Source-aggregated-poisson with applications to groupwise shape analysis and mesh segmentation

Gençtav, Murat
By computing multiple solutions to Poisson’s equation with varying source functions within the shape and aggregating those solutions, we obtain a novel function for shape analysis, which we call Source-Aggregated-Poisson, or SAP. Despite the local computations, by means of specially designed source functions, our model mimics the part-coding behavior of a previous nonlocal model. We show that SAP is robust under geometric transformations and nuisance factors including topological distortions, pose changes, and occlusions. Using SAP, we address shape analysis problems in two and three dimensions. Toward this end, firstly, we exploit the evolution of its level curves and extract a probabilistic representation of shape decomposition hierarchy. Then, in the context of a groupwise shape analysis task, we demonstrate how such a probabilistic structure enables us to select the task-dependent optimum from the set of possible hierarchies. Finally, we devise an unsupervised mesh segmentation algorithm which utilizes SAP after projecting it to the surface mesh. Benchmark evaluation shows that the algorithm performs the best among the unsupervised algorithms and even performs comparable to supervised and groupwise segmentation methods.


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Citation Formats
M. Gençtav, “Source-aggregated-poisson with applications to groupwise shape analysis and mesh segmentation,” Ph.D. - Doctoral Program, Middle East Technical University, 2018.