# Symmetry and Orbit Detection in Point Clouds

** Published:**

Symmetry and orbit are important global features for point clouds but the detection remains a huge challenge. In this project, I studied the paper: Symmetry and Orbit Detection via Lie-Algebra Voting. The main idea is to embedding patches into a Lie algebra $\mathfrak{sim}(d)$ with an optimal distance metric. Then RANSAC or Mean-shift is used to extract correponding structures.

In this project, I achieved the following goals:

Adapted the algorithm to 2D point clouds and implemented it in Python, to facilitate the visualization and parameter tuning.

Implemented the algorithm on 3d point clouds in C++, which allows a fast computation on big point cloud.

Studied the influence of different parameters

## Requirements

### 2D Case

- >= Python 3
- Numpy, Sklearn, matplotlib

### 3D Case

- CGAL
- Eigen
- cpp 11+