Math @ Duke

Publications [#265026] of Guillermo Sapiro
Papers Published
 Mahmoudi, M; Sapiro, G, Threedimensional point cloud recognition via distributions of geometric distances,
2008 Ieee Computer Society Conference on Computer Vision and Pattern Recognition Workshops, Cvpr Workshops
(September, 2008), IEEE [doi]
(last updated on 2019/06/19)
Abstract: A geometric framework for the recognition of threedimensional objects represented by point clouds is introduced in this paper The proposed approach is based on comparing distributions of intrinsic measurements on the point cloud. In particular, intrinsic distances are exploited as signatures for representing the point clouds. The first signature we introduce is the histogram of pairwise diffusion distances between all points on the shape surface. These distances represent the probability of traveling from one point to another in a fixed number of random steps, the average intrinsic distances of all possible paths of a given number of steps between the two points. This signature is augmented by the histogram of the actual pairwise geodesic distances, as well as the distribution of the ratio between these two distances. These signatures are not only geometric but also invariant to bends. We further augment these signatures by the distribution of a curvature function and the distribution of a curvature weighted distance. These histograms are compared using the χ 2 or other common distance metrics for distributions. The presentation of the framework is accompanied by theoretical justification and stateoftheart experimental results with the standard Princeton 3D shape benchmark and ISDB datasets, as well as a detailed analysis of the particular relevance of each one of the different histogrambased signatures. Finally, we briefly discuss a more local approach where the histograms are computed for a number of overlapping patches from the object rather than the whole shape, thereby opening the door to partial shape comparisons. © 2008 IEEE.


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