目录

目录

Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks


Analytic marching: An analytic meshing solution from deep implicit surface networks

Motivation

  • deep learning领域出现了很多研究,surface 的implicit functions用MLP+ReLU实现
  • 为了实现meshing (exactly recover meshes) from learned implicit functions (MLP+ReLU)
    • 现有的方法采用的事实上都是标准的marching cubes采样算法;虽然效果还行,但是损失了学到的MLP的精确度,due to 离散化的本质
    • 基于ReLU-based MLP 把input空间分为很多线性区域的事实,本篇把这些区域识别为analytic cells与analytic faces,与implicit function的零值等值面有关
    • 推导了这些identified analytic faces在什么理论条件下可以保证形成一个闭合的、piecewise的planar surface
    • 基于本篇的这些理论推导,提出了一个可并行化的算法,在这些analytic cells上做marching,来==exactly recover==这些由learned MLP学出来的mesh

overview

  • 算法的初始:先用SGD \(\underset {\boldsymbol{x}\in\mathbb{R}^3}{\min} \lvert F(\boldsymbol{x}) \rvert\) 找到表面上的一个点
  • https://longtimenohack.com/posts/paper_reading/2020icml_lei_analytic/image-20201223105803235.png

效果:解析解就是降维打击。精确度无限(exact 解) + CPU跑都比别人GPU跑快十几倍

  • https://longtimenohack.com/posts/paper_reading/2020icml_lei_analytic/image-20201209113035559.png
  • https://longtimenohack.com/posts/paper_reading/2020icml_lei_analytic/image-20201209111706863.png
  • https://longtimenohack.com/posts/paper_reading/2020icml_lei_analytic/image-20201209105817256.png
  • https://longtimenohack.com/posts/paper_reading/2020icml_lei_analytic/image-20201209105846197.png