Study On Fast Algorithms For Fractal Image Compression

Image contains rich information, and it is an important carrier of message when pepole communicating with each other, so its significance is self-evident. The data vloume of digital image is very large, thus image compression has been the only way to solve the problem of storage and transmission of mass digital image data. In the field of image compression, fractal image compression has attracted extensive attention worldwide because of its novel idea, high potential compression ratio and that decoded image has nothing to do with space resolution. Ever since Jacquin presented a self working fractal image compression algorithm, improved algorithms based on Jacquin have been carried out without respite. Untill now, fractal image compression is not yet mature enough, as manifested in low compression ratio without manual intervention, long coding time and that it is not a leading algorithm in present image compression algorithms. So it is the most important approach that to increase coding speed and compression ratio.Based on the theory of fractal and fundamental fractal image compression algorithm, this papper contains innovations as follow:(1) By means of studying the general characteristics of the domain blocks met the matching conditions, and the local features between the two blocks matched each other, found that keeping only the blocks whose standard deviation are large could finish the fractal image coding, and that the blocks matched each other have the similar or opposite distribution of brightness, thus proposed a fast fractal image compression algorithm based on standard deviation and sorting of brightness distribution. Experimental results demonstrate that the algorithm in this papper could improve coding speed by9times and5times than the algorithm of local variance and numbers of hopping, and its peak value signal-to-noise ratio (PSNR) and compression ratio do a little increase.(2) Based on the fast fractal image compression algorithm of standard deviation and sorting of brightness distribution, combined with the fast fractal image compression algorithm of no-search, modified the parameters from fixed threshold of standard deviation to fixed threshold of domain block numbers whose standard deviation are the top large, and from fixed threshold of brightness distribution function to fixed threshold of domain block numbers whose brightness distribution functions are near the range blocks. Experiments demonstrate that the improved algorithm enhances the PSNR by4dB than the fractal image compression algorithm of no-search, satisfied the demand of human vision, and accelerates the coding speed by10times than the original algorithm.(3) Based on fractal predicative image compression based on zerotrees, using zero tree coding algorithm to code the wavelet coefficients whose absolute value are small, and simplified8kinds of space transformations to4kinds because of the similarities of wavelet coefficients have direction selectivity, and at the same time, take the importance differences of wavelet coefficients in defferent levels into account in the matching criterion of range trees and domain trees, proposed an improved algorithm based on fractal predicative image compression based on zerotrees. Experiments demonstrate that the improved algorithm accelerates the coding speed by10times than the fractal predicative image compression based on zerotrees algorithm, meanwhile its compression ratio do a large raise.