Polynomial image coding with vector quantised error compensation

This resembles a fractal transform, and the coefficient values can be calculated using a least squares fit as done by Monro [3] for fractals. The major difference from fractals is that the block(x,y) values are predetermined, and therefore to render the image there is no need for the iteration associated with fractals. The RIBs are effectively the difference between the polynomial coded image and the original. Since the RIBs are taken from the image the method is still fractal in that it depends on a degree of self-similarity in the error to make the method work. We report a novel image coder which is a hybrid of fractal coding and vector quantisation. Image blocks are approximated by polynomial functions, and the residual image blocks (RIBs) are coded by vector quantisation into a code book which is small enough to transmit with an image. The method is evaluated on a number of parameters, and the results are found to be intermediate between fractal and JPEG coding in their rate/distortion performance. Possible further improvements are indicated. Vector quantisation provides a simple method to find the RIBs which minimise the RMS error. A Lloyd Max method of quantisation as described by Gray [4] was used to determine the best RIBs to use for an image. The 'seed' for the Lloyd Max quantiser was formed from the linking of a large list of RIBs from the image and then pruning the linked list. The finished coded image contained the quantised coefficients from equation (1) and residual blocks. The code book is not normally transmitted in vector quantisation, and this is a major difference between the methods. It also means that the coding technique will work well for any set of images, not a certain class of image from which the code book was determined.