DMT

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Deep Marching Tetrahedra:

A Hybrid Representation for High-Resolution 3D Shape Synthesis

Background

  • SDF and OF (occupancy) : implicit

  • Marching Cube: extract mesh from implicit and expensive

Motivation

  • Supervise directly on the target surface
  • Combine implicit and explicit

Overview

Overview

  • Input: Point Cloud \(x\), Grid Vertex \(v\)
  • Initialization: Predict SDF for each vertex
  • Training:
    1. Surface Refinement with Volume Subdivision
    2. Discriminator

Volume Subdivision

20230929-DMTest-2023-10-09-11-29-48

Marching Tetrahedra

20230929-DMTest-2023-10-09-11-31-47

3D Discriminator

  • 从目标网格中随机选择一个高曲率顶点 v，并在 v 周围的体素化区域计算真实 SDF \(S_{real}\)
  • 在预测网格同一位置得到周围的SDF \(S_{pred}\)
  • 将\(S_{real}\) 和 \(S_{pred}\) 输入到 MLP 中， 判断是真实网格的概率

Loss

Surface Alignment loss

20230929-DMTest-2023-10-09-15-09-03

Adversarial Loss

20230929-DMTest-2023-10-09-15-09-44

Loss

Regularization

Avoid flipping the SDF sign of all vertices, which may lead to disconnected conponents during training

20230929-DMTest-2023-10-09-15-21-07

My discussion

Mobile NeRF