Scale-Dependent 3D Geometric Features

Three-dimensional geometric data play fundamental roles in many computer vision applications. However, their scale-dependent nature, i.e. the relative variation in the spatial extents of local geometric structures, is often overlooked. In this paper we present a comprehensive framework for exploiting this 3D geometric scale variability. Specifically, we focus on detecting scale-dependent geometric features on triangular mesh models of arbitrary topology. The key idea of our approach is to analyze the geometric scale variability of a given 3D model in the scale-space of a dense and regular 2D representation of its surface geometry encoded by the surface normals. We derive novel corner and edge detectors, as well as an automatic scale selection method, that acts upon this representation to detect salient geometric features and determine their intrinsic scales. We evaluate the effectiveness and robustness of our method on a number of models of different topology. The results show that the resulting scale-dependent geometric feature set provides a reliable basis for constructing a rich but concise representation of the geometric structure at hand.