Multivariate Density-Based 3D Shape Descriptors

We address the 3D object retrieval problem using multivariate density-based shape descriptors. Considering the fusion of first and second order local surface information, we construct multivariate features up to five dimensions and process them by the kernel density estimation methodology to obtain descriptor vectors. We can compute these descriptors very efficiently using the fast Gauss transform algorithm. We also make use of descriptor level information fusion by concatenating descriptor vectors to increase their discrimination power further. To render the resulting descriptors storage-wise efficient, we develop two analytical tools, marginalization and probability density suppression, for descriptor dimensionality reduction. The experiments on two different databases, Princeton Shape Benchmark and Sculpteur, show that, boosted with both feature level and descriptor level information fusion, and powered with fast computational schemes, the density-based shape description framework enables effective and efficient 3D object retrieval.