Abstract
We present a new approach to the problem of two-dimensional multiscale shape representation and analysis, based on the one-dimensional continuous wavelet transform (CWT). The shape is represented by the complex signal that describes its boundary, and the CWT is applied to this signal, leading to the so-called W-representation. Wavelet theory provides the W-representation with several properties that are generally required from shape representation frameworks. In addition, we introduce algorithms for extracting meaningful information about the shape from its W-representation, for instance, detection of dominant points and shape partitioning, natural scales analysis, and fractal-based analysis. The algorithms that accomplish these tasks are tested on shapes obtained from synthetic and real images. Thus the W-representation yields a unified approach to a number of important problems of shape characterization for purposes of machine vision.
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