The generalized uniqueness wavelet descriptor for planar closed curves

In the problem of specifying a well-defined wavelet description of a planar closed curve, defining a unique start point on the curve is crucial for wavelet representation. In this paper, a generalized uniqueness property inherent in the one-dimensional (1-D) discrete periodized wavelet transformation (DPWT) is derived. The uniqueness property facilitates a quantitative analysis of the one-to-one mapping between the variation of 1-D DPWT coefficients and the starting point shift of the originally sampled curve data. By employing the uniqueness property, a new shape descriptor called the uniqueness wavelet descriptor (UWD) by which the starting point is fixed entirely within the context of the wavelet representation is proposed. The robustness of the UWD against input noise is analyzed. On the basis of local shape characteristic enhancement, several experiments were conducted to illustrate the adaptability property of the UWD for desirable starting point determination. Our experiments of pattern recognition show that the UWD can provide a supervised pattern classifier with optimal features to obtain the best matching performance in the presence of heavy noise. In addition, the generalized uniqueness property can be used for the shape regularity measurement. The UWD does not have local support and therefore it can not be applied to contour segments.