Theory and Concepts

This section provides a detailed walkthrough of the mathematics behind AquaMVS’s refractive multi-view stereo reconstruction pipeline. It covers the complete path from camera pixels to 3D surface meshes, with emphasis on the refractive ray model that distinguishes underwater reconstruction from standard multi-view stereo.

The pipeline consists of three main stages:

1. Refractive Geometry: Ray casting through a flat air-water interface using Snell’s law to model refraction effects.

2. Dense Stereo: Computing depth maps via plane sweep stereo or dense feature matching, accounting for refractive ray geometry.

3. Fusion and Surface Reconstruction: Merging multi-view depth maps into a unified point cloud and extracting surface meshes.

• Refractive Geometry
  • Coordinate System
  • Camera Model
  • Refractive Ray Casting
  • Snell’s Law: Vector Form
  • Depth Parameterization
  • Connection to Code
  • Next Steps
• Dense Stereo Matching
  • Overview
  • Sparse Feature Matching
  • Plane Sweep Stereo
  • Dense Matching Alternative
  • Connection to Code
  • Next Steps
• Multi-View Fusion and Surface Reconstruction
  • Multi-View Depth Fusion
  • Point Cloud Generation
  • Surface Reconstruction
  • Mesh Simplification
  • Mesh Export Formats
  • Connection to Code
  • Summary