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 significantly reduces computational overhead. Furthermore, adopting a non-overlapping partition for D-blocks drastically decreases the pool of D-blocks and the quantitative value of spatial coordinates while maintaining a high level of similarity matching. 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. Experimental results demonstrate that FICANRP outperforms BFIC with an average of 1.425 higher compression ratio (CR), 1.51 dB improvement in PSNR, and 67.44X acceleration encoding time efficiency for 512512 grayscale test images.