An Affine Symmetric Image Model and Its Applications

Natural images contain considerable redundancy, some of which is successfully captured using recently developed directional wavelets. In this paper, an affine symmetric image model is considered. It provides a flexible scheme to exploit geometric redundancy. A patch of texture from an image is rotated, scaled and sheared to approximate other similar parts in the image, revealing the self-similarity relation. The general scheme is derived as follows. A texture model is required that identifies structural patterns. Then the affine symmetry is exploited between structural textures at a local level, the objective being to find the minimum residual error by estimating the affine transform relating two patches of texture. Having developed a local model, the methodology is extended to the whole image to estimate the global affine relation. This global model is further developed in a multiresolution framework for multiscale analysis, by which the self similarity of the image is exploited across space and scale. The multiresolution model can be applied to a series of practical problems. Experimental evaluation demonstrates the effectiveness of the approach in affine invariant texture segmentation and image approximation.