Parametric face coding for invariant model representation

This paper addresses the development of a transformation-invariant coding system for CAD models and form features by multi-scale wavelet representations in order to automate algorithmic search and retrieval shape patterns in CAD models. The coding system is implemented in terms of the topology entity—face. A face consists of the internal surface patches and the external contours. Both the surface patch and contour information are included in the code. Discrete wavelet transforms are unstable under the translation, rotation, and dilation of an input signal. In order to overcome this limitation, one of the most intrinsic shape characteristics—curvature, which is invariant to transformation and parameterization, is used to represent the surface patches. The face contour is approximated by the radial distance function and represented by the wavelet zero-crossings. These two transformation-invariant shape descriptors are then decomposed into fine-to-coarse approximations and details by discrete wavelet transforms. A few of these wavelet detail coefficients are then selected and normalized as codes.