基于神经网络的三角网格简化算法

Triangular mesh simplification method based on neural network

针对三角网格简化问题,提出了一种利用神经网络直接优化简化网格与输入网格之间的Hausdorff距离来得到合并顶点的最优位置的算法。该算法在神经网络中使用了一个注意力模块来有效地提取网格的几何特征,同时采取了一种全局策略用于减少Hausdorff距离优化过程中不必要的计算。该策略可以得到当前待合并顶点的1-邻域三角面片与输入网格的三角面片间的对应关系,进而允许将简化网格与输入网格之间的Hausdorff距离替换为另外2个小规模三角网格之间的Hausdorff距离。所提算法可以处理任意三角网格并且能够很好地保持输入网格的几何特征。实验结果证明了所提算法的有效性和优越性。

In this article,we propose a new triangular mesh simplification algorithm,in which the optimal contraction vertex is obtained by direct optimizing the Hausdorff distance between the simplified mesh and the input mesh with neural network.The neural network uses an attention module to efficiently extract the geometric features of the meshes.At the same time,we adopt a global strategy to reduce the unnecessary computations in the process of optimizing the Hausdorff distance.The correspondence between the one neighborhood triangular patch of the vertices to be merged and the triangular patch of the input mesh can be obtained via this global strategy,based on which we can replace the Hausdorff distance between the simplified mesh and the input mesh with the Hausdorff distance between another two small-size triangular meshes.This algorithm can deal with any triangular mesh and preserve the geometric characteristics of the input mesh well,and its effectiveness and superiority are demonstrated by the experimental results.