关键词: 点云, 测地线, Dijkstra算法, 能量函数最小化

Abstract: In order to compute approximate geodesic efficiently between two points on point cloud, a weighted graph was constructed by splitting point cloud along the Cartesian coordinate axes, thus initial approximate geodesic between any two given points could be computed out using Dijkstra's algorithm. Then the conjugate gradient method was adopted to minimize the energy function defined; finally, approximate geodesic could be obtained after some iterative steps. This proposed algorithm avoids meshing or reconstructing the point cloud to be local or global surface, and it is suitable for computing geodesic on large scale point cloud.

Key words: point cloud, geodesic, Dijkstra's algorithm, energy function minimization