ff957e13-3130-4e21-a333-3970a3f17eac20211127055353821naun:naunmdt@crossref.orgMDT DepositInternational Journal of Mathematics and Computers in Simulation1998-015910.46300/9102http://www.naun.org/cms.action?id=2826329202132920211510.46300/9102.2021.15https://www.naun.org/cms.action?id=23312Image Representation Method Based on Complex Wavelet Transform and Phase Congruency, with Automatic Threshold SelectionT.ArathiDepartment of Computer Science & Engineering Amrita Vishwa Vidyapeetham Coimbatore, IndiaLathaParameswaranDepartment of Computer Science & Engineering Amrita Vishwa Vidyapeetham Coimbatore, IndiaImage representation is an active area of research with increasing applications in military and defense. Image representation aims at representing an image with lesser number of coefficients than the actual image, without affecting the image quality. It is the first step in image compression. Once the image is represented by using some set of coefficients, it is further encoded using various compression algorithms. This paper proposes an adaptive method for image representation, which uses Complex Wavelet transform and the concept of phase congruency, where the number of coefficients used for image representation depends on the information content in the input image. The efficiency of the proposed method has been assessed by comparing the number of coefficients used to represent the image using the proposed method with that used when Complex Wavelet transform is used for image representation. The resultant image quality is determined by computing the PSNR values and Normalized Cross Correlation. Experiments carried out show highly promising results, in terms of the reduction in the number of coefficients used for image representation and the quality of the resultant image.1127202111272021798314https://www.naun.org/main/NAUN/mcs/2021/a282002-014(2021).pdf10.46300/9102.2021.15.14https://www.naun.org/main/NAUN/mcs/2021/a282002-014(2021).pdfEric W. Weisstein, “Fourier Transforms” From Mathworld-a Wolfram Web Resource. http://mathworld.wolfram.com/FourierTransforms.html. M. Sifuzzaman1, M.R. Islam1 and M.Z. Ali, “Application of Wavelet Transform and its Advantages Compared to Fourier Transform”, Journal of Physica Sciences, Vol. 13, Pages 121-134, 2009. 10.1109/msp.2005.1550194I. W. Selesnick, R. G. Baraniuk, and N. G. Kingsbury, "The dualtree complex wavelet transform,” IEEE Signal Processing Magazine, vol. 22, no. 6, pp. 123–151, November 2005. P. D. Kovesi. A dimensionless measure of edge significance from phase congruency pages calculated via wavelets. International First New Zealand Conference on Image and Vision Computing, Auckland, August 1993. 10.1109/tip.2006.882016Wei Hong, John Wright, Kun Huang, Yi Ma, Multi-Scale Hybrid Linear Models for Lossy Image Representation. IEEE Transactions on Image Processing, 2006. 10.1016/j.image.2003.09.001Deepak S. Turaga, Yingwei Chen, Jorge Caviedes, “No reference PSNR estimation for compressed pictures, Signal Processing: Image Communication, Elsevier, Vol. 19, Pages: 173-184, 2004. Tania Stathaki, “Image Fusion: Algorithms and Applications”, Academic Press, 2008 edition. Felix Fernandes, ‘Directional, Shift-insensitive, Complex Wavelet Transforms with Controllable Redundancy’, PhD Thesis, Rice University, 2002. Dr. Salih Husain Ali & Aymen Dawood Salman, Image Compression Based on 2D Dual Tree Complex Wavelet Transform (2D DT-CWT), Enggineering & Technical Journal, Vol. 28, No.7, 2010. 10.1109/viprom.2002.1026654M.B. Pardo, C.T. van der Reijden, “ E mbedded lossy image compression based on wavelet transform”, Video/Image Processing and Multimedia Communications 4th EURASIP- IEEE Region 8 International Symposium on VIPromCom, November 2002. 10.1109/tpami.1986.4767851J. F. Canny. A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8(6):112– 131, 1986. 10.1007/bf00123164R. Deriche. Using Canny’s criteria to derive an optimal edge detector recursively implemented. The International Journal of Computer Vision, 1:167–187, April 1987. D. L. Donoho. De-noising by soft thresholding. Technical Report 409, Department of Statistics. Stanford University, 1992. 10.1364/josaa.4.002379D. J. Field. Relations between the statistics of natural images and the response properties of cortical cells. Journal of the Optical Society of America A, 4(12):2379–2394, December 1987. 10.1504/ijbet.2013.057715Arathi T, Latha Parameswaran, Slantlet Transform and Phase congruency based Image Compression, AICWIC’13, Proceedings published by International Journal of Computer Applications, IJCA, January 2013. Anthony Tanbakuchi, Introductory Statistics Lectures-Measures of Variation, 2009. S.E Ahmed, A P ooling Methodology for Coefficient of Variation, The Indian Journal of Statistics, Volume 57, Series B, pages 57-75, 1995. 10.1006/acha.2000.0343N G Kingsbury: “Complex wavelets for shift invariant analysis and filtering of signals”, Journal of Applied and Computational Harmonic Analysis, vol 10, no 3, May 2001, pp. 234-253.