Uniqueness wavelet descriptor for plane closed curves

Using the periodized wavelets and considering the orthonormal bases with dilation factor two, an inhered uniqueness property in the discrete periodized wavelet transform (DPWT) is found and proved. The uniqueness property denotes the one-to-one mapping characteristic between the circular shift in the original data sequence and a combination vector in which each element is the sign of the summation of the high frequency band components in each decomposition level. Based on this uniqueness property, a new wavelet descriptor called the uniqueness wavelet descriptor (UWD) is proposed which has the properties of scaling, translation, rotation, and starting point shift invariance so that it can be used as the features of a plane closed curve for pattern recognition