Lossless acceleration of fractal image compression by fast convolution

Abstract

In fractal image compression the encoding step is computationally expensive. We present a new technique for reducing the computational complexity. It is lossless, i.e., it does not sacrifice any image quality for the sake of the speedup. It is based on a codebook coherence characteristic to fractal image compression and leads to a novel application of the fast Fourier transform-based convolution. The method provides a new conceptual view of fractal image compression. This paper focuses on the implementation issues and presents the first empirical experiments analyzing the performance benefits of the convolution approach to fractal image compression depending on image size, range size, and codebook size. The results show acceleration factors for large ranges up to 23 (larger factors possible), outperforming all other currently known lossless acceleration methods for such range sizes.