核回归方法的散点拟合曲面重构

Kernel Regression Method for Fitting Surface of Scattered Points

散点曲面重构是计算机图形学中的一个基本问题,针对这个问题提出了一种全新的基于核回归方法的散点曲面重构方法,使用二维信号处理方法中非参数滤波等成熟手段进行曲面重构.这种方法可以生成任意阶数连续的曲面,在理论上保证了生成曲面的连续性,可以自定义网格的拓扑,在曲率大或者感兴趣的局部能够自适应调整网格点的密度,生成的结果方便LOD建模,数据的拟合精度也可以通过调整滤波参数控制,算法自适应调整滤波器的方向,使结果曲面可以更好保持尖锐特征.同时在构造过程中避免了传统的细分曲面方法中迭代、Delaunay剖分和点云数据中重采样等时间开销大的过程,提高了效率.对于采样不均、噪声较大的数据,该算法的鲁棒性很好.实验表明这种曲面建模方法能够散点重构出精度较高的连续曲面,在效率上有很大提高,在只需要估计曲面和其一阶导数时,利用Nadaraya-Watson快速算法可以使算法时间复杂度降为O(N),远低于其他曲面重构平滑方法.同时算法可以对曲面的局部点云密度、网格顶点法矢等信息做有效的估计.重构出的曲面对类似数字高程模型(DEM)的数据可以保证以上的优点.但如果散点数据不能被投影到2维平面上,曲面重构就需要包括基网格生成、重构面片缝合等过程.缝合边缘的连续性也不能在理论上得到保证.

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.