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ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008 A Robust Digital Image Watermarking Scheme using Singular Value Decomposition (SVD), Dither Quantization and Edge Detection B.Chandra Mohan#, S.Srinivaskumar$, B.N.Chatterji* # Research Scholar, JNTU College of Engineering, Kakinada, Andhra Pradesh, India. $ Professor, ECE Dept, JNTU College of Engineering, Kakinada, Andhra Pradesh, India. * Former Professor, Dept of E & ECE, Indian Institute of Technology, Kharagpur, West Bengal, India. chandrabhuma@yahoo.co.in, samay_ssk2@yahoo.com, bnchatterji@gmail.com Abstract Significant Substitution (LSB) is a simplest technique in This paper presents a robust algorithm for digital image the spatial domain [3,4,5]. In LSB technique, the watermarking based on Singular Value Decomposition watermark is embedded by replacing the least significant (SVD) and Dither Quantization. The eigen matrix in the bits of the image data with a bit of the watermark data. singular value decomposition is explored for data There are many variants of this technique. The data embedding. The perceptibility of the watermarked image hiding capacity of these algorithms is high. However, is enhanced by embedding the watermark image in some these algorithms are hardly robust for various attacks and selected and most complex blocks of the host image. A prone to tamper by unauthorized users. Correlation based block is said to be a complex block, if the number of approach [6,7] is another spatial domain technique in edges in the block is more than a predefined threshold. which the watermark is converted to a PN sequence The proposed method is robust and the watermark image which is then weighted & added to the host image with a can survive to many image attacks like rotation, scaling, gain factor k. For detection, the watermark image is noise, JPEG compression, JPEG 2000 compression, low correlated with the watermark image. Watermarking in pass filtering, biplane removal, row column blanking, transform domain is more secure and robust to various row column copying, cropping, image tampering and attacks. However, the size of the watermark that can be gamma correction. Results are compared with an embedded is generally 1/16 of the host image. Image existing and recent method and found to be superior in watermarking algorithms using Discrete Cosine terms of the quality of the extracted watermark image Transform (DCT) [8,9], Discrete Wavelet Transform and resilience to attacks. The metric used to test the (DWT) [10,11,12,13], Singular Value Decomposition robustness of the proposed algorithm is the Normalized (SVD) [14,15,16,17,18,19,20,21,22] are available in the Cross correlation (NC). literature. The basic philosophy in majority of the transform domain watermarking schemes is to modify Keywords : Digital Image Watermarking, Singular Value transform coefficients based on the bits in watermark Decomposition, Dither Quantization. image. Most of the domain transformation watermarking schemes works with DCT and DWT. However Singular 1. Introduction Value Decomposition (SVD) is one of the most powerful Digital Watermarking is a process of embedding numerical analysis techniques and used in various information in the multimedia content (host or cover applications [23,24]. Gorodetski et al. used SVD domain image) for image authentication. An ideal watermarking for watermarking a 600x512 RGB image. They quantized system would embed an amount of information that could the Singular Value (SV) of each 4x4 block of R, G and B. not be removed or altered without making the cover The watermark is a 240x120 gray scale image. But, this object entirely unusable. Over the past few years digital is shown to resist only for JPEG compression. Liu and watermarking has become popular due to its significance Tan applied SVD to the entire host image. The in content authentication and legal ownership for digital watermark is a pseudo gaussian random number matrix multimedia data. A digital watermark is a sequence of weighed with appropriate scaling factor is added to the information containing the owner’s copyright for the diagonal matrix of SVs. The modified D (Diagonal multimedia data [1]. It is inserted invisibly in another matrix) is inserted back in the host image. This method is image so that it can be extracted at later times for the able to resist Gaussian Noise, Gaussian Low pass filter, evidence of rightful ownership. Available digital JPEG with 5% compression, rotation of 300 and cropping. watermarking techniques can be categorized into one of Chandra et al. proposed an algorithm based on the SVD the two domains, viz., spatial and transform, according to of both the host image and visual watermark. The the embedding domain of the host image [2]. Least singular values (SV) of the watermark are multiplied by a 17 ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008 scaling factor and added to the SV of the host image. The In section 2 SVD Transformation is discussed. The attacks used are JPEG (QF =25 and 10), and 3x3 low proposed method is introduced in section 3. In section 4 pass filter. But this method is non-blind in nature. In the experimental results are shown. The conclusions are 2002, Sun et al. Proposed an SVD and quantization given in section 5. based watermarking scheme where in D component with a diagonal matrix is explored for embedding. The basic 2. Singular Value Decomposition mechanism used is the quantization of the largest SVD is an algorithm of matrix transformation based on component with a fixed constant integer, called eigen vector. SVD is a mathematical tool used to analyze Quantization coefficient. A trade-off can be achieved matrices. In SVD, a matrix is decomposed into three between transparency and robustness by varying the matrices of same size. Let A be m x n matrix with m ≥ n. quantization coefficient. However, the method failed in One form of singular value decomposition of A is extracting the watermark with zero error rate. The A= UTDV. Here U and V are orthogonal and D is original watermark image and retrieved watermark image square diagonal. That is, UUT = Irank(A), VVT= Irank(A), U is are not exact. Later in 2005, Chang et al. Proposed a rank(A) x m, V is rank(A) x n and watermarking scheme based on SVD domain. Later in 2005 Chang et al. proposed a watermarking scheme ⎛σ 1 0 . . . 0 0 ⎞ based on SVD domain. They explored U matrix for ⎜ ⎟ watermark embedding. They used a 512x512 Lena, ⎜ 0 σ2 . . . 0 0 ⎟ Airplane and Baboon as host images and two watermark ⎜ . . . . . . . ⎟ images IEEE logo and CCU logo of 32x32 size. Here U ⎜ ⎟ D = ⎜ . . . . . . . ⎟ matrix is explored for data embedding. They modified the absolute difference between two rows of U matrix. ⎜ . . . . . . . ⎟ They identified that the positive relationships between ⎜ ⎟ the rows of U matrix is preserved even after JPEG ⎜0 0 0 0 0 σrank ( A) − 1 0 ⎟ ⎜ ⎟ compression. The attacks shown in their paper are only ⎝0 0 0 0 0 0 σrank ( A) ⎠ JPEG (QF=70), Gaussian Noise, Cropping, sharpening, (1) blurring and tampering. The watermarked image is of is a rank(A) x rank(A) diagonal matrix. These diagonal good quality. They embedded a 32x32 binary logo in a entries σi' s are called singular values of A and their 512x512 image. There are two major issues with Chang et al.’s method. The first one is, the watermark extraction number is equal to the rank of A. These singular values is not complete. The error rate between the original satisfy the relation watermark and extracted watermark is not zero. It is very σ 1 ≥ σ 2 ≥ σ 3......σrank ( A) > 0. (2) close to zero. That means, the Normalized correlation Each singular value specifies the luminance of an image coefficient is not ‘1’. If perfect extraction is required, layer while the corresponding pair of singular vectors robustness has to be sacrificed. Both robustness and specifies the geometry of the image. For majority of the perfect extraction (zero error rate) cannot be achieved attacks, the change in the largest singular value is very simultaneously. The reason for this can be attributed to small. the nature of U matrix elements, which are real numbers The concept of dither quantization was of magnitude less than ‘1’. Any modification of U matrix introduced to digital watermarking community by Chen values beyond the threshold value will affect the and Wornell. Dither quantizers are set of basic extracted watermark. The second issue is in the process quantizers. Each quantization cell in the set is of complex block selection. A block is said to be a constructed from a basic quantizer. The basic quantizer is complex block if the block’s diagonal matrix contains shifted to get the reconstruction point. The shift depends more number of non zero coefficients. It has been on the watermark bit. The basic quantizer is a uniform observed that for majority of the blocks, the number of scalar quantizer with a fixed step size t. A quantizer in non zero coefficients is same. So, it is difficult to the ensemble consists of two quantizers shifted by t/2 identify a block as complex block based on the number of with respect to each other. In the proposed algorithm the non zero coefficients in the diagonal matrix of the block largest singular values of each 8 x 8 block are quantized in the host image. In this paper, we propose an using either quantizer 1 or quantizer 2 which depends on algorithm which addresses both the issues. The first issue watermark bit to be embedded. The quantized value is the is resolved by exploring the diagonal matrix using dither center of the quantizer. quantization [25] and the second one is resolved by identifying a complex block based on the number of edges in a block. We define a block as a complex block if 3. The Proposed Scheme the block contains more number of edges. So an edge In the proposed scheme diagonal matrix (D) is used for detection algorithm [26] is applied for this purpose prior watermark embedding. Any modification of D to watermark embedding. The proposed method is highly component degrades the perceptibility of the robust and the perceptibility of the image is better than watermarked image. To improve perceptibility, the Chang et al.’s method. In terms of robustness also our watermark is embedded in some selected complex blocks method is superior to Chang et al.’s method as our only. The strategy for selecting a block is based on the method can survive to many attacks. number of edges in a block. A block is qualified as a complex block if the number edges in a block is greater 18 ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008 than some predefined threshold. The watermark 5. A look-up table is formed with the entries embedding algorithm is as follows: [[dmin-t dmin],[dmin dmin+t],…. …..[dmax dmax+t]] 1. Cany’s edge detection algorithm is applied to the entire host image of size 512x512. [6] 2. In each 8x8 non-overlapping block, number of edges is 6. The dlarge value of each selected block is computed. checked for its position in the look-up table. 3. Blocks are arranged based on descending order of 7. The watermark bit is ‘1’ if dlarge lies in the the number of edges in each block. The first 1024 dl + dh interval dl to . (32x32) blocks having more number of edges are 2 selected and indexed for watermark embedding. [7] 8. The watermark bit is ‘0’ if dlarge lies in the 4. SVD transformation is applied on each individual dl + dh selected block. interval to dh 2 5. A matrix Dlarge, is formed with largest singular values [8] of each block. The size of the Dlarge is 32 x32. The embedding methodology and extraction technique are summarized in the flow chart 6. The maximum and minimum values of Dlarge are (Figure 1(a) & Figure 1(b)). represented as dmax and dmin respectively. The range [dmax dmin] is divided into uniform intervals [dl dh] of Host Image width t. [[dmin-t dmin], [dmin dmin+t],…. ……..[dmax dmax+t]] Apply Edge Detection [3] 7. For each selected block, identify the interval j to Non-overlapping which the block belongs, based on its dlarge value, block Decomposition and modify it as: dl + dh Sorting of selected Blocks dl + dlarge = 2 , if the watermark bit is ‘1’ SVD (Block wise) 2 U, D, V Decomposition [4] dl + dh 1 0 dh + dlarge = 2 , if the watermark bit is ‘0’ Watermark Bit 2 [5] Modify Modify Dlarge as in Eq [ 4] Dlarge as in Eq [5] 8. After the modification of dlarge values, inverse SVD is applied on each selected block to get the watermarked image. Inverse SVD The watermark extraction algorithm is as follows: Watermarked Image 1. The watermarked image is partitioned into 8 x 8 non overlapping blocks. Figure 1.(a) Embedding Methodology 2. Blocks having number of edges greater than the predefined threshold are identified. 3. SVD transformation is applied on each selected 4. Experimental Results To test the robustness of the proposed scheme, block. experiments are conducted using host image ‘Lena’ as shown in Figure 2. The size of the host image is 512 x 4. A matrix Dlarge is formed with the dlarge values of the individual D matrices. 512. The watermark image is of 32 x 32 size which is a logo having the letters ‘JNTU’ as shown in Figure 3. In Figure 4(a) watermarked LENA is shown and in Figure 4(b) tampered Lena is shown. 19 ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008 experiment, first the watermarked image is reduced from 512x512 size to 256x256. By using bicubic interpolation Watermarked Image its dimensions are increased to 512x512. The extracted watermark as shown in Figure 8(b) is clearly visible. In row column blanking attack, a set of rows and columns Identification of Watermarked Blocks are deleted. In this experiment 10,30,40,70,100,120 &140 rows and columns are removed. In row-column copy attack a set of rows and columns are copied to the SVD decomposition (On Selected blocks) adjacent or random locations. In this experiment 10th row is copied to 30th row, 40 to 70, 100 to 120 and 140th row is copied to 160th row. Extracted watermarks from row Dlarge Matrix Formation column blanking and copying attack are shown in Figure 8(c) and Figure 8(d). The watermarked image is attacked Look-up Table by salt & pepper noise with a noise density of Formulation 0.001,.002,0.003 and 0.004. The extracted watermarks are shown in Figure 9. All the extracted watermarks are clearly visible indicating the proposed method’s Comparison of dlarge resilience to noise attack. But, Chang et al.’s method is with Look Table.Eq [7,8] superior to our method for noise and row column blanking attack. Finally, the proposed algorithm also is Watermark Extraction resistant to biplane removal, image tampering, and gamma correction, as shown in Figure 10 and Figure 11. The Normalized Cross correlation value ‘NC’ is used as a Figure 1.(b) Extraction Methodology metric to compare the robustness and summarized in Table 1. All the attacks except image tampering and JPEG2000 attack were tested using MATLAB 5.3. JPEG2000 attack is tested using MORGAN JPEG2000 tool box and image tampering is done with PAINTBRUSH. Various attacks used to test the robustness of the watermark are JPEG2000, JPEG compression, rotation, resizing, low pass filtering, median filtering, cropping, row column blanking, row column copying, salt & pepper noise, bit plane removal, image tampering and gamma correction. The perceptibility of the watermarked image is excellent with a PSNR of 47.02 dB. Figure 2. 512x512 Lena (Host Image) The extracted watermarks after applying various attacks are shown in Figure 5 to Figure 11. The watermarked image is rotated by 100, 200, 400 and 600 to the right and then rotated back to their original position using bilinear interpolation. The recovered watermark shows good Figure 3. Watermark Image similarity with the original watermark image as shown in Figure 5. The watermarked image is compressed using lossy JPEG compression. The index of the JPEG compression ranges from 0 to 100, where 0 is best compression and 100 is best quality. The reconstructed watermarks for various indices are shown in Figure 6. The proposed scheme works well even for extreme compression. Similarly, JPEG2000 compression is used to test the robustness with varying quality factor. The results are extremely good indicating that the proposed (a) (b) method is able to survive after JPEG2000 compression. Figure 4(a). 512x512 Watermarked Lena (b) Tampered This fact is evident from Figure 7. For low pass filtering Lena attack a 3x3 mask consisting of 0.9 intensity values is used. The recovered watermark image as shown in Figure 8(a) is distinguishable, showing its resilience to low pass filtering attack. Resizing operation first reduces or 100 200 400 600 increases the size of the image and then generates the (a) (b) (c) (d) original image by using an interpolation technique. This Figure 5. Extracted watermarks: Rotation attack operation is a lossy operation and hence the watermarked image also looses some watermark information. In this 20 ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008 Salt&Pepper 0.9516 0.8257 Noise 0.9368 0.7374 30% 40% 60% 100% (Noise Density) 0.9148 0.6472 Figure 6. Extracted watermarks: JPEG Compression .1%,.2%,.3%,.4% 0.8165 0.5441 Row-Column blanking 10,30,40,70,100, 0.9502 0.5889 120, 5% 10% 30% 50% Figure 7. JPEG 2000 Compression with various Quality factors Row-Column Copying 10-30,40-70,100- 0.7678 0.7781 120,40-160 rows (a) (b) (c) (d) and columns are Figure 8. (a) Low pass filtering attack (b) Resizing copied (c) Row column blanking (d) Row column copying Cropping 1/16th top left 0.5058 0.8941 corner 0.9802 1.0000 Bit Plane Removal 0.001 0.002 0.003 0.004 1st , IInd & IIIrd 0.9544 0.9009 Figure 9. Salt & pepper noise with various noise densities 0.4354 0.8076 Image Tampering 0.9353 0.9907 Gamma Correction 0.1927 0.56 1st plane 2nd plane 3rd plane Gamma=0.9 Figure 10. Bit plane Removal 5. Conclusions In this paper, a watermarking scheme based on Singular Value Decomposition, dither quantization and edge (a) (b) (c) detection is proposed. The proposed method is highly Figure 11 (a). Gamma correction (gamma=0.9) robust and can survive many image processing attacks. (b) Cropping (1/16th top left corner) (c) Image Tampering The quality of the watermarked image is good in terms of perceptibility and PSNR (47.02dB). The proposed algorithm is shown to be robust to rotation, low pass Table 1. Performance Comparison with Chang et al.’s filtering, resizing, JPEG compression, JPEG2000 Method compression, salt&pepper noise attack, row column blanking, row column copying attack, cropping, bit plane NC Value NC Value removal, image tampering and gamma correction. For Type of Attack Chang et Proposed salt & pepper noise attack and row column blanking al.’s Method Method attack, Chang et al.’s method is superior to our method. 0.5333 0.7422 The proposed method is superior to Chang et al.’s Rotation 0.6874 0.4988 method in terms of NC value of the extracted watermarks. (in degrees) 0.4712 0.5889 PSNR of the watermarked image is comparable to Chang (10,20,40,60) 0.4856 0.6031 et al.’s method. In our future work, we will investigate Low pass in embedding multiple watermarks in D and U matrices Filtering 0.0265 0.4890 so that the watermark image can survive to more number 3x3 Kernel of image attacks. Resizing 0.8155 0.2492 6. References 512-256-512 JPEG 0.1616 0.4732 [1] N.F. Johnson and S.C.Katezenbeisser, A survey Compression 0.0919 0.9245 of steganographic techniques in Information (Quality Factor) Techniques for steganography and digital 0.1729 1.0000 30,40,60,100 watermarking, Eds. Northwood, Artech House, 0.9953 1.0000 December, 1999. JPEG2000 0.3323 0.6502 [2] Mohamed Kallel and Mohamed Salim Compression 0.2819 0.9953 Bouhlel and Jean-Christophe Lapayre Improved (Quality Factor) 0.8765 1.0000 Tian’s Method for Medical Image Reversible 5,10,30,50. 0.8989 1.0000 Watermarking GVIP Journal, Volume 7, Issue 2, pp.1-5, 2007. 21 ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008 [3] I.J.Cox, J.Kilian, T.Leighton and T.Shamoon, of 45th IEEE Midwest Symposium on Circuits and Secure Spread Spectrum Watermarking for Systems, Tulsa, OK, pp. 264-267, 2002. Multimedia, IEEE Transactions on Image [19] E.Ganic and A.M. Eskiciogulu et al. Robust SVD- Processing, 6(12), 1673-1687, December, 1997. DCT domain Image Watermarking for copyright [4] C.I.Podilchuk and E.J.Delp, Digital Watermarking: Protection: Embedding data in All Frequencies. Algorithms and Applications, IEEE Signal 13th European Signal Processing Conference Processing Magazine, pp.33-46, July 2001. (EUSIPCO 2005), Antalya, Turkey, September 4- [5] I.J.Cox, M.L.Miller, and J.A. Bloom, “Digital 8, 2005. Watermarking”, Morgan Kaufmann Publishers, [20] E.Ganic and A.M. Eskiciogulu et.al., Robust 2002. embedding of Visual Watermarks using DWT- [6] Mohamed Kallel and Mohamed Salim SVD Journal of Electronic Imaging, October- Bouhlel and Jean-Christophe Lapayre A new December, 2005. Multiple Watermarking Scheme in Spatial Field [21] Sun, R., Sun, H., Yao, T., A SVD and quantization GVIP Journal, Volume 7, Issue 1, pp.37-42, 2007. based semi-fragile watermarking technique for [7] Mehul, S. Raval and Priti P. Scalar Quantization image authentication. Proc. IEEE International Based Multiple Patterns Data Hiding Technique Conf. Signal Process. 2. 1592-95, 2002. for Gray Scale Images, GVIP Journal, Volume 5, [22] Y. Yongdong Wu. On the Security of an SVD Issue 9, pp.55-61, December 2005. based Ownership Watermarking IEEE transactions [8] Barni, F. Bartolini and A. Piva. A DCT domain on Multimedia, Vol 7. No.4, August, 2005. system for robust image watermarking. IEEE [23] H.C.Andrews and C.L.Patterson, Singular value Transactions on Signal Processing. 66, 357-372, Decomposition (SVD) Image Coding, IEEE 1998. Transactions on Communications 24(4), April [9] W.C.Chu, DCT based image watermarking using 1976, pp.425-432. sub sampling. IEEE Trans Multimedia 5, 34-38, [24] P.Waldemar and T.A.Ramstad, Hybrid KLT-SVD 2003. Image Compression, IEEE International Conf on [10] M.Barni, M., Bartolini, F., V., Piva, A., Improved Acoustics, Speech and Signal Processing, Vol.4, wavelet based watermarking through pixel-wise Munich, Germany, April 21-24, 1997, pp.2713- masking. IEEE Trans Image Processing 10, 783- 2716, 1997. 791, 2001. [25] Brian Chen and G.W.Wornell, Digital [11] Y. Wang, J.F.Doherty and R.E.Van Dyck, A watermarking and information embedding using wavelet based watermarking algorithm for dither modulation. Proceedings of the IEEE ownership verification of digital images, IEEE workshop on Multimedia Signal Processing Transactions on Image Processing, Volume 11, (MMSP-98), Redondo Beach, CA, December No.2, pp.77-88, February 2002. 1998. [12] Karras D.A. A Second Order Spread Sprectrum [26] Canny, John. A Computational Approach to Edge Modulation Scheme for Wavelet Based Low Error Detection, IEEE Transactions on Pattern Analysis Probability Digital Image Watermarking., GVIP and Machine Intelligence,. Vol. PAMI-8, No. 6, pp. Journal, Volume 5, Issue 3, February 2005. 679-698, 1986. [13] G.S.El-Taweel and H.M. Onsi and M.Samy and M.G. Darwish. Secure and Non-Blind Watermarking Scheme for Color Images Based on DWT, GVIP Journal, Volume 5, Issue 4 , pp. 1-5, April 2005. [14] Chin-Chen Chang, Piyu Tsai and Chia-Chen Lin, 2005 SVD based digital image watermarking scheme. Pattern Recognition Letters 26, 1577- 1586, 2005. [15] Chung, K.L., Shen, C.H., Chang, L.C., A Novel SVD and VQ-based image hiding scheme. Pattern Recognition Letters, 22, 1051-58, 2001. [16] R.Liu, T.Tan, An SVD-based watermarking scheme for protecting rightful ownership. IEEE Trans. Multimedia, vol.4, no.1, pp, 121-128, 2002. [17] V. I. Gorodetski, L. J. Popyack, V. Samoilov and V. A. Skormin, SVD-based Approach to Transparent Embedding Data into Digital Images, International Workshop on Mathematical Methods, Models and Architectures for Computer Network Security (MMM-ACNS 2001), St. Petersburg, Russia, May 21-23, 2001. [18] D. V. S. Chandra, Digital Image Watermarking Using Singular Value Decomposition, Proceedings 22 ICGST-GVIP Journal, ISSN: 1687-398X , Volume 8, Issue 1, June 2008 Biographies B.Chandra Mohan is currently B.N.Chatterji is a former working as Professor in ECE Professor in E&ECE Department, Bapatla Engineering Department IIT, Kharagpur. He College, Bapatla, India. He is received B.Tech. and Ph.D. working towards his Ph.D.at (Hons.) from E&ECE JNTU College of Engineering, Department IIT, Kharagpur in Kakinada, India. He received his 1965 and 1970, respectively. M.Tech from Cochin University He has served the Institute of Science & Technolgoy, under various administrative Cochin, India. He has fifteen capabilities as Head of years experience of teaching undergraduate students and Department, Dean (Academic), etc. He has chaired many post graduate students.His research interests are in the international and national symposium and conferences areas of image watermarking, and image compression. organized in India and abroad, apart from organizing 15 short term courses for Industries and Engineering college teachers. He has guided 35 Ph.D. scholars. Presently, he S. Srinivas Kumar is currently is active in research by guiding three research scholars. Professor and HOD in ECE He has published more than 150 papers in reputed Department, JNTU College of international and national journals apart from authoring Engineering, Kakinada, India. three scientific books. His research interests are low-level He received his M.Tech. from vision, computer vision, image analysis, pattern Jawaharlal Nehru Technological recognition and motion analysis. University, Hyderabad, India. He received his Ph.D. from E&ECE Department IIT, Kharagpur. He has nineteen years experience of teaching undergraduate and post- graduate students and guided number of post-graduate theses. He has published 15 research papers in National and International journals. Presently he is guiding five Ph.D students in the area of Image processing. His research interests are in the areas of digital image processing, computer vision, and application of artificial neural networks and fuzzy logic to engineering problems. 23

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