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In this paper, some similarity measures for fractal image compression (FIC) are introduced, which are robust against noises. In the proposed methods, robust estimation technique from statistics is embedded into the encoding procedure of the fractal inverse problem to find the parameters. When the original image is corrupted by noises, we hope that the proposed scheme is insensitive to those noises presented in the corrupted image. This leads to a new concept of robust estimation of fractal inverse problem. The proposed least absolute derivation (LAD), least trimmed squares (LTS), and Wilcoxon FIC are the first attempt toward the design of robust fractal image compression which can remove the noises in the encoding process. The main disadvantage of the robust FIC is the computational cost. To overcome this drawback, particle swarm optimization (PSO) technique is utilized to reduce the searching time. Simulation results show that the proposed FIC is robust against the outliers in the image. Also, the PSO method can effectively reduce the encoding time while retaining the quality of the retrieved image.

In this paper, an edge property-based neighborhood region search method is proposed to speedup the fractal encoder. The method searches for the best matched solution in the frequency domain. A coordinate system is constructed using the two lowest discrete cosine transformation (DCT) coefficients of image blocks. Image blocks with similar edge shapes will be concentrated in some specific regions. Therefore the purpose of speedup can be reached by limiting the search space. Moreover, embedding the edge property of block into the proposed search method, the speedup rate can be lifted further. Experimental results show that, under the condition of the same PSNR, the encoding time of the proposed method is only about two-fifth of Duh’s classification method. Compared with Tseng’s method, the proposed method is near or superior to the performance of their method. Moreover, the encoding speed of the proposed method is about 120 times faster than that of the full search method, while the penalty of retrieved image quality is only decaying 0.9 dB.