Similarity Detection Algorithms for CAD Models

This document presents two spectral methods for shape matching and recognition. Our first method computes the Laplace-Beltrami spectra on a domain to describe its shape. Since the spectrum is an isometry invariant and contains geometrical information, it is optimally suited for shape analysis and shape matching of geometric data. We have recently focused on global shape comparison with an application to medical imaging. In our second approach, a wavelet-based spectral method has been studied. A new form of wavelet transform is employed to greatly reduce the sensitivity to translation and rotation of a model. We also take advantage of the multi-resolution attribute to operate on reduced data sets at lower resolutions, where we are able to rapidly detect the similarity 1. Laplace Spectra for Shape Recognition: This section describes our study on global shape analysis