Combining fractal image compression and vector quantization

In fractal image compression, the code is an efficient binary representation of a contractive mapping whose unique fixed point approximates the original image. The mapping is typically composed of affine transformations, each approximating a block of the image by another block (called domain block) selected from the same image. The search for a suitable domain block is time-consuming. Moreover, the rate-distortion performance of most fractal image coders is not satisfactory. We show how a few fixed vectors designed from a set of training images by a clustering algorithm accelerate the search for the domain blocks and improve both the rate-distortion performance and the decoding speed of a pure fractal coder, when they are used as a supplementary vector quantization codebook. We implemented two quadtree-based schemes: a fast top-down heuristic technique and one optimized with a Lagrange multiplier method. For the 8 bits per pixel (bpp) luminance part of the 512 × 512 Lenna image, our best scheme achieved a peak-signal-to-noise ratio of 32.50 dB at 0.25 bpp.