Research On Surface Reconstruction Of Point Cloud Via Dictionary Learning

Surface reconstruction from point cloud is an important problem in computer graph-ics,the aim of surface reconstruction is to get the3D points with some information (po-sition,normal,colors,etc) via laser scanner or depth camera(Kinect,PrimeSense,etc),and find some mathematical description or model to represent the input point cloud. The following analysis, modification and drawing for the curve and surface of the point cloud all depend on it. Existing methods can roughly be classified into combinatorial approaches and implicit approaches. Both involve a few separate phases. For exam-ple, while combinatorial approaches may require denoising, vertex subset determina-tion, feature detection, and triangulation, implicit approaches require normal estima-tion, level set function construction and iso-surfacing. However, some of these phases such as normal estimation are themselves challenging tasks. They are designed for their respective goals. As a result, the integration of them may not achieve the best perfor-mance, especially when the input data have imperfections(noise and outliers).To avoid the inherent limitations of multi-phase processing in the prior art, we propose a unified framework that treats geometry and connectivity construction as one joint optimization problem. The framework is based on dictionary learning in which the dictionary consists of the vertices of the reconstructed triangular mesh and the sparse coding matrix encodes the connectivity of the mesh. The dictionary learning is formu-lated as a constrained l2,q-optimization(0<q<1), aiming to find the vertex position and triangulation that minimize an energy function composed of point-to-mesh metric and regularization.Our formulation takes many factors into account within the same framework, in-cluding distance metric, noise/outlier resilience, sharp feature preservation, no need to estimate normal, etc., thus providing a global and robust algorithm that is able to effi-ciently recover a piecewise smooth surface from dense data points with imperfections. Extensive experiments using synthetic models, real world models, and publicly avail-able benchmark show that our method improves the performance of the state-of-the-art in terms of accuracy, robustness to noise and outliers, geometric feature and detail preservation, and mesh connectivity.