Fast and Efficient 4x4 Tchebichef Moment Image Compression

Majlesi Journal of Electrical Engineering

مقاله 4، دوره 4، شماره 3، آذر 2010، صفحه 37-45   

نوع مقاله: Review Article

شناسه دیجیتال (DOI): 10.1234/mjee.v4i3.311

نویسندگان

Nur Azman Abu؛ Siaw Lang Wong^* ؛ Hidayah Rahmalan؛ Shahrin Sahib

چکیده

Orthogonal moment functions have long been used in image analysis. This paper proposes a novel approach based on 4x4 discrete orthogonal Tchebichef moment for fast and efficient image compression. The method incorporates a simplified mathematical framework technique using matrices as well as a block-wise reconstruction technique to eliminate possible occurrences of numerical instabilities at higher moment orders. Then the 4x4 Tchebichef Moment Transform and Discrete Cosine Transform have been compared. The results show that the 4x4 Tchebichef moment has significant advantages over the other technique in terms of its error reconstruction, average bit-length of Huffman codes and image quality.  Moreover, Tchebichef moment provides a compact support to sub-block reconstruction for image compression. Tchebichef Moment Compression clearly performs potentially better for broader domains on real digital images and graphically generated images.

کلیدواژه‌ها

image processing؛ Image Coding؛ This work is supported by Fundamental Research Grant Scheme؛ en؛ Tchebichef Moment Transforms؛ Ministry of Higher Education Malaysia؛ Orthogonal Moment Functions؛ JPEG Compression؛ Discrete Cosine Transform

مراجع

[1] Cho-Huak Teh and Roland T. Chin; “On Image Analysis by the Methods of Moments”, IEEE Transactions on Pattern Analysis Machine Intelligence, Vol. 10, No. 4, pp. 496-513, ISSN 0162-8828, (1988)

[2] Tuceryan M., “Moment Based Texture Segmentation”, Pattern Recognition Letters, Vol. 15, pp. 659-668, (July 1994)

[3] Wang L. and Healey G.; “Using Zernike Moments for the Illumination and Geometry Invariant Classification of Multispectral Texture”, IEEE Transactions on Image Processing, Vol. 7, pp. 196-203, (1998)

[4] Shutler J.D.; “Velocity Moments for Holistic Shape Description of Temporal Features”, PhD thesis, Department Electronic and Computer Science, University of Southampton, (2001)

[5] Zhu Hongqing, Shu Huazhong, Xia Ting, Luo Limin, and Coatrieux Jean Louis; “Translation and scale invariants of Tchebichef moments”, Pattern Recognition, Vol. 40, No. 9, pp. 2530-2542, ISSN 0031-3203, (2007)

[6] Li Zhang, Qian Gong bin, Xiao Wei wei, and Ji Zhen; “Geometric Invariant Blind Image Watermarking by Invariant Tchebichef Moments”, Optics Express Journal, Vol. 15, pp. 2251-2261, (2007)

[7] Rahmalan H., Nixon M.S. and Carter J.N.; “On Crowd Density Estimation for Surveillance”, Proceedings of International Conference on Crime Detection and Prevention, London UK, (13-14 June 2006)

[8] Rahmalan H., Suryana N. and Abu N.A.; “A General Approach for Measuring Crowd Movement”, Malaysian Technical Universities Conference and Exhibition on Engineering and Technology (MUCEET2009), pp. 98-103, Kuantan, Pahang, (20-22 June 2009)

[9] H. Rahmalan; “Detecting Crowd Movement Using Moment Invariants”, International Conference on Image Processing, Computer Vision and Pattern Recognition IPCV'09, Las Vegas, Nevada, (13-16 July 2009)

[10] Mukundan R.; “Improving Image Reconstruction Accuracy Using Discrete Orthonormal Moments”, Proceedings of International Conference On Imaging Systems, Science and Technology, pp. 287-293, (June 2003)

[11] Mukundan R.; “Some Computational Aspects of Discrete Orthonormal Moments”, IEEE Transactions on Image Processing, Vol. 13, No. 8, pp. 1055-1059, (Aug. 2004)

[12] Abu Nur Azman, Lang Wong Siaw and Sahib Shahrin; “Image Projection Over The Edge”, International Conference on Industrial and Intelligent Information (ICIII 2010), Proceedings 2nd International Conference on Computer and Network Technology (ICCNT 2010), pp. 344-348, Bangkok, Thailand, 23–25 April 2010)

[13] Rabbani M. and Jones P.W.; Digital Image Compression Techniques (SPIE Press Book), Vol. TT07, ISBN 9780819406484, (1991)

[14] Abu Nur Azman, Suryana Nanna and Mukundan R.; “Perfect Image Reconstruction Using Discrete Orthogonal Moments”, Proceedings of The 4th IASTED International Conference on Visualization, Imaging, and Image Processing (VIIP2004), pp. 903-907, Marbella, SPAIN, (6-8 September 2004)

[15] Mukundan R. and Hunt O.; “A Comparison of Discrete Orthogonal Basis Functions for Image Compression”, Proceedings Conference on Image and Vision Computing New Zealand (IVCNZ 2004), pp. 53-58, (2004)

[16] Lang Wong Siaw, Abu Nur Azman, Rahmalan Hidayah; “Fast 4x4 Tchebichef Moment Image Compression”, Proceedings International Conference of Soft Computing and Pattern Recognition (SoCPaR) 2009, pp. 295‒300, Melaka, Malaysia, (4-7 December 2009)

[17] Abu Nur Azman, Lang Wong Siaw, Suryana Nanna and Mukundan Ramakrishnan; “An Efficient Compact Tchebichef moment for Image Compression”, 10th International Conference on Information Science, Signal Processing and their applications (ISSPA2010), pp.448-451, Kuala Lumpur, (10–13 May 2010)

[18] Mukundan R., Ong S.H. and Lee P.A.; “Image Analysis by Tchebichef Moments”, IEEE Transactions on Image Processing, Vol. 10, No. 9, pp. 1357–1364, (September 2001)

[19] Ahmed N., Neterajan T. and Rao K.R.; “Discrete Cosine Transform”, IEEE Transactions on Computers, Vol. 23, pp. 90-93, (January 1974)

[20] Anil K. Jain; Fundamentals of Digital Image Processing, Prentice Hall, pp. 172, (2006)

[21] Wallace Gregory K.; “The JPEG Still Picture Compression Standard”, Communication of the ACM, Vol. 34, No. 4, pp. 31-44, (April 1991)

[22] Acharya Tinku and Ajoy K. Ray; Image Processing: Principles and Applications, John Wiley, pp. 365, (2005)

[23] Rahmalan Hidayah, Abu Nur Azman and Wong Siaw Lang; “Using Tchebichef Moment for Fast and Efficient Image Compression”, Journal of Pattern Recognition and Image Analysis, No. 4, to be published, (2010)

[24] Abu Nur Azman, Wong Siaw Lang and Sahib Shahrin; “Image Super-Resolution via Discrete Tchebichef Moment”, Proceedings of International Conference on Computer Technology and Development (ICCTD 2009), Vol. 2, pp. 315–319, Kota Kinabalu, Malaysia, (13–15 November 2009)

[25] Nakagaki Kiyoyuki and Mukundan Ramakrishnan; “A Fast 4x4 Forward Discrete Tchebichef Transform Algorithm”, IEEE Signal Processing Letters, Vol. 14, No. 10, pp. 684-687, (October 2007)

[26] Christopoulos C.A., Philips W., Skodras A.N. and Cornelis J.; “Discrete Cosine Transform Coding of Images”, Proceedings of International Conference on DSP and CAES, Vol. I, pp. 164-169, Nicosia, Cyprus, (14-16 July 1993)