Similarity and Aanity Hashing: a Computer Vision Solution to the Inverse Problem of Linear Fractals

The diicult task of nding a recurrent representation of an input shape is called the inverse problem of fractal geometry. Previous attempts at solving this problem have applied techniques from numerical minimization, heuristic search and image compression. The most appropriate domain from which to attack this problem is not numerical analysis nor signal processing, but model-based computer vision. Self-similar objects cause an existing computer vision algorithm called geometric hashing to malfunction. Similarity and aanity hashing capitalize on this observation to not only detect a shape's morphological self-similarity but also nd the parameters of its self-transformations. The similarity hashing procedure illustrated here will form the basis of a system which will automatically obtain recurrent models from digitized input shapes.