This paper presents a matching method for 3D shapes, which comprises a new technique for surface sampling and two algorithms for matching 3D shapes based on point-based statistical shape descriptors. Our sampling technique is based on critical points of the eigenfunctions related to the smaller eigenvalues of the Laplace-Beltrami operator. These critical points are invariant to isometries and are used as anchor points of a sampling technique, which extends the farthest point sampling by using statistical criteria for controlling the density and number of reference points. Once a set of reference points has been computed, for each of them we construct a point-based statistical descriptor (PSSD, for short) of the input surface. This descriptor incorporates an approximation of the geodesic shape distribution and other geometric information describing the surface at that point. Then, the dissimilarity between two surfaces is computed by comparing the corresponding sets of PSSDs with bipartite graph matching or measuring the L 1 -distance between the reordered feature vectors of a proximity graph. Here, the reordering is given by the Fiedler vector of a Laplacian matrix associated to the proximity graph. Our tests have shown that both approaches are suitable for online retrieval of deformed objects and our sampling strategy improves the retrieval performances of isometry-invariant matching methods. Finally, the approach based on the Fiedler vector is faster than using the bipartite graph matching and it has a similar retrieval effectiveness.

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We present an efficient 3D scene representation method from a set of 3D range scans captured from a large-scale indoor or outdoor scene based on range planar segmentation and model fusion. In our method, range images are partitioned into planar patches and non-planar regions. We first partition the range image into a set of rectangle blocks and fit a planar patch to all points of each block. Blocks that are not successfully fitted as planar patches, are iteratively partitioned into sub-blocks until reaching a minimum size. Second, we iteratively merge the planar patches and identify unclassified rectangle blocks or points. The segmentation is then refined by relabelling the boundary points of fitted planar patches with respect to the neighbouring planar patches. We further simplify the scene model representation by fusing range scans and welding neighbouring planar patches with clean straight boundaries. An efficient texture mapping approach is proposed to automatically map the reflectance/colour images onto the fused scene model composed of a set of planar patches. Finally we successfully demonstrate the performance of our algorithms on several challenging range data sets.

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