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Performance Enhancement of Fractional Coefficients of the Discrete Hartley Transform for Palm Print Recognition Dr. H. B. Kekre, Dr. Tanuja K. Sarode and Aditya A. Tirodkar ABSTRACT—One of the most rapidly growing techniques in Biometric Identification is that of Palm Print Recognition. One commonplace technique for this purpose is that of applying Discrete Fourier-related Transforms to Palm Prints and then using these transformed images for comparison. The Discrete Hartley Transform is one such integral transform closely related to the Fourier Transform. As compared to generally used transforms such as the Discrete Cosine Transform, it is seen that the Discrete Hartley Transform performs poorly especially showing a decrease in accuracy when it is applied in the form of fractional coefficients. When applied as fractional coefficient, other transformations are found to show vast improvements in accuracy. Our paper provides a solution to this problem based on an analysis of the transformed image obtained by using the Discrete Hartley Transform. We then test this hypothesized solution on a database of over 8000 Palm Print images, calculating and comparing accuracy values for different fractional coefficients of the Palm Print images obtained using the DCT, the original DHT coefficient extraction method and our improvised technique for the same, along with a quantitative comparison for processing time and provide inferences based on our findings. Keywords— Palm Print, Biometrics, DCT, Hartley, Fractional Coefficients.

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1 INTRODUCTION

T

ransform coding is currently a stalwart in the world of image/video processing applications. It is seen that in most images, pixels have a high amount of correlation with their neighbouring pixels. In video, this feature is seen in each subsequent frame [13]. Thus, the aforementioned correlation can be applied in order to extricate details about pixels from their neighbours. Each individual pixel contains a rather small amount of detail, generally limited to a small numeric value. Thus, one can obtain large amounts of information about an entire image by isolating its details to a certain number of pixels, each able to tell information about subsequent surrounded pixels. An entire image matrix can thus be transformed into a compressed matrix where all the required information is stored in certain discrete blocks of data. The Discrete Fourier Transform is one of the oldest and most widely used transform. It is able to remove an entire image’s details and separate it into real and complex components [1]. One of the more undesirable features of a Discrete Fourier Transform is its ability of transforming an image into both a real and complex domain. Thus, even a real input is converted into an output having both real as well as complex values. The Discrete Hartley Transform is analogous to the Discrete Fourier Transform in both its ————————————————

Dr. H. B. Kekre is Sr. Professor in Computer Engineering Department with the Mukesh Patel School of Technology Management and Engineering, NMIMS University, Bandra (W), Mumbai-50, India. Dr. Tanuja K. Sarode is Asst. Professor in Computer Engineering Department with the Thadomal Shahani Engineering College, Bandra (W), Mumbai-50, India. Mr. Aditya A. Tirodkar Kekre is B.E. Computer Engineering Student with the Thadomal Shahani Engineering College, Bandra (W), Mumbai-50, India.

applications as well as in the principle of obtaining data in a discrete, periodic form. Also, applying the DHT on an image does not cause the kind of loss seen in doing the same with a D.F.T. and its inverse is the DHT itself [2] [6]. It is factors such as this that have led to it being used in areas such as image and signal processing as well as crystallography, interferometry etc. [1] A competing transform can be found in the Discrete Cosine Transform. The DCT like other transforms tries to remove any correlation pixels might have with their neighbours and exploiting this to compress the entropy of the image into one particular corner. The DCT is found to be extremely efficient, especially in pattern recognition and its feature of clubbing all the entropy in one corner enables it to be subjected to fractional coefficients. In fractional coefficients, we crop out that part of the image matrix that has the highest store of entropy values. It is seen that this decrease in matrix size, corresponds to an increase in pattern recognition accuracy till a threshold [4]. The DCT is the preferred transform in areas such as JPEG based image transform coding. However, it is seen that the DHT has an appreciable amount of hardware saving and much less computations as compared to the DCT [5]. Yet, it is not used to as high an extent as the DCT, especially in the field of pattern recognition. In the field of Biometrics, to which this paper relates to has studies which site a lower amount of accuracy seen in the usage of the Discrete Hartley Transform for the purpose of biometric recognition. One can dissect the reason for this lack of accuracy by analysing the way the DHT works on an image matrix and then figuring out a solution for the same.

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2 LITERATURE REVIEW The Hartley Transform has been subject to a lot of research ever since the Discrete Hartley Transform was first proposed in 1983 by Robert Bracewell expanding upon the continuous Hartley Transform by Robert Hartley [3]. Our study involves the application of the Hartley Transform in Biometrics, particularly in the field of Palm Print Recognition. Palm Print recognition generally involves the transformation of an image into a transformed Feature Vector [4]. The image is then compared with a Training Set of Images and the best match is obtained by calculating the minimum mean square error. These same techniques have been used in many other areas such as Face Recognition and Knuckle Recognition. A cited study [4] in Palm Print Recognition has provided conclusive evidence that the Discrete Hartley Transform is not as efficient with respect to recognition as compared to other transforms such as Slant, Walsh and DCT etc. One particular research observation is that the Hartley Transform performs better at 100% fractional coefficient or with no cropping that it does at any other value. Thus, it is seen that the image is not found to give any increase in results when fractional coefficients are taken, something generally not seen in the outputs obtained after applying other transforms. One may surmise that since the accuracy with fractional coefficients is found to be decreasing, there is a chance that the wrong parts of the images may be getting cropped. Generally, fractional coefficients are obtained in the manner shown in Figure 1 with respect to the original image, from the left hand side, top corner [14].

256

256

Figure 1. The coloured regions correspond to the fractional coefficients cropped from the original image, seen in black.

3 PROPOSED SOLUTION Before showing the proposed solution, let us first understand the implementation procedure. A database of 8000 palm print images of the right hand of 400 people, obtained from the Honkong Polytechnic University [7] was used for for checking the efficiency of the Hartley Transform. For each person, 10 prints were taken one month after the initial 10 were taken. The Regions of Interest were extracted from these Palm Print Images [8][9][10][11][12].The entire identification procedure was done in MATLAB R2010a. One crucial step was the application of Histogram Equalization on each image as it was seen to increase the accuracy. Without it, the accuracy was found to be 78% whereas with the Histogram Equalization, it was found to increase to over 92%. Thus, in our algorithm we have carried out the following steps:

4 ALGORITHM & RESULTS Step 1:

For every image from the Training set (Consisting of 4000 images) and perform Histogram Equalization on it. Step 2: Apply the Discrete Hartley Transform on it. Now, this image is to be compared against a training set of 4000 images. These images constitute the images in the database that were taken a month later. Step 1: Obtain the Image Matrix for all images in the training set and perform Histogram Equalization on it. Step 2: Apply the Discrete Hartley Transform on each Image. Step 3: Calculate the mean square error between each Image in the Training set and the query image. If partial energy coefficients are used, calculate the error between only that part of the images which falls inside the fractional coefficient. The image with the minimum mean square error is the closest match. In this fashion, we checked for all 4000 images that were taken one month before and without using histogram equalization and applying DCT, obtained an accuracy of 78.4%. With Histogram Equalization, we obtained an accuracy of 94.45% for all images when a fractional coefficient of 0.0061 or 20x20 on a 256x256 image was applied . However, when the Hartley Transform was applied, we found the accuracy to diminish to 86%. This coincided with the findings in [4] that the Hartley tranform gave a lower accuracy. At 256x256, both DCT and DHT were found to give the same accuracy of 92%. A comparison of the values obtained for both transforms is given in Table 1.

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Table 1: Comparison of Accuracy values at Different Fractional Coefficient Values for the DHT and DCT when the Coefficient is removed from the Top Left Corner as in Figure 1.

Figure 2 : Graphs Comparing the percentage Accuracy for palmprint using DCT and DHT.

It is rather apparent from the graph in Figure 2 that the accuracy obtained from the DHT is much lower than that from DCT; in some cases over 8%. Even though one can state that this is because of the transform itself, on inspection of the faculties of the Hartley Transform in relation to the Discrete Cosine Transform, one highly important fact becomes clear: The fundamenal equation for a Hartley Transform is given below: (1) It is clear from Equation (1) that the Hartley transform polarizes the entropy of the entire image into the four corners of the image matrix [13]. The DCT Transform on the other hand, polarizes all the entropy in only one corner. This is apparent in the images in Figure 3.

(a)

(b)

(c)

Figure 3: In (a) we see the Histogram Equalized Image of a Query Palm Print image. In (b) we see its DCT Transformed Image and (c) represents its DHT transformed Image. The algorithm above for obtaining the fractional coefficient was tested on the values in each corner of the image matrix seen in Figure 4. By rotating the transformed image. On checking for each single corner, the maximum accuracy results were obtained as seen in Table 2:

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Table 2: Accuracy Values for DHT transformed images applied on Fractional Coefficients in each corner of the image isolated

If one now considers the usual method by which the fractional coefficients are obtained [14], it is rather obvious that the amount of accuracy is sure to decrease for the Discrete Hartley Transform, since the entropy polarization in the DHT transform is divided into the four corners of the matrix as compared to the DCT Thus, analysis with

traditional fractional coefficients does not yield that good an accuracy. Hence, a newer strategy for obtaining fractional coefficients is required. This modification for obtaining the fractional coefficient is highlighted in Figure 3:

Figure 4: The above image illustrates the method proposed for obtaining fractional (partial energy) coefficients. Each similar colored square in each corner is concatenated just as it is oriented with the others. The resulting image matrix is thus twice as much in order as the fractional coefficient obtained from any corner as seen in Figure 5 (b). Thus, instead of removing the fractional coefficient from the left hand side, top corner as in Figure ; we now remove the fractional coefficient by extracting four equal sized portions from each corner and then concatenating them to form one whole image. This image is then used in

(a)

the comparison Step 3 to calculate the mean square error. This results in us getting a set of images of a much smaller size, corresponding to the fractional coefficient as seen in Figure 5.

(b)

Figure 5: (a) Represents the DHT of a Histogram Equalized Palm Print Image as seen in Figure 3 (c) and (b) represents its concatenated fractional equivalent as elucidated in Figure 4

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Table 3: A Comparison of the Accuracies obtained from Fractional Coefficients using the newer concatenated matrix method (left) and the normal way (right) for DHT.

Thus, it is seen that for a corresponding resolution seen for an image with the fractional coefficients removed as in Figure, when the fractional coefficients are removed using the newer technique shown in Figure, it yields a much

larger rate of accuracy, comparable to that obtained from the DCT Transform. A graph comparing the three is given in Figure 6:

Figure 6: comparing the accuracy values obtained from for DCT, DHT and Concatenated Matrix Method for the DHT. Table 4: Accuracy Values for Palm Print Identification obtained from DCT, the Concatenated DHT Matrix Method and the normal DHT method

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It is to be noted that in the case of the proposed, concatenated Hartley fractional coefficients, the size of the matrix for each fractional coefficient is of an order 2N as compared to the coefficient matrix for DCT and the old Hartley coefficient. To check just how much this affects processing time, we run all three algorithms comparing 4000 training images with 4000 query images at a fractional coefficient of 32x32. For the newer solution technique, this corresponds to parts of 16x16 removed from each corner. For DCT and the older fractional coefficient, it means selecting 32x32 from the top left corner.Also, the usage of this transform provides us an accuracy comparable to the Discrete Cosine Transform and also provides us with a decrease in processing time and matrix size, one of the requisite characteristics for a good Biometric and Palm Print Recognition Technique.

6 CONCLUSION Thus, we have obtained empirical data by carrying out tests related to the efficiency and accuracy of our proposed algorithm for obtaining fractional coefficients from palm print images that have the Discrete Hartley Transform applied on them. The results show that the accuracy of the Discrete Hartley Transform increases vastly by over 8% in certain cases and is comparable with the accuracy obtained from the Discrete Cosine Transform. On applying further contrasting techniques, the accuracy is found to further increase. All this also results in a decrease in processing time. Thus, we can say that when the newer algorithmic technique for obtaining fractional coefficients is used, the accuracy of the Hartley transform increases to a level where it can be found to be comparably useful as the Discrete Cosine Transform, thus refuting previous studies which stated a lack of comparable accuracy with the Hartley Transform.

REFERENCES [1] John D. Villasenor “Optical Hartley Transform” Proceedings of the IEEE Vol. 82 No. 3 March 1994 [2] R. N. Bracewell, “The Hartley Transform” New York: Oxford Univ. Press, 1986. [3] R.V.L. Hartley “A More Symmetrical Fourier Analysis Applied to Transmission Problems” Proceedings of the I.R.E. March 1942 [4] H. B. Kekre, Sudeep D. Tepade, Ashish Varun, Nikhil Kamat, Arvind Viswanathan, Pratic Dhwoj. “Performance Comparison of Image Transforms for Palm Print Recognition with Fractional Coefficients of Transformed Palm Print Images.” I.J.E.S.T. Vol.2(12), 2010, 7372-7379. [5] Vijay Kumar Sharma, Richa Agrawal, U. C. Pati, K. K. Mahapatra “2-D Separable Discrete Hartley Transform Architecture for Efficient FPGA Resource” Int’l Conf. on Computer & Communication Technology [ICCCT’ 10] [6] R. P. Millane “Analytic Properties of the Hartley Transform and their Implications” Proceedings of the IEEE, Col. 82, No. 3 March 1994 [7] PolyU 3D Palmprint Database, http://www.comp.polyu.edu.hk/~biometrics/2D_3D_Palmprint.htm [8] W. Li, D. Zhang, L. Zhang, G. Lu, and J. Yan, "Three Dimensional Palmprint Recognition with Joint Line and Orientation Features", IEEE Transactions on Systems, Man, and Cybernetics, Part C, In Press. [9] W. Li, L. Zhang, D. Zhang, G. Lu, and J. Yan, “Efficient Joint 2D and 3D Palmprint Matching with Alignment Refinement”, in: Proc. CVPR 2010. [10] D. Zhang, G. Lu, W. Li, L. Zhang, and N. Luo, "Palmprint Recognition Using 3-D Information", IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, Volume 39, Issue 5, pp.

505 - 519, Sept. 2009. [11] W. Li, D. Zhang, and L. Zhang, "Three Dimensional Palmprint Recognition", IEEE International Conference on Systems, Man, and Cybernetics, 2009. [12] D. Zhang, G. Lu, W. Li, L. Zhang, and N. Luo, "Three Dimensional Palmprint Recognition using Structured Light Imaging", 2nd IEEE International Conference on Biometrics: Theory, Applications and Systems, BTAS 2008, pp. 1-6 [13] Syed Ali Khayam., “The Discrete Cosine Transform (DCT): Theory and Application.” ECE 802-602: Information Theory and Coding. Seminar 1. [14] H. B. Kekre, Sudeep .D. Thepade, Akshay Maloo“Performance Comparison of Image Retieval Using Fractional Coefficients of Transformed Image Using DCT, Walsh, Haar and Kekre’s Transform” International Journal of Image Processing (IJIP) Volume (4): Issue (2)

Author Biographies Dr. H. B. Kekre has received B.E. (Hons.) in Telecomm. Engineering. from Jabalpur University in 1958, M.Tech (Industrial Electronics) from IIT Bombay in 1960, M.S.Engg. (Electrical Engg.) from University of Ottawa in 1965 and Ph.D. (System Identification) from IIT Bombay in 1970 He has worked as Faculty of Electrical Engg. and then HOD Computer Science and Engg. at IIT Bombay. For 13 years he was working as a professor and head in the Department of Computer Engg. at Thadomal Shahani Engineering. College, Mumbai. Now he is Senior Professor at MPSTME, SVKM’s NMIMS. He has guided 17 Ph.Ds, more than 100 M.E./M.Tech and several B.E./ B.Tech projects. His areas of interest are Digital Signal processing, Image Processing and Computer Networking. He has more than 300 papers in National / International Conferences and Journals to his credit. He was Senior Member of IEEE. Presently He is Fellow of IETE and Life Member of ISTE Recently seven students working under his guidance have received best paper awards. Currently 10 research scholars are pursuing Ph.D. program under his guidance.

Dr. Tanuja K. Sarode has Received Bsc.(Mathematics) from Mumbai University in 1996, Bsc.Tech.(Computer Technology) from Mumbai University in 1999, M.E. (Computer Engineering) degree from Mumbai University in 2004, Ph.D. from Mukesh Patel School of Technology, Management and Engineering, SVKM’s NMIMS University, Vile-Parle (W), Mumbai, INDIA. She has more than 11 years of experience in teaching. Currently working as Assistant Professor in Dept. of Computer Engineering at Thadomal Shahani Engineering College, Mumbai. She is life member of IETE, member of International Association of Engineers (IAENG) and International Association of Computer Science and Information Technology (IACSIT), Singapore. Her areas of interest are Image Processing, Signal Processing and Computer Graphics. She has more than 100 papers in National /International Conferences/journal to her credit. Aditya A. Tirodkar is currently pursuing his B.E. in Computer Engineering from Thadomal Shahani Engineering College, Mumbai. Having passionately developed a propensity for computers at a young age, he has made forays into website development and is currently pursuing further studies in Computer Science, looking to continue research work in the field of Biometrics.