Marching Cubes & Variants

Marching Cubes Algorithm

  • 1987
  • Iso-surface extraction
  • Input: discretized implicit field
  • Output: triangle mesh.

    • Issues of MC Variants & Challenges

    Issues of MC Variants

  • Cannot recover sharp features
    • Some algorithms from MC can recover sharp features,
    but they all require additional inputs.

    Issues of MC Variants

  • Model-driven
    • The mesh topology in each cube and the vertex positions are decided by manually designed rules.

    Solutions

  • Templates: can not represent sharp features
    • Design new templates or use existing templates that can better represent geometric features.

  • Model-driven: relies on the trilinear interpolant assumption
    • Use machine learning to learn the rules from training data.

    Challenges

  • Represent the output mesh

  • Design an efficient neural network

    • Templates: From 2D to 3D

    Templates: From 2D to 3D

    二维正方形的结构表示
  • Input: $ m \times n $
  • Output:
    • $\quad m \times n \times (5+12) \Rightarrow m \times n \times (2+10) $

    Templates: From 2D to 3D

  • Output = Type + Vertices + Edges + Faces

    • Marching Cubes Algorithm

  • Input: $ m \times n \times k $
  • Output:
    • $\quad m \times n \times k \times (15+84)$
    $\Rightarrow m \times n \times k \times (5+51) $

    NMC Templates

    NMC结构

    NMC-lite Templates

    NMC-lite结构

    Data Preparation & Networks

    Data Preparation

    数据集的生成

    Network Related

  • 3D ResNet
  • Loss function:
    • BCE for Boolean part
    • MSE for Float part
    • Smooth loss if input is voxel

    在输入是voxel的情况下开启光滑性loss的对比
    深度学习网络结构

    Results & Comparison

    Beamer

    论文Beamer

    Smooth Features

    在平滑表面的效果

    Sharp Features

    NMC算法的锐利边缘效果

    Noisy Data Input

    噪声数据验证

    NMC vs MC33

    MC33与NMC的结果对比

    Weakness & Future Work

    Issues of NMC

  • Rotation sensitive
    • Most of the training data is axis aligned
    • Loss function of smooth prefers axis-aligned outputs
    旋转敏感性

    Issues of NMC

  • Cannot reconstruct some topological cases.
  • Self-intersections
    • 匹配失败的情况

    Future Work: NDC


  • Neural Dual Contouring

  • Finished in February 2022

  • https://arxiv.org/abs/2202.01999

  • SDF: Signed Distance Function
    •

    Future Work: NDC

    Thanks for your watching!