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In recent decades, the use of 3D point clouds has been widespread in computer industry. The development of techniques in analysing point clouds is increasingly important. In particular, mapping of point clouds has been a challenging problem. In this talk, I will introduce a discrete analogue of the Teichmuller extremal mappings, which guarantees uniform conformality distortions, on point cloud surfaces. Based on the discrete analogue, we develop a novel method called TEMPO for computing Teichmuller extremal mappings between feature-endowed point clouds. Using our proposed method, the Teichmuller metric can be computed for evaluating the dissimilarity between point clouds. Consequently, our algorithm enables accurate shape recognition and classification. The idea can also be applied to geometry processing of 3D shapes. Experimental results will be demonstrated to show the effectiveness of our proposed method.
This presentation is part of Minisymposium “MS75 - Geometric methods for shape analysis with applications to biomedical imaging and computational anatomy, Part II (2 parts)”
organized by: Joan Alexis Glaunès (MAP5, Université Paris Descartes) , Sergey Kushnarev (Singapore University of Technology and Design) , Mario Micheli (Harvey Mudd College) .