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Journal of Applied Mathematics
Volume 2014, Article ID 634848, 11 pages
Research Article

Fractal Image Coding Based on a Fitting Surface

College of Information Science and Technology, Dalian Maritime University, Dalian 116026, China

Received 5 June 2014; Revised 5 August 2014; Accepted 6 August 2014; Published 21 August 2014

Academic Editor: Filomena Cianciaruso

Copyright © 2014 Sheng Bi and Qiang Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.