Image Retrieval using Energy Compaction in Transformed Colour Mean. Vectors with Cosine, Sine, Walsh, Haar, Kekre, Slant & Hartley

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1 Image Retrieval using Energy Compaction in Transformed Colour Mean Vectors with Cosine, Sine, Walsh, Haar, Kekre, Slant & Hartley Transforms Dr. H.B. Kekre 1, Dr. Sudeep D. Thepade 2, Akshay Maloo 3 1 Sr.Professor, 2 Associate Professor and HoD, 3 Systems Engineer, 1,2 Computer Engg., MPSTME, SVKM s NMIMS (Deemed-to-be University), Mumbai, India 3 Infosys Limited, Pune, India 1 hbkekre@yahoo.com, 2 sudeepthepede@gmail.com, 3 akshaymaloo@gmail.com Abstract The paper presents new image retrieval methods using energy compaction in transformed colour averages with seven orthogonal transforms. The six colour mean feature vectors (colour averages) considered are row mean, column mean, combination of row and column mean, forward diagonal mean, backward diagonal mean and combination of diagonal means. The seven considered orthogonal image transforms are Cosine transform, Sine transform, Walsh transform, Haar transform, Kekre transform, Slant transform and Hartley transform. The image transforms are applied on respective colour means and the size of the to be considered feature vector of image for image retrieval is reduced to hold 98% of energy, 96% of energy and 94% of energy (if the full transformed colour mean is considered as 100% energy). Using six colour means, seven image transforms and four energy percentages; in all 168 variations of proposed image retrieval method are considered for experimental analysis and comparison. The experimental results tested with generic image database of 1000 images have shown improvement in image retrieval performance in lower energy percentages with smaller feature vector sizes. So the conclusion that energy compaction helps for better discrimination capability resulting into better and faster image retrieval can be drawn. Keywords: CBIR, Energy Compaction, Row Mean, Column Mean, Diagonal Mean, Image Transform 1. Introduction The new set of image retrieval methods based on energy compaction in transform domain is proposed here. In transform domain, all the transforms have characteristic to compress most of the signal energy in low frequency region. In transform domain very few high frequency coefficients do contain most of the energy, these small number of coefficients if considered as feature vector gives performance improvement in image retrieval with tremendously reduced complexity of query execution as compared to consideration of all coefficients as feature vector. Reducing the feature vector size in image retrieval using these low frequency (high energy) components with retention of signal energy to 98%, 96% and 94% is the basis of the work elaborated in this paper. Instead of randomly selecting few starting transform domain coefficients as feature vector, average energy and cumulative energy vectors do logically help in finding the number of coefficients for retaining some percentage of energy. Here image retrieval techniques are proposed by considering the row mean, column mean, diagonal means elaborated in section 2 in transform domain with energy compaction using seven assorted image transforms namely Cosine transform, Sine transform, Walsh transform, Haar transform, Kekre transform, Slant transform and Hartley transform. 2. Colour Mean Vectors The row mean vector [24,25] is the set of averages of the intensity values of the respective rows. The column mean vector is the set of averages of the intensity values of the respective columns. For the sample image with n rows and n columns, the row and column mean vectors for this image will be as given in equation 1 and equation 2. Row Mean Vector = [Avg(Row 1), Avg(Row 2),., Avg(Row n)] (1) International Journal of Intelligent Information Processing(IJIIP) Volume2, Number4, December 2011 doi : /ijiip.vol2.issue4.1 1

2 Column Mean Vector = [Avg(Col. 1), Avg(Col. 2),., Avg(Col. n)] (2) The forward diagonal mean (FDM) vector [25] is the set of averages of the intensity values of the diagonal elements considered in the direction of a forward slash. The backward diagonal mean (BDM) vector [25] is the set of averages of the intensity values of the diagonal elements considered in the direction of a backward slash. Forward Diagonal Mean Vector = [Avg(FDM 1), Avg(FDM 2),., Avg(FDM n-1)] (3) Backward Diagonal MeanVector =[Avg(BDM. 1), Avg(BDM. 2),., Avg(BDM. n-1)] (4) 3. Energy Compaction [28,29] Any transform when applied on an image, transfers the high frequency components at the higher end and low frequency components towards lower end. This can be used as an advantage to reduce the image feature vector size in image retrieval by eliminating the coefficients which do not contribute significantly. The energy compaction method therefore aids in reducing the feature vector size, which gives faster image retrieval. 3.1 Average Energy Vector [30] Average Energy depicts the average energy compaction done by the applied transform on all the database images. The average energy can be obtained for each of the above specified feature vector techniques, i.e., row, column and diagonal mean. First, all the feature vectors are arranged into a two dimensional array, each column an image in the database. Now, the average feature vector is computed by adding corresponding values and dividing it by number of feature vectors. The database considered consists of 1000 generic images. Hence 1000 feature vectors for row, column or diagonal mean as per the selection, are obtained. Once the average vector is obtained transform is applied on it. By application of transform, the high frequency components are obtained at the higher side of the vector. Then all coefficients of average feature vector are squared to obtain positive values of energy, now they are sorted in descending order and with each sort the corresponding index value of the coefficient is swapped. The sorted list i.e. average energy vector and the index value list are stored for all discussed feature vectors and transforms. 3.2 Cumulative Energy Vector [10,14] The cumulative energy vector signifies the cumulative energy up to the considered feature vector coefficient. After obtaining the average energy vector, the energy values are added cumulatively from first coefficient to the last coefficient of the feature vector. Therefore cumulative energy at the last coefficient denotes the total energy (100% energy) of the image. It is found that energy at the lower coefficients (high frequency and low energy coefficients) in sorted average energy vector is very less and hence they do not add significantly to the cumulative energy vector. 3.3 Compaction by use of Energy Percentage [28] The compaction of energy is done by considering percentages of total energy which is obtained from cumulative energy vector. The proposed method considers 100% energy, 98% energy, 96% energy, 94% energy. The sorted energy values from the average energy vector are added till the desired amount of energy (98% or 96% or 94% of total energy) is obtained. From the average energy vector a particular amount of energy is selected to determine the number of coefficients of the feature vector to be considered for image retrieval. As the percentage of energy considered is reduced, the number of coefficients required also drastically reduces, reducing the candidate feature vector size for image retrieval. 2

3 4. Content Based Image Retrieval (CBIR) using Energy Compaction Transform is applied to the colour mean vector of image to get transformed coefficients, these generated coefficients are then used to generate feature vectors for respective energy percentages which then are used for proposed image retrieval using energy compaction. The various used colour mean vector selection techniques are row mean of image (RM), column mean of image (CM), combination row and column means of image (RCM), forward diagonal mean of image (FDM), backward diagonal mean of image (BDM), combination of forward and backward diagonal means of image (FBDM). With help of image transform and percentage amount of energy to be retained the number of coefficients of transformed feature vector selection to be considered for image retrieval are found with the help of average and cumulative energy vectors. Thus, features of all images in the database are obtained and stored in feature vector tables for respective image transforms namely DCT, DST, Walsh transform, Haar transform, Kekre transform, Slant transform and Hartley transform. The advantage of using the means of images over the complete pixel data of image is reduced complexity of image retrieval technique, which further is reduced to next extent using the proposed principle of energy compaction. 5. Implementation The implementation of the proposed CBIR techniques is done in MATLAB 7.0 using a computer with Intel Core 2 Duo Processor T8100 (2.1GHz) and 2 GB RAM. Figure 1 gives the sample database images from generic image database [9]. The CBIR techniques are tested on the image database [9] of 1000 variable size colour images spread across 11 categories of human being, animals, natural scenery and manmade things. To compare the techniques and to check their performance we have used the precision and recall. Total 55 queries (5 from each category of image database) for generic database are tested to get average precision and average recall of respective image retrieval techniques. The average precision and average recall are computed by grouping the number of retrieved images sorting them according to ascending values of Euclidian distances with the query image. The crossover point [2] of the average precision and average recall curves are used as performance measures to compare the performances of proposed CBIR methods. Figure 1. Sample Images from Generic Image Database [Image database contains total 1000 images with 11 categories] 6. Results of CBIR using Energy Compaction The proposed image retrieval using energy compaction is applied on different transforms with 100%, 98%, 96% and 94% energy retention for respective colour averaging feature vectors. In each transform the number of coefficients to consider particular amount of energy are computed (and given in tables in the respective transform sub-sections 6.1 to 6.7 as table 1 to table 7). There is a significant amount of reduction in number of coefficients considered for image retrieval (in some cases the reduction is as 3

4 high as 98.8%) this saves a lot of retrieval time for very large image databases and in most of the cases gives better performance than considering 100% energy CBIR using DCT Energy Compaction The results of considering DCT [1,5,12,13,14] for proposed CBIR with energy compaction are proposed here. From table 1, it can be observed that as the percentage of energy consideration is reduced the amount of coefficients required for image retrieval are reduced drastically (e.g. for RM technique for 6% reduction in energy there is 98.8% reduction in the number of coefficients to be considered). Table 1. Size of Feature Vectors according to considered Energy Percentage using DCT Energy Compaction (%) Feature Vector Technique RM CM RCM FDM BDM FBDM To determine which energy compaction method is better, precision-recall crossover plots for each image retrieval method are drawn. Only for DCT the detailed graphs of precision-recall crossover points are shown, for other transforms directly the heights of these crossover points are plotted for performance comparison. Figure 2. Crossover points for DCT transformed row mean based CBIR techniques for 100%, 98%, 96%, 94% energy Figure 2, shows the crossover points of precision and recall values for DCT transformed row mean based CBIR techniques considered for various energy percentages. Highest crossover point value denotes best image retrieval performance, hence it could be concluded that, for Row mean technique 96% energy compaction method outperforms other compaction techniques (including 100%) with highest crossover point value This indicates that precision and recall obtained by using DCT transformed row mean feature vector of size 4 performs better than that of size

5 Figure 3. Crossover points for DCT transformed column mean based CBIR techniques for 100%, 98%, 96%, 94% energy Figure 3, shows the crossover points of precision and recall values for DCT transformed column mean based CBIR methods considered for different energy compaction percentages. Highest crossover point value denotes best image retrieval performance, hence it could be concluded that, here 98% energy compaction method (with crossover point value 0.410) outperforms other compaction techniques. This indicates that higher precision and recall are obtained by using feature vector of size 8 than using feature vector of size 256. Here image retrieval methods with all suggested energy compaction values outperform image retrieval considering 100% energy, with reduced feature vector size, less computations and faster retrieval. Figure 4, shows the crossover points of precision and recall values for DCT transformed row & column mean based image retrieval techniques considered for different energy percentages. Here the best results are obtained using 100% energy. The loss in performance for lower energy percentages is very low compared to the time and calculations saved on retrieval. Figure 4. Crossover points for DCT transformed row & column mean based CBIR techniques for 100%, 98%, 96%, 94% energy Figure 5, shows the crossover points of precision and recall values for DCT transformed forward diagonal mean based CBIR methods considered for different energy compactions. Here the best results are obtained using 100% energy. The loss in performance is very low compared to the time and 5

6 calculations saved on retrieval with lower percentages of energy consideration. All energy compaction methods perform similarly and there is no significant difference in the crossover values. Figure 5. Crossover points for DCT transformed forward diagonal mean based CBIR techniques for 100%, 98%, 96%, 94% energy Figure 6, shows the crossover points of precision and recall values for DCT transformed backward diagonal mean based CBIR techniques considered for different energy percentages. Here the best results are obtained using 100% energy. Here using 96% or 94% energy give the same result so cannot be seen separately in the graph. All energy compaction methods perform similarly and there is no significant difference in the crossover values. The loss in performance is very low compared to the time and calculations saved on retrieval. Figure 7, shows the crossover points of precision and recall values for DCT transformed combination of forward & backward diagonal mean based CBIR methods for different energy compaction percentages. Here the best results are obtained using 100% energy. The loss in performance is very low compared to the time and calculations saved on retrieval with lower energy percentages. The performance by all energy percentages except 100% energy is almost same with no significant difference. Figure 6. Crossover points for DCT transformed backward diagonal mean based CBIR techniques for 100%, 98%, 96%, 94% energy 6

7 Figure 7. Crossover points for DCT transformed forward & backward diagonal mean based CBIR techniques for 100%, 98%, 96%, 94% energy 6.2. CBIR using DST Energy Compaction DST [22,23] was applied for all discussed feature vector creation techniques and the obtained results are discussed in this section. From table 2, it can be observed that as the percentage of energy consideration is reduced the amount of coefficients required for image retrieval are reduced drastically (for FBDM technique for 6% reduction in energy results 98.4% reduction in the number of coefficients need to be considered) for all techniques. For all discussed feature vector creation techniques energy compaction using 98%, 96%, 94% gives better performance than using 100% energy with Discrete Sine Transform. Table 2. Size of Feature Vectors for considered Energy Percentage using DST Energy Compaction (%) Feature Vector Technique RM CM RCM FDM BDM FBDM CBIR using Walsh Transform Energy Compaction Walsh Transform [1,6,11,12,15,26] was applied on all discussed feature vector creation techniques and the obtained results are discussed in this section. From table 3 it can be observed that as the percentage energy considered is reduced slightly the number of coefficients required for image retrieval are reduced drastically (for RCM technique for 6% reduction in energy we have a 97.46% reduction in the size of feature vector. For CM and BDM feature vector creation techniques the energy compaction using 98%, 96%, 94% energy gives better performance than using 100% energy with Walsh Transform. Table 3. Size of Feature Vectors for considered Energy Percentage using Walsh Transform Energy Compaction (%) Feature Vector Technique RM CM RCM FDM BDM FBDM

8 6.4. CBIR using Haar Transform Energy Compaction Haar Transform [16,17] is applied for all discussed energy compaction based feature vector creation techniques and the obtained results are discussed in this section. For all discussed feature vector creation techniques except forward and backward diagonal mean (FBDM), energy compaction using 98%, 96%, 94% gives better performance than using 100% energy using Haar Transform. Table 4. Size of Feature Vectors according to considered Energy Percentage using Haar Transform Energy Compaction (%) Feature Vector Technique RM CM RCM FDM BDM FBDM CBIR using Slant Transform Energy Compaction Slant transform [28] is applied on all discussed feature vector creation techniques and the obtained results are discussed here. From table 5 it can be observed that as the percentage of energy consideration is reduced even slightly the number of coefficients required to be considered for image retrieval are reduced drastically (for RM technique for 6% energy reduction energy results in 98.82% reduction in number of coefficients to be considered) for all techniques. To determine which energy compaction method is better, precision-recall crossover points for each image retrieval method using Slant transform method are plotted. For all discussed feature vector creation techniques using Slant transform except combination of forward & backward diagonal mean (FBDM), energy compaction using 98%, 96%, 94% gives better performance than using 100% energy. Table 5. Size of Feature Vectors for considered Energy Percentage using Slant Transform Energy Compaction (%) Feature Vector Technique RM CM RCM FDM BDM FBDM CBIR using Hartley Transform Energy Compaction Discrete Hartley transform [18,19,20,21,27] is applied on all proposed image retrieval methods using energy compaction and the obtained results are discussed in this section. For all discussed CBIR techniques using Hartley transform, except row mean (RM) and forward & backward diagonal mean (FBDM), energy compaction (using 98%, 96%, 94% of energy) gives better performance than using 100% energy. Table 6. Size of Feature Vectors for considered Energy Percentage using DHT Energy Compaction (%) RM CM Feature Vector Technique RCM FDM BDM FBDM

9 6.7. CBIR using Kekre Transform Energy Compaction The section gives the results obtained by using Kekre Transform [1,3,4,7,8,9] in proposed image retrieval methods with energy compaction. From table 7, it can be observed that as the percentage of energy consideration is reduced even slightly the number of coefficients required to be considered for image retrieval are reduced drastically (for RM technique only 6% reduction in energy gives 56.64% reduction in the size of feature vector) for all techniques. With Kekre transform and proposed CBIR methods using energy 98%, 96%, 94% give better performance than using 100% energy. Table 7. Size of Feature Vectors for considered Energy Percentage using Kekre Transform Energy Compaction (%) Feature Vector Technique RM CM RCM FDM BDM FBDM Performance Comparison of Energy Compaction based CBIR methods In proposed CBIR methods using energy compaction in transform domain the feature vector dimensionality is reduced greatly resulting in to faster query execution with better performance for image retrieval. The section has performance comparisons of considered image transforms with energy percentages for respective colour averaging methods (colour means). Figure 8. Performance comparison of transformed row mean based CBIR techniques for all considered image transforms In figure 8, it can be observed that for transformed row mean base CBIR, except Walsh in all other transforms the lower energy percentages have given better performance than 100% energy. The best performance is given by Kekre transformed row mean based CBIR with 94% energy (Kekre-RM-94%) followed by Slant transformed row mean with 96% energy (Slant-RM-96%). In all transforms except Walsh, the energy compaction for transformed row means help in CBIR performance improvement. Here in figure 8, for DCT of row mean vector the 96% energy compaction proves to be the best. Even the 98% energy compaction bade BIR gives better performance than 100% energy consideration when row mean is considered with DST for proposed CBIR methods, the best performance is shown by 98% of energy followed by 100 % energy. For Walsh transformed row mean based CBIR methods the 100% energy perform marginally better than all other energy percentages. For Haar transformed row mean based CBIR methods 94% energy outperforms other considered energy percentages 9

10 including 100% energy. For Slant transformed row mean based CBIR methods 96% energy gives better performance than other considered energy percentages. For Hartley transformed row mean based CBIR methods the 96% energy performs better than other energy percentages. For Kekre transformed row mean based CBIR methods the 94% energy performs better than other energy percentages. All the lower energy percentages have performed better than 100% energy consideration. Figure 9. Performance comparison of transformed column mean based CBIR techniques for all considered image transforms Figure 9, shows the performance improvement for CBIR using transformed column means in all considered image transforms using lower energy percentages than 100% energy consideration. Here the best performance is given by DST transformed column mean based CBIR with 98% energy (DST- CM-98%) followed by Kekre transformed column mean based CBIR with 94% energy (Kekre-CM- 94%) and 96% energy (Kekre-CM-96%). In case of DCT of column mean vector the 98% energy compaction proves to be the best. All the suggested energy compaction based image retrieval methods outperform the CBIR with 100% energy consideration. For DST transformed column mean based proposed CBIR methods, the best performance is shown by 98% of energy. In fact all energy percentages have performed better than 100 % energy. In Walsh transformed column mean based CBIR methods all considered energy percentages perform better than 100% energy, 98% being the best. For Haar transformed column mean based CBIR methods all considered energy percentages perform better than 100% energy and 94% energy gives best performance. For Slant transformed column mean based CBIR methods 98% energy gives better performance than other considered energy percentages. For Hartley transformed column mean based CBIR methods the 98% energy performs better than other energy percentages. For Kekre transformed column mean based CBIR methods the 94% energy performs better than other energy percentages. All lower energy percentages perform far better than 100% energy. In figure 10, the improvement in performance of CBIR using transformed row & column mean with lower energy percentages than 100% energy is seen for most of the considered image transforms. Best performance is given by Kekre transformed row & column mean based CBIR with 94% energy (Kekre-RCM-94%) followed by 96% energy (Kekre-RCM-96%) in the same transform. When combination of row and column mean is considered with DCT, none of the energy compaction performed better than the 100% energy, but 98% energy compaction gives the performance very close to that of 100% energy. For DST transformed combination of row and column mean based proposed CBIR methods, the best performance is shown by 96% of energy. For Walsh transformed row & column mean based CBIR methods the 100% energy perform slightly better than all other considered energy percentages. For Haar transformed row and column mean based CBIR methods both 98% energy and 100% energy gives same performance. For Slant transformed row and column mean based CBIR methods 94% and 96% energy gives better performance than other considered energy 10

11 percentages. For Hartley transformed row and column mean based CBIR methods the 100% energy performs slightly better than other energy percentages Figure 10. Performance comparison of transformed row & column mean based CBIR techniques for all considered image transforms Figure 11. Performance comparison of transformed forward diagonal mean based CBIR techniques for all considered image transforms In figure 11, for all image transforms the performance improvement is observed for image retrieval using transformed forward diagonal mean with lower energy percentages than 100% energy. The best performance is shown by DST transformed forward diagonal mean based CBIR with 96% energy (DST-FDM-96%) followed by 98% energy (DST-FDM-98%) again in DST. For DCT transformed forward diagonal mean, the 100% energy has performed marginally better than other considered energy percentages. For DST transformed forward diagonal mean based CBIR methods the 96% energy gives best performance. Even 98% energy outperforms the 100% energy. For Walsh transformed forward diagonal mean based CBIR methods the 100% energy perform slightly better than all other considered energy percentages. For Haar transformed forward diagonal mean based CBIR methods 96% energy shows best performance followed by 98% energy. For Slant transformed forward diagonal mean based CBIR methods 94% and 96% energy gives better performance than other considered energy percentages. For Hartley transformed forward diagonal mean based CBIR methods the 96% energy performs better than other energy percentages. Here image retrieval with all energy percentages 11

12 perform better than 100% energy consideration. For Kekre transformed forward diagonal mean based CBIR methods the 96% energy performs better than other considered energy percentages. Figure 12. Performance comparison of transformed backward diagonal mean based CBIR techniques for all considered image transforms In figure 12, it can be observed that in all transforms except DCT the performance of CBIR using transformed backward diagonal means with lower energy percentages is improved than 100% energy consideration. The best performance is given in CBIR using DST transformed backward diagonal mean with 98% energy (DST-BDM-98%) followed by also 96% energy in DST (DST-BDM-94%). In DCT transformed backward diagonal mean, none of the energy compaction performed better than the 100% energy, but the performance difference is negligible among the other energy percentages considered and 100% energy. Figure 13. Performance comparison of transformed forward & backward diagonal mean based CBIR techniques for considered image transforms As observed from figure 13, only DST and Kekre transforms show the performance improvement in CBIR using lower energy percentages of transformed forward & backward diagonal means. The best performance is given in CBIR using Kekre transformed forward & backward diagonal means with 96% energy (Kekre-FBDM-96%). In case of DCT transformed combination of forward and backward diagonal means based CBIR, none of the energy compaction performed better than the 100% energy, 12

13 but 98% energy gives the performance next to the 100% energy. For DST transformed backward diagonal mean based CBIR methods the 94% energy perform better than all other energy percentages including 100%. For Walsh transformed forward and backward diagonal mean based CBIR methods all considered energy percentages perform inferior to 100% energy. For Haar transformed forward and backward diagonal mean based CBIR methods 100% energy gives slightly better performance than other considered energy percentages. For Slant transformed forward & backward diagonal mean based CBIR methods the 100% energy performs marginally better than other energy percentages. For Hartley transformed forward & backward diagonal mean based CBIR methods the 100% energy performs better than other energy percentages. For Kekre transformed forward & backward diagonal mean based CBIR methods the 100% energy performs marginally better than other energy percentages considered especially 96%. Table 8 shows the top five energy compaction based CBIR methods with respect to their performances. Table 8. Top five Performance rankings of proposed content based image retrieval methods based on Energy Compaction Size of Feature Average Precision- Performance CBIR techniques using Energy Compaction in Vector for Recall crossover point Rank Transform Domain 256x256x3 Image value 1 (Best) DST-FDM-96% 21x DST-FDM-98% 34x Hartley-FDM-96% 258x3 Hartley-FDM-94% 214x Walsh-FDM-96% 393x3 Walsh-FDM-94% 335x Haar-FDM-98% 15x3 Haar-FDM-96% 13x Conclusion In CBIR with energy compaction of colour mean vectors in transform domain it is observed that the compacted energy for the transformed colour mean vectors give better performance with drastically reduced feature vector size. In row mean, column mean and row-column mean combination Kekre transform with 94% energy proved to be better. In forward diagonal mean and backward diagonal means the discrete Sine transform is observed to give better image retrieval. The marginal difference is observed in the performances of all the image transforms for energy compaction based CBIR methods. 9. References [1] H.B.Kekre, Sudeep D. Thepade, Improving the Performance of Image Retrieval using Partial Coefficients of Transformed Image, International Journal of Information Retrieval (IJIR), Serials Publications, Volume 2, Issue 1, 2009, pp (ISSN: ) [2] H.B.Kekre, Sudeep D. Thepade, Image Retrieval using Augmented Block Truncation Coding Techniques, ACM International Conference on Advances in Computing, Communication and Control (ICAC3-2009), pp , Jan 2009, Fr. Conceicao Rodrigous College of Engg., Mumbai. Is uploaded on online ACM portal. [3] H.B.Kekre, Sudeep D. Thepade, Scaling Invariant Fusion of Image Pieces in Panorama Making and Novel Image Blending Technique, International Journal on Imaging (IJI), Volume 1, No. A08, pp , autumn [4] H.B.Kekre, Sudeep D. Thepade, Creating the Color Panoramic View using Medley of Grayscale and Color Partial Images, WASET International Journal of Electrical, Computer and System Engineering (IJECSE), Volume 2, No. 3, Summer [5] H.B.Kekre, Tanuja Sarode, Sudeep D. Thepade, DCT Applied to Row Mean and Column Vectors in Fingerprint Identification, In Proceedings of International Conference on Computer Networks and Security (ICCNS), Sept. 2008, VIT, Pune. 13

14 [6] Zhibin Pan, Kotani K., Ohmi T., Enhanced fast encoding method for vector quantization by finding an optimally-ordered Walsh transform kernel, ICIP 2005, IEEE International Conference, Volume 1, pp I , Sept [7] H.B.kekre, Sudeep D. Thepade, Improving Color to Gray and Back using Kekre s LUV Color Space, IEEE International Advanced Computing Conference 2009 (IACC 09), Thapar University, Patiala, INDIA, 6-7 March [8] H.B.Kekre, Sudeep D. Thepade, Image Blending in Vista Creation using Kekre's LUV Color Space, SPIT-IEEE Colloquium and International Conference, Sardar Patel Institute of Technology, Andheri, Mumbai, Feb [9] (Last referred on 23 Sept 2008) [10] H.B.Kekre, Sudeep D. Thepade, Archana Athawale, Anant Shah, Prathmesh Verlekar, Suraj Shirke, Walsh Transform over Row Mean and Column Mean using Image Fragmentation and Energy Compaction for Image Retrieval, International Journal on Computer Science and Engineering (IJCSE),Volume 2S, Issue1, January [11] H.B.Kekre, Sudeep D. Thepade, Image Retrieval using Color-Texture Features Extracted from Walshlet Pyramid, ICGST International Journal on Graphics, Vision and Image Processing (GVIP), Volume 10, Issue I, Feb.2010, pp [12] H.B.Kekre, Tanuja Sarode, Sudeep D. Thepade, Color-Texture Feature based Image Retrieval using DCT applied on Kekre s Median Codebook, International Journal on Imaging (IJI), Volume 2, Number A09, Autumn 2009,pp [13] H.B.Kekre, Sudeep D. Thepade, Image Retrieval using Non-Involutional Orthogonal Kekre s Transform, International Journal of Multidisciplinary Research and Advances in Engineering (IJMRAE), Ascent Publication House, 2009, Volume 1, No.I, pp , [14] H.B.Kekre, Sudeep D. Thepade, Archana Athawale, Anant Shah, Prathmesh Verlekar, Suraj Shirke, Performance Evaluation of Image Retrieval using Energy Compaction and Image Tiling over DCT Row Mean and DCT Column Mean, Springer-International Conference on Contours of Computing Technology (Thinkquest-2010), BGIT, Mumbai, March [15] H.B.Kekre, Tanuja K. Sarode, Sudeep D. Thepade, Image Retrieval by Kekre s Transform Applied on Each Row of Walsh Transformed VQ Codebook, (Invited), ACM-International Conference and Workshop on Emerging Trends in Technology (ICWET 2010),Thakur College of Engg. And Tech., Mumbai, Feb 2010, The paper is invited at ICWET [16] Haar, Alfred, Zur Theorie der orthogonalen Funktionensysteme. (German), Mathematische Annalen, volume 69, No. 3, 1910, pp [17] Charles K. Chui, An Introduction to Wavelets, Academic Press, 1992, San Diego, ISBN [18] R. N. Bracewell, "Discrete Hartley transform," J. Opt. Soc. Am. 73 (12), (1983). [19] R. N. Bracewell, "The fast Hartley transform," Proc. IEEE 72 (8), (1984). [20] R. N. Bracewell, The Hartley Transform (Oxford Univ. Press, New York, 1986). [21] R. N. Bracewell, "Computing with the Hartley Transform," Computers in Physics 9 (4), (1995). [22] S. A. Martucci, "Symmetric convolution and the discrete sine and cosine transforms," IEEE Trans. Sig. Processing SP-42, (1994). [23] M. Frigo and S. G. Johnson, "The Design and Implementation of FFTW3," Proceedings of the IEEE, Volume 93, Number (2),pp , [24] H.B.Kekre, Tanuja Sarode, Sudeep D. Thepade, DCT Applied to Row Mean and Column Vectors in Fingerprint Identification, In Proceedings of Int. Conf. on Computer Networks and Security (ICCNS), Sept. 2008, VIT, Pune. [25] H.B.Kekre, Sudeep D. Thepade, Akshay Maloo CBIR Feature Vector Dimension Reduction with Eigenvectors of Covariance Matrix using Row, Column and Diagonal Mean Sequences, International Journal of Computer Applications (IJCA), Volume 3, Number 12, pp , July Published By FCS (Foundation of Computer Science, USA), [26] H.B.Kekre, Sudeep D. Thepade, Akshay Maloo, Image Retrieval using Fractional Coefficients of Transformed Image using DCT and Walsh Transform, International Journal of Engineering Science and Technology (IJEST), Volume 2, Number 4, 2010, pp [27] R. V. L. Hartley, "A more symmetrical Fourier analysis applied to transmission problems," Proc. IRE 30, pp ,

15 [28] Dr. Sudeep Thepade, Ph.D. Thesis, New Approached of Feature Vector Extraction for Content Based Image Retrieval, pp. C3-24 to C3-27, Supervisor Dr.H.B.Kekre, MPSTME, SVKM s NMIMS (deemed to be University), Mumbai, [29] H.B.Kekre, Sudeep D. Thepade, Archana A., Anant S., Prathamesh V., Suraj S., Kekre Transform over Row Mean, Column Mean and Both using Image Tiling for Image Retrieval, International Journal of Computer and Electrical Engineering (IJCEE), Volume 2, Number 6, October 2010, pp [30] H.B.Kekre, Sudeep D. Thepade, Archana Athawale, Anant S., Prathamesh V., Suraj S., Energy Compaction and Image Splitting for Image Retrieval using Kekre Transform over Row and Column Feature Vectors, International Journal of Computer Science and Network Security (IJCSNS), Volume:10, Number 1, January