary power in all sectors.Sum of absolute difference The proposed algorithm makes novel use of Walsh measure is used to check the closeness of the query image transform to design the sectors to generate the feature from the database image and precision and recall are vectors for the purpose of search and retrieval of database calculated to measure the overall performance of the images. The complex Walsh transform is conceived by algorithm. multiplying all sal functions by j = √-1 and combining them with real cal functions of the same sequency. Thus it is B. Eight Walsh Transform Sectors: possible to calculate the angle by taking tan-1 of sal/cal. However the values of tan are periodic with the period of π Each quadrants formed in the previous obtained 4 sectors radians hence it can resolve these values in only two sectors. are individually divided into 2 sectors each considering the To get the angle in the range of 0-360 degrees we divide angle of 45 degree. In total we form 8 sectors for R,G and B these points in four sectors as explained below. These four planes separately as shown in the Table 2. The percentage 157 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 7, October 2010 density distribution of sal and cal in all 8 sectors are determined using equation (1) to generate the feature vector. IV. RESULTS AND DISCUSSION The sample Images of the database of 1055 images of 12 TABLE 2. EIGHT WALSH SECTOR FORMATION different classes such as Flower, Sunset, Barbie, Tribal, Quadrant of 4 Condition New sectors Formed Puppy, Cartoon, Elephant, Dinosaur, Bus, Parrots, Scenery, Walsh sectors Beach are shown in the Figure 1.The algorithm is tested by taking 5 query images from each class and then averaging I (0 – 90 0 ) Cal >= Sal I (0-45 Degrees) the performance in terms of precision and recall over all the Sal > Cal II (45-90 Degrees) classes. II ( 90 – 1800 ) |Sal | > |Cal| III(90-135 Degrees) |Cal| >= |Sal| IV(135-180 Degrees) 0 III ( 180- 270 ) |Cal| >= |Sal| V (180-225 Degrees ) |Sal| > |Cal| VI (225-270 Degrees) 0 IV ( 270 – 360 ) |Sal| > |Cal| VII (270-315 Degrees) |Cal| >= |Sal| VIII (315-360 Degrees ) C. Twelve Walsh Transform Sectors: Each quadrants formed in the previous section of 4 sectors are individually divided into 3 sectors each considering the angle of 30 degree. In total we form 12 sectors for R,G and B planes separately as shown in the Table 3. The percentage density distribution of sal and cal in all 12 sectors are determined using equation (1) to generate the feature vector TABLE 3. TWELVE WALSH SECTOR FORMATION 4 Quadrants Condition New sectors 0 I (0 – 90 ) Cal >= √3 * Sal I (0-30 0) 1/√3 cal <=sal<= √3 II (30-60 0) cal Otherwise III (60-90 0) II ( 90 – 1800) Cal >= √3 * Sal IV (90-120 0) 1/√3 |cal| <=|sal|<= V (120-150 0) √3 |cal| Otherwise VI (150-1800) III(180-2700 ) |Cal|>= √3 * |Sal| VII (180-2100 ) 1/√3 cal <=|sal|<= √3 VIII(210-240 0) |cal| Figure 1. Sample Image Database Otherwise IX (240-270 0) IV ( 270 – |Cal|>= √3 * |Sal| X (270-300 0) 3600) 1/√3 |cal| <=|sal|<= XI (300-330 0 ) √3 |cal| Otherwise XII (330-360 0) Figure 2. Query Image 158 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 7, October 2010 The dinosaur class image is taken as sample query image as shown in the Figure 2. The first 21 images retrieved in the case of sector mean in 12 Walsh sector used for feature vectors and Absolute difference as similarity measure is shown in the Figure 3. It is seen that all images retrieved among first 21 images are of same class of query image i.e. dinosaur. Figure 3: First 21 Retrieved Images based on individual sector mean with augmentation of zero-cal and highest-sal components of 12 Walsh Sectors with Absolute Difference as similarity measures for the query image shown in the Figure 2. Once the feature vector is generated for all images in the database a feature database is created. A query image of each class is produced to search the database. The image with exact match gives minimum sum of absolute difference. To check the effectiveness of the work and its performance with respect to retrieval of the images we have calculated the precision and recall as given in Equations (1) and (2) below: Number of relevant images retrieved Precision=---------------------------------------------- (1) Total Number of images retrieved Number of relevant images retrieved Recall= ------------------------------------------------- (2) Total number of relevant images in database The Figure 4 – Figure 7 shows the Overall Average Precision and Recall performance of mean of only sal components of each sectors in 4, 8, 12 and 16 Walsh Transform sectors with absolute Difference respectively. Figure 8 – Figure 11 shows the overall average cross over performance of individual sector mean of only cal components in 4, 8, 12 and 16 Walsh sectors. The comparison bar chart of cross over points of overall average of precision and recall for 4, 8, 12 and 16 sectors of with augmentation of extra zero-cal and highest-sal components with individual sector mean w.r.t. two different similarity measures namely Euclidean distance and Absolute difference is shown in the Figure 12 and Figure13. It is observed that performance of 12 sectors with extra components of zero-cal and highest-sal with consideration of only cal components of each sector is the best. The performance of absolute difference is quite closed to Euclidean distance. 159 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 7, October 2010 Figure 4: Overall Average Precision and Recall performance of Sector mean with only sal component in 4 Walsh Transform sectors with Absolute Difference(AD) and Figure 6: Overall Average Precision and Recall performance Euclidian Distance (ED) as similarity measures. of Sector mean with only sal component in 12 Walsh Transform sectors with Absolute Difference(AD) and Euclidian Distance (ED) as similarity measures. Figure 5: Overall Average Precision and Recall performance Figure 7: Overall Average Precision and Recall performance of Sector mean with only sal component in 8 Walsh of Sector mean with only sal component in 16 Walsh Transform sectors with Absolute Difference(AD) and Transform sectors with Absolute Difference(AD) and Euclidian Distance (ED) as similarity measures. Euclidian Distance (ED) as similarity measures. 160 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 7, October 2010 Figure 8: Overall Average Precision and Recall performance Figure 10: Overall Average Precision and Recall of Sector mean with only cal component in 4 Walsh performance of Sector mean with only cal component in 12 Transform sectors with Absolute Difference(AD) and Walsh Transform sectors with Absolute Difference(AD) and Euclidian Distance (ED) as similarity measures. Euclidian Distance (ED) as similarity measures. Figure 9: Overall Average Precision and Recall performance Figure 11: Overall Average Precision and Recall of Sector mean with only cal component in 8 Walsh performance of Sector mean with only cal component in 16 Transform sectors with Absolute Difference(AD) and Walsh Transform sectors with Absolute Difference(AD) and Euclidian Distance (ED) as similarity measures. Euclidian Distance (ED) as similarity measures. 161 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 7, October 2010 only cal for feature vector generation with sum of absolute difference as similarity measuring parameter. These results are compared with Euclidian distance as similarity measure. Both thease approaches are experimented with and without augmentation of extra component of zero-cal and highest- sal. The cross over point performance of overall average of precision and recall for both approaches on all applicable sectors are compared. It is found that the sector mean of only cal component with augmentation of extra component of zero-cal and highest-sal always gives the best outcome of retrieval as shown in the bar chart of the figure 13. It is also observed that sum of absolute difference is found economical similarity measuring parameter. Using Walsh transform and absolute difference as similarity measuring parameter reduces the computational complexity reducing the search time and calculation of feature vector [8][9]. REFERENCES Figure 12: Comparison of Overall Precision and Recall [1] Kato, T., “Database architecture for content based cross over points based on individual sector mean in Walsh image retrieval in Image Storage and Retrieval 4, 8, 12 and 16 sectors with Absolute Difference (AD) and Systems” (Jambardino A and Niblack W eds),Proc Euclidean Distance (ED) as similarity measure. SPIE 2185, pp 112-123, 1992. [2] John Berry and David A. Stoney “The history and development of fingerprinting,” in Advances in Fingerprint Technology, Henry C. Lee and R. E. Gaensslen, Eds., pp. 1-40. CRC Press Florida, 2nd edition, 2001. [3] Emma Newham, “The biometric report,” SJB Services, 1995. [4] H. B. Kekre, Dhirendra Mishra, “Digital Image Search & Retrieval using FFT Sectors” published in proceedings of National/Asia pacific conference on Information communication and technology(NCICT 10) 5TH & 6TH March 2010.SVKM‟S NMIMS MUMBAI [5] H.B.Kekre, Dhirendra Mishra, “Content Based Image Retrieval using Weighted Hamming Distance Image hash Value” published in the proceedings of international conference on contours of computing technology pp. 305-309 (Thinkquest2010) 13th & 14th March 2010. [6] H.B.Kekre, Dhirendra Mishra,“Digital Image Figure 13: Comparison of Overall Precision and Recall Search & Retrieval using FFT Sectors of Color cross over points based on individual sector mean in Walsh Images” published in International Journal of 4, 8, 12 and 16 sectors with Absolute Difference (AD) and Computer Science and Engineering (IJCSE) Vol. Euclidean Distance (ED) as similarity measure. 02,No.02,2010,pp.368-372 ISSN 0975-3397 available online at .V. CONCLUSION http://www.enggjournals.com/ijcse/doc/IJCSE10- 02- 02-46.pdf The Innovative idea of using complex Walsh transform 4, 8, [7] H.B.Kekre, Dhirendra Mishra, “CBIR using upper 12 and 16 sectors of the images to generate the feature six FFT Sectors of Color Images for feature vector vectors for content based image retrieval is proposed. We generation” published in International Journal of have proposed two different approaches using only sal and 162 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 7, October 2010 Engineering and Technology(IJET) Vol. 02, No. Advances in Computing, Communication and 02, 2010, 49-54 ISSN 0975-4024 available online Control (ICAC3-2009), pp.: 384-390, 23-24 Jan at 2009, Fr. Conceicao Rodrigous College of Engg., http://www.enggjournals.com/ijet/doc/IJET10-02- Mumbai. Available online at ACM portal. 02-06.pdf [ 16 ] H.B.Kekre, Tanuja K. Sarode, Sudeep D. Thepade, [8] H.B.Kekre, Dhirendra Mishra, “Four walsh “DCT Applied to Column mean and Row Mean transform sectors feature vectors for image retrieval Vectors of Image for Fingerprint Identification”, from image databases”, published in international International Conference on Computer Networks journal of computer science and information and Security, ICCNS-2008, 27-28 Sept 2008, technologies (IJCSIT) Vol. 1 (2) 2010, 33-37 ISSN Vishwakarma Institute of Technology, Pune. 0975-9646 available online at [ 17 ] H.B.Kekre, Sudeep Thepade, Archana Athawale, http://www.ijcsit.com/docs/vol1issue2/ijcsit201001 Anant Shah, Prathmesh Velekar, Suraj Shirke, “ 0201.pdf Walsh transform over row mean column mean [9] H.B.Kekre, Dhirendra Mishra, “Performance using image fragmentation and energy compaction comparison of four, eight and twelve Walsh for image retrieval”, International journal of transform sectors feature vectors for image retrieval computer science and engineering from image databases”, published in international (IJCSE),Vol.2.No.1,S2010,47-54. journal of Engineering, science and [ 18 ] H.B.Kekre, Vinayak Bharadi, “Walsh Coefficients technology(IJEST) Vol.2(5) 2010, 1370-1374 of the Horizontal & Vertical Pixel Distribution of ISSN 0975-5462 available online at Signature Template”, In Proc. of Int. Conference http://www.ijest.info/docs/IJEST10-02-05-62.pdf ICIP-07, Bangalore University, Bangalore. 10-12 [ 10 ] H.B.Kekre, Dhirendra Mishra, “Density distribution Aug 2007. in Walsh Transform sectors as feature vectors for image retrieval”, International journal of computer application (IJCA), ISSN NO. 975-8887, Vol.4, AUTHORS PROFILE No.6, July 2010, pp-30-36.available online at http://www.ijcsonline.org/archives/volume4/number Dr. H. B. Kekre has received B.E. 6/829-1072. (Hons.) in Telecomm. Engg. from [ 11 ] Arun Ross, Anil Jain, James Reisman, “A hybrid Jabalpur University in 1958, M.Tech fingerprint matcher,” Int’l conference on Pattern (Industrial Electronics) from IIT Recognition (ICPR), Aug 2002. Bombay in 1960, M.S.Engg. (Electrical [ 12 ] A. M. Bazen, G. T. B.Verwaaijen, S. H. Gerez, L. Engg.) from University of Ottawa in P. J. Veelenturf, and B. J. van der Zwaag, “A 1965 and Ph.D.(System Identification) from IIT Bombay in correlation-based fingerprint verification system,” 1970. He has worked Over 35 years as Faculty and H.O.D. Proceedings of the ProRISC2000 Workshop on Computer science and Engg. At IIT Bombay. From last 13 Circuits, Systems and Signal Processing, years working as a professor in Dept. of Computer Engg. at Veldhoven, Netherlands, Nov 2000. Thadomal Shahani Engg. College, Mumbai. He is currently [ 13 ] H.B.Kekre, Tanuja K. Sarode, Sudeep D. Thepade, Senior Professor working with Mukesh Patel School of “Image Retrieval using Color-Texture Features Technology Management and Engineering, SVKM‟s from DCT on VQ Codevectors obtained by NMIMS University vile parle west Mumbai. He has guided Kekre‟s Fast Codebook Generation”, ICGST 17 PhD.s 150 M.E./M.Tech Projects and several International Journal on Graphics, Vision and B.E./B.Tech Projects. His areas of interest are Digital signal Image Processing (GVIP), Available online at processing, Image Processing and computer networking. He http://www.icgst.com/gvip has more than 300 papers in National/International [ 14 ] H.B.Kekre, Sudeep D. Thepade, “Using YUV Conferences/Journals to his credit. Recently ten students Color Space to Hoist the Performance of Block working under his guidance have received the best paper Truncation Coding for Image Retrieval”, IEEE awards. Currently he is guiding 8 PhD. Students. Two of his International Advanced Computing Conference Students have recently completed Ph. D. He is life member 2009 (IACC‟09), Thapar University, Patiala, of ISTE and Fellow of IETE. INDIA, 6-7 March 2009. [ 15 ] H.B.Kekre, Sudeep D. Thepade, “Image Retrieval using Augmented Block Truncation Coding Techniques”, ACM International Conference on 163 http://sites.google.com/site/ijcsis/ ISSN 1947-5500 (IJCSIS) International Journal of Computer Science and Information Security, Vol. 8, No. 7, October 2010 Dhirendra S.Mishra has received his BE (Computer Engg) degree from University of Mumbai in 2002.Completed his M.E. (Computer Engg) from Thadomal shahani Engg. College, Mumbai, University of Mumbai. He is PhD Research Scholar and working as Assistant 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 164 http://sites.google.com/site/ijcsis/ ISSN 1947-5500