A Comparison of Integer Cosine and Tchebichef Transforms for Image Compression Using Variable Quantization

DOI: 10.4236/jsip.2015.63019   PDF   HTML   XML   4,323 Downloads   5,003 Views   Citations


In the field of image and data compression, there are always new approaches being tried and tested to improve the quality of the reconstructed image and to reduce the computational complexity of the algorithm employed. However, there is no one perfect technique that can offer both maximum compression possible and best reconstruction quality, for any type of image. Depending on the level of compression desired and characteristics of the input image, a suitable choice must be made from the options available. For example in the field of video compression, the integer adaptation of discrete cosine transform (DCT) with fixed quantization is widely used in view of its ease of computation and adequate performance. There exist transforms like, discrete Tchebichef transform (DTT), which are suitable too, but are potentially unexploited. This work aims to bridge this gap and examine cases where DTT could be an alternative compression transform to DCT based on various image quality parameters. A multiplier-free fast implementation of integer DTT (ITT) of size 8 × 8 is also studied, for its low computational complexity. Due to the uneven spread of data across images, some areas might have intricate detail, whereas others might be rather plain. This prompts the use of a compression method that can be adapted according to the amount of detail. So, instead of fixed quantization this paper employs quantization that varies depending on the characteristics of the image block. This implementation is free from additional computational or transmission overhead. The image compression performance of ITT and ICT, using both variable and fixed quantization, is compared with a variety of images and the cases suitable for ITT-based image compression employing variable quantization are identified.

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Prattipati, S. , Swamy, M. and Meher, P. (2015) A Comparison of Integer Cosine and Tchebichef Transforms for Image Compression Using Variable Quantization. Journal of Signal and Information Processing, 6, 203-216. doi: 10.4236/jsip.2015.63019.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Mukundan, R., Ong, S.H. and Lee, P.A. (2001) Image Analysis by Tchebichef Moments. IEEE Transactions on Image Processing, 10, 1357-1364. http://dx.doi.org/10.1109/83.941859
[2] Nakagaki, K. and Mukundan, R. (2007) A Fast 4 × 4 Forward Discrete Tchebichef Transform Algorithm. IEEE Signal Processing Letters, 14, 684-687.
[3] Feig, E. and Winograd, S. (1992) Fast Algorithms for the Discrete Cosine Transform. IEEE Transactions on Signal Processing, 40, 2174-2193. http://dx.doi.org/10.1109/78.157218
[4] Loeffler, C., Ligtenberg, A. and Moschytz, G.S. (1989) Practical Fast 1-D DCT Algorithms with 11 Multiplications. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2, 988-991. http://dx.doi.org/10.1109/icassp.1989.266596
[5] Arai, Y., Agui, T. and Nakajima, M. (1988) A Fast DCT-SQ Scheme for Images. Transactions-IEICE, E-71, 1095-1097.
[6] Ishwar, S., Meher, P.K. and Swamy, M.N.S. (2008) Discrete Tchebichef Transform—A Fast 4 × 4 Algorithm and Its Application in Image/Video Compression. IEEE International Symposium on Circuits and Systems, Seattle, 18-21 May 2008, 260-263. http://dx.doi.org/10.1109/ISCAS.2008.4541404
[7] Prattipati, S., Iswar, S., Swamy, M.N.S. and Meher, P.K. (2013) A Fast 8 × 8 Integer Tchebichef Transform and Comparison with Integer Cosine Transform. IEEE International Midwest Conferences on Circuits and Systems, Colubus, 4-7 August 2013, 1294-1297.
[8] (2011) Joint Collaborative Team on Video Coding (JCT-VC) of ITU-T SG16 WP3 and ISO/IEC JTC1/SC29/WG11 7th Meeting, Geneva, 21-30 November 2011, 21-30.
[9] Kakarala, R. and Bagadi, R. (2009) A Method for Signalling Block-Adaptive Quantization in Baseline Sequential JPEG. IEEE TENCON, Singapore City, 23-26 January 2009, 1-6.
[10] Mukundan, R. (2006) Transform Coding Using Discrete Tchebichef polynomials. Proceedings of IASTED International Conference on Visualization Imaging and Image Processing, Palma de Mallorca, Spain, 29-31 August 2006, 270- 275.
[11] Pennebaker, W.B. and Mitchell, J.L. (1992) JPEG Still Image Data Compression Standard. Kluwer Academic Publishers, Norwell.
[12] Grgic, S., Mrak, M. and Grgic, M. (2001) Comparison of JPEG Image Coders. Proceedings of 3rd International Symposium on Video Processing and Multimedia Communications, VIPromCom-2001, Zadar, Croatia, 13-15 June 2001, 79-85.
[13] Eskicioglu, A.M. and Fisher, P.S. (1995) Image Quality Measures and Their Performance. IEEE Transactions on Communications, 43, 2959-2965. http://dx.doi.org/10.1109/26.477498
[14] (2013) Digital Image Processing Database.
[15] (2013) Footage: Small World Productions, Inc.; Tourism New Zealand. Producer: Gary F. Spradling. Music: Steve Ball.

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