[3D Geometry] 1. 3D Representations: Types / pros and cons / Conversion between different types

이 글은 성민혁 교수님의 CS479: Machine Learning for 3D Data (Fall 2023)을 듣고 (필자의 이해를 위해) 정리한 글입니다.

• Intro: Application of 3D data
  • 3D Generation (e.g., used for simulator, games)
  • 3D Reconstruction (e.g., AR/VR)
  • 3D Perception (e.g., waymo, home-environment)

Types of 3D Representations

We are interested in 2D surfaces in 3D space.

Explicit representations

1. 3D Grid (Voxels): 3D 창
2. Multi-view images
3. Point cloud
   1. Collections of (x,y,z) coordinates, possibly with normal.
4. Polygon Mesh / Triangular Mesh
   1. Graph like structure, but not exactly the same.
   2. Collections of vertices, edges, and faces that defines the shape of a polyhedral object. 
   3. Valid Mesh: Each local region should be mappable to a 2D flat plane
5. CAD Representations

Implicit Representations, later for Implicit neural rendering

A function that takes coordinates as input and returns occupancy or signed distance. 

For example, SDF(Signed distance function) and occupancy networks are famous. Occupancy models don't provide information about how far a point is from the object's surface, which can limit their usefulness in more complex applications. The resolution of the model (how small the voxels are) can significantly affect the accuracy and computational requirements.

Conversion between different types

• Voxel to mesh
  • Marching cubes: Coverting from implicit to explicit representations.
• Point cloud to implicit function