In this paper, a novel learning-based network, named DeepDT, is proposed to reconstruct the surface from Delaunay triangulation of point cloud. DeepDT learns to predict inside/outside labels of Delaunay tetrahedrons directly from a point cloud and corresponding Delaunay triangulation. The local geometry features are first extracted from the input point cloud and aggregated into a graph deriving from the Delaunay triangulation. Then a graph filtering is applied on the aggregated features in order to add structural regularization to the label prediction of tetrahedrons. Due to the complicated spatial relations between tetrahedrons and the triangles, it is impossible to directly generate ground truth labels of tetrahedrons from ground truth surface. Therefore, we propose a multi-label supervision strategy which votes for the label of a tetrahedron with labels of sampling locations inside it. The proposed DeepDT can maintain abundant geometry details without generating overly complex surfaces, especially for inner surfaces of open scenes. Meanwhile, the generalization ability and time consumption of the proposed method is acceptable and competitive compared with the state-of-the-art methods. Experiments demonstrate the superior performance of the proposed DeepDT.
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