Robust Volumetric Shape Descriptor

This paper introduces a volume-based shape descriptor that is robust with respect to changes in pose and topology. We use modified shape distributions of [OFCD02] in conjunction with the interior distances and barycentroid potential that are based on barycentric coordinates [RLF09]. In our approach, shape distributions are aggregated throughout the entire volume contained within the shape thus capturing information conveyed by the volumes of shapes. Since interior distances and barycentroid potential are practically insensitive to various poses/deformations and to non-pervasive topological changes (addition of small handles), our shape descriptor inherits such insensitivity as well. In addition, if any other modes of information (e.g. electrostatic potential within the protein volume) are available, they can be easily incorporated into the descriptor as additional dimensions in the histograms. Our descriptor has a connection to an existing surface based shape descriptor, the Global Point Signatures (GPS) [Rus07]. We use this connection to fairly examine the value of volumetric information for shape retrieval.We find that while, theoretically, strict isometry invariance requires concentrating on the intrinsic surface properties alone, yet, practically, pose insensitive shape retrieval still can be achieved/enhanced using volumetric information.