Efficient Fractal Image Coding using Fast Fourier Transform

Abstract

The fractal coding is a novel technique for image compression. Though the technique has many attractive features, the large encoding time makes it unsuitable for real time applications. In this paper, an efficient algorithm for fractal encoding which operates on entire domain image instead of overlapping domain blocks is presented.The algorithm drastically reduces the encoding time as compared to classical full search method. The reduction in encoding time is mainly due to use of modified crosscorrelation based similarity measure. The implemented algorithm employs exhaustive search of domain blocks and their isometry transformations to investigate their similarity with every range block. The application of Fast Fourier Transform in similarity measure calculation speeds up the encoding process. The proposed eight isometry transformations of a domain block exploit the properties of Discrete Fourier Transform to minimize the number of Fast Fourier Transform calculations. The experimental studies on the proposed algorithm demonstrate that the encoding time is reduced drastically with average speedup factor of 538 with respect to the classical full search method with comparable values of Peak Signal To Noise Ratio.