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Mathematical Problems in Engineering
Volume 2016, Article ID 1725051, 11 pages
Research Article

Fractal Video Coding Using Fast Normalized Covariance Based Similarity Measure

Center for VLSI and Nanotechnology, Department of Electronics Engineering, Visvesvaraya National Institute of Technology, Nagpur 440010, India

Received 18 July 2016; Revised 13 October 2016; Accepted 1 November 2016

Academic Editor: Yakov Strelniker

Copyright © 2016 Ravindra E. Chaudhari and Sanjay B. Dhok. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Fast normalized covariance based similarity measure for fractal video compression with quadtree partitioning is proposed in this paper. To increase the speed of fractal encoding, a simplified expression of covariance between range and overlapped domain blocks within a search window is implemented in frequency domain. All the covariance coefficients are normalized by using standard deviation of overlapped domain blocks and these are efficiently calculated in one computation by using two different approaches, namely, FFT based and sum table based. Results of these two approaches are compared and they are almost equal to each other in all aspects, except the memory requirement. Based on proposed simplified similarity measure, gray level transformation parameters are computationally modified and isometry transformations are performed using rotation/reflection properties of IFFT. Quadtree decompositions are used for the partitions of larger size of range block, that is, 16 × 16, which is based on target level of motion compensated prediction error. Experimental result shows that proposed method can increase the encoding speed and compression ratio by 66.49% and 9.58%, respectively, as compared to NHEXS method with increase in PSNR by 0.41 dB. Compared to H.264, proposed method can save 20% of compression time with marginal variation in PSNR and compression ratio.