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Abstract

A method has been developed for characterizing and averaging shape from 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 wavelet decomposition to obtain normalized wavelet descriptors (NWD) which characterize shape. The NWD exploits the global signal characterization 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 description. The mean and standard error of the normalized wavelet descriptors are 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, includes confidence intervals which describe the location and extent of variation within the set of objects. Results from the method as applied to shape representation and averaging for biological objects are presented, along with its applications to contour data compression.

Keywords

Shape description shape averaging Fourier descriptors wavelet descriptors automated medical diagnosis.

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2-D Shape Representation and Averaging Using Normalized Wavelet Descriptors

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