Comparative analysis of the quality of fractal image compression with JPEG and JPEG2000 standards

This paper presents a comparative analysis of three image compression methods: JPEG, JPEG2000, and fractal compression (FIC). The theoretical foundations of each method are reviewed, including the discrete cosine transform (DCT) for JPEG, the discrete wavelet transform (DWT) for JPEG2000, and the iterated function system (IFS) for FIC. The performance of the algorithms is evaluated using a set of metrics: compression ratio (CR), peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and the learned fragment image similarity metric (LPIPS). The analysis shows that JPEG2000 generally provides better quality at a given bitrate than JPEG, especially at high compression ratios, and offers additional features such as scalability, but this advantage is rather small. JPEG remains popular due to its simplicity and speed, but suffers from block artifacts. Fractal compression, despite its theoretical advantages, such as potential resolution independence, has significant drawbacks, including extremely slow encoding and often uncompetitive quality on general images. The application areas, reasons for limited implementation, and the current relevance of FIC are discussed. It is concluded that it is necessary to use various metrics for comprehensive quality assessment and that the choice of the optimal compression method depends on the specific requirements of the application.