Fast sparse fractal image compression

Abstract

As a structure-based image compression technology, fractal image compression (FIC) has been applied not only in image coding but also in many important image processing algorithms. However, two main bottlenecks restrained the develop and application of FIC for a long time. First, the encoding phase of FIC is time-consuming. Second, the quality of the reconstructed images for some images which have low structure-similarity is usually unacceptable. Based on the absolute value of Pearson’s correlation coefficient (APCC), we had proposed an accelerating method to significantly speed up the encoding of FIC. In this paper, we make use of the sparse searching strategy to greatly improve the quality of the reconstructed images in FIC. We call it the sparse fractal image compression (SFIC). Furthermore, we combine both the APCC-based accelerating method and the sparse searching strategy to propose the fast sparse fractal image compression (FSFIC), which can effectively improve the two main bottlenecks of FIC. The experimental results show that the proposed algorithm greatly improves both the efficiency and effectiveness of FIC.

Orthogonal sparse fractal coding algorithm based on image texture feature

“…The proposed algorithm was compared with different algorithms, including the baseline FIC (BFIC) algorithm, fast fractal compression algorithm based on standard deviation and local binary pattern (LFS) [13], dynamic domain classification algorithm based on fractal dimension (FDD) [40] and sparse FIC algorithm (SFIC) [35]. The parameters in the proposed algorithm were set as η = 200, K = 10 and e min = 30.…”

“…According to baseline FIC algorithm, every range block R needs to match only one domain block D in the virtual codebook. It is found for some images with the low structural similarity that baseline FIC algorithm has poor image reconstruction quality [34,35]. By analogy with linear fitting, the fitting result of a multivariate function is generally better than the fitting result of a unary function.…”

“…The quality of reconstructed images becomes worse as the value of e min increases. Parameter e min sets in the interval [30,35], the encoding time declines rapidly. Meanwhile, the CR increases gradually and the PSNR value is within the acceptable range.…”

“…Meanwhile, the CR increases gradually and the PSNR value is within the acceptable range. Considering the coding quality, it is reasonable to set e min in the interval [30,35].…”

Computational complexity of fractal image compression algorithm

“…Images block with better discriminative and representative information is easy to map as compared to other image blocks [44–46]. Articles in literary works [20, 47–49] claimed to improve encoding speed of FIC by using the robust features for efficient representation of image blocks. Consequently, better mapping of image sub‐blocks computation cost is reduced.…”