论文标题
分析行军：深层隐式表面网络的分析网络解决方案
Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks
论文作者
论文摘要
本文通过在深度学习表面重建的新兴领域中通过隐式功能学习表面网格的问题，其中隐式函数通常用作具有整流线性单元（RELU）的多层感知器（MLP）。为了从学习的隐式功能中获得网络，现有方法采用了行进立方体的事实上的标准算法；在有前途的同时，由于游行立方体的离散性质，他们在MLP中学习的精确度丧失。我们从基于RELU的MLP将其输入空间划分为许多线性区域的知识的动机，我们从这些区域中识别与隐式函数的零级等值相关的分析细胞和分析面，并表征了理论条件，并在这些区域中保证已确定的分析面可确保连接并形成封闭的封闭式平面表面。基于我们的定理，我们提出了一种自然可行的分析算法，该算法在分析细胞之间进行了游行，以精确地恢复学到的MLP捕获的网格。深度学习网格重建的实验验证了我们算法的优势而不是现有算法。
This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified linear units (ReLU). To achieve meshing from learned implicit functions, existing methods adopt the de-facto standard algorithm of marching cubes; while promising, they suffer from loss of precision learned in the MLPs, due to the discretization nature of marching cubes. Motivated by the knowledge that a ReLU based MLP partitions its input space into a number of linear regions, we identify from these regions analytic cells and analytic faces that are associated with zero-level isosurface of the implicit function, and characterize the theoretical conditions under which the identified analytic faces are guaranteed to connect and form a closed, piecewise planar surface. Based on our theorem, we propose a naturally parallelizable algorithm of analytic marching, which marches among analytic cells to exactly recover the mesh captured by a learned MLP. Experiments on deep learning mesh reconstruction verify the advantages of our algorithm over existing ones.
