Extracting 3D Shape Features in Discrete Scale-Space

3D shape features are inherently scale-dependent. For instance, on a 3D model of a human body, the top of the head and a fingertip can both be detected as corner points, however, at entirely different scales. In this paper, we present a method for extracting and integrating 3D shape features in the discrete scale-space of a triangular mesh model. We first parameterize the surface of the mesh model on a 2D plane and then construct a dense surface normal map. In general, the parametrization is not isometric. To account for this, we compute the relative stretch of the original edge lengths. Next, we compute a dense distortion map which is used to approximate the geodesic distances on the normal map. Then, we construct a discrete scale-space of the original 3D shape by successively convolving the normal map with distortion-adapted Gaussian kernels of increasing standard deviation. We derive corner and edge detectors to extract 3D features at each scale in the discrete scale-space. Furthermore, we show how to combine the detector responses from different scales to form a unified representation of the 3D features.