TreeSha: 3D shape retrieval with a tree graph representation based on the autodiffusion function topology
In this paper we present a new method for shape description and matching based on a tree representation built upon the scale space analysis of maxima of the Autodiffusion function (ADF). The use of the Heat Kernel based approach makes the method invariant to articulated deformations. By coupling maxima of the Autodiffusion function with the related basins of attraction, it is possible to link the information at different scales encoding spatial relationships in a tree structure. Furthermore, texture information can be easily included in the descriptor by adding regional color histograms to the node attributes of the tree. Dedicated graph kernels have been designed to evaluate shape dissimilarity from the obtained representations using both structural, geometric and color information. Preliminary experiments performed on the SHREC 2013 non-rigid textured dataset showed very good retrieval performances.
SUMMARY ::: ::: In this paper six distribution-free (nonparametric) stereological methods for the solution of Wicksell's corpuscle problem—i.e. the determination of the distribution of diameters of spheres embedded in an opaque specimen from the diameters of their profiles on plane sections—are compared as regards their numerical stability, sensitivity to underlying distributions and certain error criteria. The study is based on the results of simulation studies for several types of distribution (one-point, normal, exponential, logarithmic normal) of sphere diameters. Recommendations are suggested for the choice of methods, sample size and the optimal number of classes for grouping sample data.