Neighborhood Selection for Differential Coordinates of 3D Point Clouds Using Genetic Algorithm

• Main Authors: Jyun-Yuan Chen, 陳俊元
• Other Authors: Chao-Hung Lin
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/80892900564489130370

碩士 === 國立成功大學 === 測量及空間資訊學系碩博士班 === 96 === Many digital geometric processinges (DGP) that process polygon models benefit greatly from the differential coordinates and its associated Laplacian operator. The differential coordinate is an intrinsic surface representation, which encodes each vertex as a local coordinate relative to its topological neighbors. In the area of differential geometry, it is well-known that the direction of differential coordinate approximates the direction of surface normal and the magnitude proportionally approximates the mean curvature. The normal and curvature are significant geometry information for 3D point clouds. Given a point cloud data sampled from an unknown surface, the problem is how to determine proper topological neighbors of a vertex for accurately calculating the differential coordinate. In this thesis, we introduce a novel approach to select proper neighbor vertices by optimizing an objective function defined according to the properties of differential coordinate. The neighbor selection is regarded as an optimization problem and solved by a genetic algorithm. Our approach can obtain three most important geometry information for point clouds: surface normal, curvature and connectivity (point neighbors). The experimental results show that the generated differential coordinates can faithfully represent the geometry of 3D point models, and thus are very helpful for the related applications such as meshless smoothing, meshless parameterization, and feature detection and modeling.