2-D SHAPE REPRESENTATION AND AVERAGING USING NORMALIZED WAVELET DESCRIPTORS

A method has been developed for characterizing and averaging shaped fr om a set of two-dimensional (2-D) instances of a population of objects . The algorithm is based on a novel approach for shape description of 2-D contours. This approach uses a unique combination of Fourier and w avelet decomposition to obtain normalized wavelet descriptors (NWD) wh ich characterize shape. The NWD exploits the global signal characteriz ation of a Fourier decomposition to normalize contours for a standard position, starting point, and rotation, while the local properties of the wavelet transform provide for a means of accurate shape descriptio n. The mean and standard error of the normalized wavelet descriptors a re obtained and the average shape is reconstructed from these averaged descriptors. Because the shape descriptors that we use are reversible , the average shape produced is visualizable and, in addition, include s confidence intervals which describe the location and extent of varia tion within the set of objects. Results from the method as applied to shape representation and averaging for biological objects are presente d, along with its applications to contour data compression.