On the reduction of fractal image compression encoding time

Lossy image coding by partitioned iterated function systems, popularly known as fractal image compression, has recently become an active area of research. An image is coded as a set of contractive transformations in a complete metric space. As a result of a well known theorem in metric space theory, the set of contractive transformations (subject to a few constraints) is guaranteed to produce an approximation to the original image, when iteratively applied to any initial image. While rapid decompression algorithms exist, the compression process is extremely time consuming; an exhaustive search for the optimum mappings is O(n⁴) for an n×n image. The most common solution involves classification of domain and range blocks according to features such as the presence of edges, after which matches across class boundaries are excluded. We propose a geometric construction, allowing clustering, as well as providing upper and lower bounds for the best match between domain and range blocks, allowing blocks to be excluded from the computationally costly matching process