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 wa velet representation. In this paper, a generalized uniqueness property inhe ring in the one-dimensional (1-D) discrete periodized wavelet transformatio n (DPWT) is derived. The uniqueness property facilitates a quantitative ana lysis of the one-to-one mapping between the variation of 1-D DPWT coefficie nts and the starting point shift of the originally sampled curve data. By e mploying the uniqueness property, a new shape descriptor called the uniquen ess wavelet descriptor (UWD) by which the starting point is fixed entirely within the context of the wavelet representation is proposed. The robustnes s of the UWD against input noise is analyzed, On the basis of local shape c haracteristic enhancement, several experiments were conducted to illustrate the adaptability property of the UWD for desirable starting point determin ation. Our experiments of pattern recognition show that the UWD can provide a supervised pattern classifier with optimal features to obtain the best m atching performance in the presence of heavy noise. In addition, the genera lized 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.