This invention relates to a method and apparatus for accurate compression and decompression of data. More specifically, this invention relates to a method and apparatus for compressing three dimensional spatial points (so called “point cloud”) and decompressing such data to produce an accurate point cloud. In one embodiment of the present invention, a level set based method is used to reconstruct a surface to approximate the surface of the point cloud. This reconstructed surface is defined implicitly as the zero level set of a function, which can be computed on a regular three-dimensional rectangular grid. Furthermore, the three-dimensional grid may be rearranged into a two-dimensional grid where the data are compressed and stored in a form of gradient. In order to recover the point cloud, the three-dimensional grid is rebuilt from the two-dimensional data and an interpolating algorithm on the implicit function is utilized to compute the points on the surface.