Abstract
A no-search fractal image coding method based on a fitting surface is proposed. In our research, an improved gray-level transform with a fitting surface is introduced. One advantage of this method is that the fitting surface is used for both the range and domain blocks and one set of parameters can be saved. Another advantage is that the fitting surface can approximate the range and domain blocks better than the previous fitting planes; this can result in smaller block matching errors and better decoded image quality. Since the no-search and quadtree techniques are adopted, smaller matching errors also imply less number of blocks matching which results in a faster encoding process. Moreover, by combining all the fitting surfaces, a fitting surface image (FSI) is also proposed to speed up the fractal decoding. Experiments show that our proposed method can yield superior performance over the other three methods. Relative to range-averaged image, FSI can provide faster fractal decoding process. Finally, by combining the proposed fractal coding method with JPEG, a hybrid coding method is designed which can provide higher PSNR than JPEG while maintaining the same Bpp.
Highlights
The basic idea of fractal image coding was first proposed by Barnsley [1]
We suppose that, for arbitrary range block R, the best matching domain block D is very similar to the range block R and can provide minor matching error with the same fitting surface SR
From (16), we know that, since the proposed fitting surface SR can approximate the range block R better than the fitting plane, smaller matching errors can be achieved in our method
Summary
The basic idea of fractal image coding was first proposed by Barnsley [1]. Its kernel issue is to find an iterated function system whose fixed point can approximate the input image well. In order to reduce the computational complexity of fractal encoding, converting the global search to local search is an effective way to solve this problem It mainly consists of classification techniques and feature vector techniques. Afterwards, Wang et al [19, 20] proposed the adaptive plane and fitting plane to improve the quality of the decoded image, respectively The latter one can achieve higher compression ratio, better decoded image quality, and shorter encoding time than the previous similar methods. Since the proposed fitting surface itself is more similar to the corresponding range block, all the fitting surfaces can constitute a better fitting surface image (FSI) as the initial image in fractal decoding process without extra computations.
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