3D Geometric Scale Variability in Range Images: Features and Descriptors

Despite their ubiquitous presence, little has been investigated about the scale variability—the relative variations in the spatial extents of local structures—of 3D geometric data. In this paper we present a comprehensive framework for exploiting this 3D geometric scale variability in range images that provides rich information for characterizing the overall geometry. We derive a sound scale-space representation, which we refer to as the geometric scale-space, that faithfully encodes the scale variability of the surface geometry, and derive novel detectors to extract prominent features and identify their natural scales. The result is a hierarchical set of features of different scales which we refer to as scale-dependent geometric features. We then derive novel local shape descriptors that represent the surface structures that give rise to those features by carving out and encoding the local surface that fall within the support regions of the features. This leads to scale-dependent or scale-invariant local shape descriptors that convey significant discriminative information of the object geometry. We demonstrate the effectiveness of geometric scale analysis on range images, and show that it enables novel applications, in particular, fully automatic registration of multiple objects from a mixed set of range images and 3D object recognition in highly cluttered range image scenes.