Optimization Method for Fractal Image Compression Based on Self-similarity Evaluation and Gradient Bisection Algorithm

Fractal Image Compression (FIC) is a spatial domain compression technique with high compression ratio and good image quality. It is widely used in the fields of image restoration, denoising and watermarking. However, in terms of coding time, traditional fractal coding takes a certain amount of time for coding due to its need to find the best matching block traversal for sub-blocks. The long coding time is one of the main problems of fractal coding to be solved, which has a certain impact on the efficiency of fractal coding in practical applications. Meanwhile, since fractal coding itself is the application of self-similarity of images, the self-similarity of different categories of images also has a certain impact on the coding effect. To address the above problems, we first designed an algorithm based on SSIM to evaluate the overall self-similarity of images. Secondly, by analyzing the distribution of low-frequency coefficients of the image, we realize the dynamic classification of the sub-blocks to be coded based on the discrete cosine transform (DCT). And an adaptive threshold adjustment mechanism based on gradient bisection is proposed. Through comparative experiments, our optimization method significantly reduced encoding time (i.e., 96.12%) with only a 0.01 dB decrease in PSNR compared to the original FIC. The proposed scheme in this paper increases the usability of fractal coding, and provides a certain reference value for the subsequent fractal coding optimization research.