A robust and efficient method for direct projection on point-sampled surfaces

Abstract

A novel and robust approach for computing the direct projection onto a point cloud for a given 3D point with associated projection vector is proposed. An energy function is presented to model the active contour, and the curve evolving method is applied to track the projection in certain iterations. In each step of the iteration, the energies of the related points are used to estimate the step length and orientation of the evolution. Then the point’s position is continuously updated and approximates the solution until the given accuracy is reached. The proposed approach directly operates on the point cloud, which is followed by a refining process to correct the results for under-sampled regions. Since the algorithm is carried out on a small point set (i.e., the neighborhood of the test point, generally composed of 30∼60 points) it is not expensive computationally. By numerical experiments, the method has been demonstrated to be more robust and efficient than the existing direct projection approaches on processing discrete point clouds.