The basic fractal theory and the fractal interpolation are studied, and the fractal property of remote sensing images is refered in this paper. As to LIDAR points data, due to its difficulty of being handled by the traditional arithmetics, a arithmetic of rapid regularization of LIDAR point cloud based on fractal interpolation with enhancement of edge features is proposed on the analysis of the organizing forms of the point cloud. The arithmetic regularizes the points cloud into a "rough image" by direct resample, and the edge pixels are differentiated from it, which are given new value by fractal interpolation. And the non-edge ones retain their original value. The experiment proves that it can reduce the computation, and enhance the main features effectively.
