Point Feature Histograms (PFH)

This project implements Point Feature Histograms (PFH), a method for capturing local geometric features around a point in a 3D point cloud.

🐎 1. Point Feature Histogram Introduction

PFHs are designed to be pose-invariant and encapsulate surface model properties through the spatial relationships of a point and its nearest neighbors. The process involves analyzing 3D coordinates and surface normals to compute angular variations between points, offering a robust descriptor for 3D shapes. This technique is particularly effective in representing complex geometries and has been optimized for efficiency.

⚙️ 2. Install Dependencies

virtualenv pfh_env
source pfh_env/bin/activate
pip install -r requirements.txt

📖 3. Theory

1. For each point $p$, all of $p$'s neighbors enclosed in the sphere with a given radius(self.radius) are selected.
2. For every pair of point $p_i$ and $p_j$ ($i$ $\neq$ $j$) in the k-neighborhood of $p$ and their estimated normals $n_i$ and $n_j$ ($p_i$ being the point with a smaller angle between its associated normal and the line connecting the points), we define a Darboux $uvn$ frame and computes the angular variation of $n_i$ and $n_j$.

• Define Darboux $uvn$ frame

$$ u = n_i $$

$$ v = (p_j − p_i) × u $$

$$ w = u × v $$

• Computes the angular variation of $n_i$ and $n_j$

$$ \alpha = v \cdot n_j $$

$$ \phi = \frac{ (u \cdot (p_j − p_i)) }{||p_j − p_i||} $$

$$ \theta = arctan(w \cdot n_j, u \cdot n_j) $$

📈 4. Result

📝 Report

Horse	Cat

📄 5. Related Papers & Reference

• Paper: Fast Point Feature Histograms (FPFH) for 3D registration
• Estimating Surface Normals in a PointCloud
• Point Feature Histograms (PFH) descriptors

📫 6. Contact

• Yi-Cheng Liu, Email: liuyiche@umich.edu
• Tien-Li Lin, Email: tienli@umich.edu