An Enhanced Fractal Image Compression Algorithm Based on Adaptive Non-Uniform Rectangular Partition

The Basic Fractal Image Compression (BFIC) method is widely known for its high computational complexity and long encoding time under a fixed block segmentation. To address these limitations, we propose an enhanced fractal image compression algorithm based on adaptive non-uniform rectangular partition (FICANRP). This novel approach adaptively partitions the image into variable-sized range blocks (R-blocks) and non-overlapping domain blocks (D-blocks) guided by local texture and feature. By converting the similarity-matching process for R-blocks into a localized search strategy based on block size and feature classification, the FICANRP method significantly reduces computational overhead. Moreover, employing a non-overlapping partition strategy for D-blocks drastically reduces the number of D-blocks and the associated spatial coordinate data while preserving high matching accuracy. This reduction, coupled with the block similarity matching algorithm that overcomes traditional fractal computation redundancy, significantly decreases algorithmic complexity and encoding time. Additionally, by adaptively segmenting R-blocks into varying sizes according to local texture, the proposed method minimizes redundancy in smooth regions while preserving fine details in complex areas. The experimental results show that compared with BFIC, FICANRP has a compression ratio (CR) improvement range of 0.84–2.29 times, a PSNR improvement range of 0.25–4.8 dB, and an acceleration encoding time efficiency improvement of 54.14×–1448.73×. Compared with QFIC, under the same PSNR, the FICANRP compression ratio (CR) improvement range is 0.87–19.12 times, and the accelerated encoding time (ET) efficiency is increased by 37.26×–114.83×.