The generalized uniqueness wavelet descriptor

The theorem of the generalized uniqueness property inherent in the 1-D discrete periodized wavelet transform (DPWT) is developed in this paper. 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 generalized uniqueness wavelet descriptor (GUWD) by which the starting point is fixed entirely within the context of the wavelet representation is proposed. The existence theorem of the GUWD supports the availability of the wavelet descriptor for pattern recognition and can provide an effective method to solve the problem of starting point dependency in the wavelet-based applications. In addition, the generalized uniqueness property can be used for shape regularity measurement