Discrete Plane Segmentation and Estimation from a Point Cloud Using Local Geometric Patterns

This paper presents a method for segmenting a 3D point cloud into planar surfaces using recently obtained discrete-geometry results.In discrete geometry,a discrete plane is defined as a set of grid points lying between two parallel planes with a small distance,called thickness.In contrast to the continuous case,there exist a finite number of local geometric patterns(LGPs) appearing on discrete planes.Moreover,such an LGP does not possess the unique normal vector but a set of normal vectors.By using those LGP properties,we first reject non-linear points from a point cloud,and then classify non-rejected points whose LGPs have common normal vectors into a planar-surface-point set.From each segmented point set,we also estimate the values of parameters of a discrete plane by minimizing its thickness.