An Improved Algorithm for k-Nearest-Neighbor Finding and Surface Normals Estimation

This paper is to improve the speed of k-nearest-neighbor search and put forward algorithms related to tangent plane estimation based on existing methods. Starting from the points cloud, the algorithm segments the whole data into many different small cubes in space, and the size of cube is related to the density of the points cloud. Considering the position of the point in the cube, the algorithm enlarges the area around the given point step by step until the k-nearest-neighbor is accomplished. The neighbor's least-squares tangent plane is estimated. In order to orient the planes, the k-nearest-neighbor is introduced into the problem of seeking the minimum spanning trees instead of searching the whole data. The research proved that the algorithms put forward in this paper were effective in processing data in short time and with high precision. The theory was useful for the practical application in reverse engineering and other areas related. Solution for finding k-nearest-neighbor problem, which still costs much time in present, was provided, and a propagation algorithm for orienting the planes was also discussed. The algorithm chose the orientation among the k-nearest-neighbor of the current point.