Abstract
Abstract Fractal image compression (FIC) is recognized as a NP-hard problem, and it suffers from a high number of mean square error (MSE) computations. In this paper, a two-phase algorithm was proposed to reduce the MSE computation of FIC. In the first phase, based on edge property, range and domains are arranged. In the second one, imperialist competitive algorithm (ICA) is used according to the classified blocks. For maintaining the quality of the retrieved image and accelerating algorithm operation, we divided the solutions into two groups: developed countries and undeveloped countries. Simulations were carried out to evaluate the performance of the developed approach. Promising results thus achieved exhibit performance better than genetic algorithm (GA)-based and Full-search algorithms in terms of decreasing the number of MSE computations. The number of MSE computations was reduced by the proposed algorithm for 463 times faster compared to the Full-search algorithm, although the retrieved image quality did not have a considerable change.
Highlights
Image compression is the current mainstream research topic in image processing [1,2] and is still a viable research area, owing to the growing need for multimedia data transmission and storage [3]
5 Experimental results Some tests are conducted on the proposed algorithm, and its performance has been compared to that of the Vences-genetic algorithm (GA) [12], Wu-GA1 [20], Wu-GA2 [21], ICAFIC, and basic algorithm of fractal compression (Full-search) in terms of the number of mean square error (MSE) computation and peak signal-to-noise ratio (PSNR)
6 Conclusion The main problem of Fractal image compression (FIC) is the high number of MSE computations that has classified it in the NP-hard problems
Summary
Image compression is the current mainstream research topic in image processing [1,2] and is still a viable research area, owing to the growing need for multimedia data transmission and storage [3]. Jacquin [5] presented an automatic algorithm called baseline fractal image compression. In [6,7], classification methods for determining the domain blocks were proposed. In [8], the information existing within the matched range block (a neighborhood matching method) is used for the encoding process, but is based on the spatial correlation between the range and the domain block. Truong and Jeng [9] proposed the use of the discrete cosine transform (DCT) inner product-based algorithm for removing the redundancy that exists while the eight mapping of the domain block is computed. Furao and Hasegawa [10] introduced a no-search encoding fractal algorithm for faster encoding process by choosing a domain block
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