Fractal Image Coding Based on a Fitting Surface

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.

Competitive Improvement of the Time Complexity to Encode Fractal Image: By Applying Symmetric Central Pixel of the Block

“…Davoine and Chassery (1994) used 8 bits for the brightness adjust. Bi and Wang (2014) used 2 bits for the contrast adjust when quantize to 0.25, 0.50, 0.75, so bits required per block are 25 bits. As a result, the total bits required for a image to encode are (Distasi et al (2005)).…”

Prediction of the PSNR Quality of Decoded Images in Fractal Image Coding

“…Due to the lower dimension of features and more effective searching strategies, such as kdtree method [11], the fractal encoding process can be finished in a short time. Finally, no-search fractal coding method is another way to provide faster fractal encoding and higher compression ratio at the expense of poor quality of the decoded image [12][13][14][15]. Furthermore, during the past two decades, it has been successfully applied in many other image processing applications such as image denoising [16,17], image magnification [18][19][20], image retrieval [21,22], and digital watermarking [23][24][25].…”