基于SOM的散乱数据点集的B样条曲面重建

利用自组织映射神经网络(SOM)技术对散乱数据点集进行B样条曲面重建时,往往存在网络学习时间过长和学习效果不理想等问题。提出了一种新的神经元初始化方法和分块学习算法,该算法首先运用主元素分析方法(PCA)对散乱数据进行分块,将拓扑结构为四边形的输出层神经元初始化在每块散乱数据的最小二乘平面上进行网络学习和训练,将分块学习得到的各网格曲面拼接成一个整体;然后对该整体网格曲面的边界和内部单独学习,得到一张逼近待重建曲面的双线性B样条曲面;最后对该B样条曲面误差进行了修正。实例证明,该算法可以明显地减少SOM网络学习时间,并改善网络学习效果。

B-spline Surface Reconstruction from Scattered Data Points Based on SOM Neural Network

There often exist some problems,such as long training time and bad training effect etc.,when self-organizing map neural network(SOM) technology is employed in reverse engineering to reconstruct B-spline surface from scattered data points.In this paper,a new initialization method and a divide-and-conquer training scheme is presented.The approach functions as follows: firstly,the scattered data points are split into segments through principal component analysis(PCA);the neurons of output layer with quadrilateral topology are initialized on the least-square fitting planes of every segment.All the mesh surfaces obtained by training every segment respectively are integrated into a whole.Secondly,the boundary and interior neurons in the whole mesh surface are then trained and an approximate bi-linear B-spline surface is reconstructed.Finally,the B-spline surface reconstruction error is improved.Experiments show the proposed method can reduce SOM network training time and improve neural network training effect obviously.