The fractal neighbor distance measure

Abstract

Fractal image coding has been used successfully to compress and segment images, and more recently, utilized in a new distance measure to recognize objects. This paper discusses how the process of decoding a set of region-based contractive transformations has invariance properties that can be advantageous in object recognition. We will show that the recognition ability of the proposed fractal neighbor classifier (FNC), utilizing the fractal neighbor distance (FND) measure is a function of the contrast scaling factor and the illumination shift factor. Our investigation of the FND required accurate control over the convergence of a fractal decoding process. Convergence can be determined by examining the contractivity and eventual contractivity factors. We have derived theorems that allow these two factors to be calculated for a general class of fractal codes consisting of affine transformations with integral geometric scaling. Experiments were performed that verified our ability to control and modify these convergence properties. Furthermore, experiments on human face recognition revealed that the performance of the FNC improved through the use of eventual convergence and the imposition of limits on the illumination shift factor.