Kernel Regression Method for Fitting Surface of Scattered Points

The fitting surface of scattered points is a basic problem in computer graphics. This paper proposed a new way to reconstruct meshes from unorganized points, which uses a mature technique nonparametric filter in 2D signal processing. This method generates a order-n continuous surface to guarantee the continuity of the surface, and the user can define any type of mesh topology. It’s easy to adjust the density of the mesh points in the region of interest or where the curvature is large. And the LOD model is easy to set up. The accuracy of the fitting can be modified by the filter parameter, and the direction of the filter is adaptive to maintain the characteristic of the result surface. On the other hand, it avoids the time consuming reconstructing process like iterative subdivision surface, Delaunay triangulation and the resampling in point cloud data. The robustness of the method is better when dealing with noisy and nonuniform sampling data cloud. The experiments show that this algorithm generates accurate continuous surfaces, and becomes more efficient. If only the surface and its first derivative should be estimated, the Nadaray-Watson fast algorithm reduce the time complexity of the algorithm to O(N), far less then other surface reconstructed methods. And some useful information such as the density of local points cloud and the normal vectors of the vertexes on the mesh can be estimated in the process. The surface constructed by this algorithm can retains all the advantage listed above on DEM data. But if the points cannot be projected onto a 2D plan, the reconstructed process will include generating basic meshes and stitching the surface path. And the continuity on the margin cannot be guaranteed.