Novel hybrid fractal image encoding algorithm using standard deviation and DCT coefficients
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O R I G I N A L PA P E R
Novel hybrid fractal image encoding algorithm using standard deviation and DCT coefficients Xingyuan Wang · Dandan Zhang · Xing Guo
Received: 2 September 2012 / Accepted: 22 January 2013 / Published online: 5 February 2013 © Springer Science+Business Media Dordrecht 2013
Abstract In this paper, a fast fractal encoding algorithm using standard deviation (STD) and DCT coefficients is proposed. First, the STD values of domain blocks are calculated. Then, domain blocks are sorted by their STD values. During the encoding process, each range block is limited to search in the domain blocks with similar STD values. Since the searching space is reduced, the encoding speed is improved. Moreover, for improving the quality of the retrieved image, an auxiliary encoding algorithm (AEA) is proposed, and it could encode range blocks in which the pixel values fluctuate greatly. In the decoding step, a kind of simple line fitting on block boundaries is used to reduce the blocking effects. Simulation results show that the runtime of the proposed method is reduced greatly compared to the full search method. And the new algorithm could obtain good quality and higher compression ratio than the baseline encoding algorithm.
X. Wang · D. Zhang () · X. Guo Faculty of Electronic Information & Electrical Engineering, Dalian University of Technology, Dalian, Liaoning 116024, P.R. China e-mail: [email protected] X. Wang e-mail: [email protected] X. Guo e-mail: [email protected]
Keywords Fractal image compression · Standard deviation · DCT coefficients · Peak signal to noise ratio · Blocking effects
1 Introduction Fractal image compression was proposed by Barnsley in 1988 [1], and implemented by Jacquin [2] in 1992. Partition iterated function system (PIFS) theory [3, 4] and Collage theorem form its basis. By utilizing the self-similarity characteristic in a natural image, fractal image compression can achieve a high compression ratio and good retrieved image quality. But the calculation of similarity between a range block and a domain block in the encoding step is very complex and time-consuming. There are many encoding techniques have been presented by the researchers to overcome this problem [5–17]. These techniques include classification techniques [5, 6, 11], spatial correlation [7], quad-tree techniques [8], DCT coefficients and STD [9, 14, 15] etc. Fisher [5] and Wang et al. [6] proposed their classification methods based on the feature of the domain blocks, respectively. Truong et al. [7] proposed a kind of neighborhood matching method based on spatial correlation which makes use of the information of matched range blocks and effectively reduced the encoding time. In this paper, a fast fractal encoding algorithm using standard deviation (STD) and DCT coefficients is proposed. First, domain blocks are sorted by their
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Fig. 1 The arrangement of range and domain blocks
STD values. Then, in the encoding process, each range block is limited to search in the domain blocks with simil
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