Reconstruction of object or scene surfaces has tremendous applications in computer vision, computer graphics, and robotics. In this paper, we study a fundamental problem in this context about recovering a surface mesh from an implicit field function whose zero-level set captures the underlying surface. To achieve the goal, existing methods rely on traditional meshing algorithms; while promising, they suffer from loss of precision learned in the implicit surface networks, due to the use of discrete space sampling in marching cubes. Given that an MLP with activations of Rectified Linear Unit (ReLU) partitions its input space into a number of linear regions, we are motivated to connect this local linearity with a same property owned by the desired result of polygon mesh. More specifically, we identify from the linear regions, partitioned by an MLP based implicit function, the analytic cells and analytic faces that are associated with the function's zero-level isosurface. We prove that under mild conditions, the identified analytic faces are guaranteed to connect and form a closed, piecewise planar surface. Based on the theorem, we propose an algorithm of analytic marching, which marches among analytic cells to exactly recover the mesh captured by an implicit surface network. We also show that our theory and algorithm are equally applicable to advanced MLPs with shortcut connections and max pooling. Given the parallel nature of analytic marching, we contribute AnalyticMesh, a software package that supports efficient meshing of implicit surface networks via CUDA parallel computing, and mesh simplification for efficient downstream processing. We apply our method to different settings of generative shape modeling using implicit surface networks. Extensive experiments demonstrate our advantages over existing methods in terms of both meshing accuracy and efficiency.
翻译:对象或场景表面的重建在计算机视觉、计算机图形和机器人方面有着巨大的应用。 在本文中, 我们研究从一个隐含的字段函数中恢复表面网格的问题, 该隐含功能的零层设置能够捕捉基本表面表面。 为了实现这一目标, 现有方法依靠传统的网格算法; 虽然很有希望, 但是由于在立体中使用离散空间取样, 在隐含的表面网络中, 它们的精确度已经丧失了。 鉴于一个具有校正线性线性单位( ReLU) 启动将其输入空间分割到一些线性区域, 我们在这方面研究了一个根本性的问题。 我们的本地线性功能从一个隐含功能中回收一个表层图案; 我们从线性线性单位( RELU) 将它的输入空间分割到一个封闭的表层空间空间空间空间空间, 我们准备将这个本地线性线性与一个相同的属性连接起来。 更具体地说, 我们从线性网络的直径直径直线性内线性内线性内线性内线, 我们用一种直径直径直径的计算法系的内径直径直径分析方法, 我们用一种直径直到正向地算法系的内向着的内基的内基的轨道的轨道的轨道的轨道结构向内向内向内流法系, 我们用一个直径直径直向内流法系, 我们的内算法系,, 我们用一个正向式法向的内算法系的内算法, 向地算法系法系法系法系法系法系法系,,,, 向着法系, 向向向向着法系, 我们用一个直向着, 向向向向向向向向向向向向向向向向向向向向向向向向向向向向向,, 向向向向, 向向向向向向向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向内向