P3P: From Qualitative to Quantitative

Geometric Degeneracy and Algebraic Conditioning in Minimal Pose Estimation

This repository provides the reference implementation for the paper:

Luo, P. "From Qualitative to Quantitative: Geometric Degeneracy and Algebraic Conditioning in Minimal Pose Estimation."

Repository Structure

├── cpp/
│   ├── CMakeLists.txt           # CMake build
│   ├── include/                 # Header files (p3p_luo.h, benchmark.h, data.h)
│   ├── src/                     # P3P solver (p3p_luo.cpp) + benchmarks
│   ├── banno/                   # Banno's solver
│   ├── ding/                    # Ding's solver
│   ├── ke/                      # Ke's solver
│   └── kneip/                   # Kneip & Nakano solvers
├── matlab/                      # MATLAB experiments & figure generation
├── python/                      # Python figure generation
└── README.md

Building the C++ Solver

cd cpp
mkdir build && cd build
cmake .. -DCMAKE_BUILD_TYPE=Release
make -j4

Running Benchmarks

./build/benchmark          # Monte Carlo accuracy benchmark
./build/benchmark_ransac   # RANSAC framework benchmark
./build/benchmark_tum      # 7-Scenes real-data benchmark
./build/benchmark_cylinder # Danger cylinder conditioning experiment

Key Components

C++ P3P Solver (cpp/src/p3p_luo.cpp)

Local-homography formulation with geometrically explicit constraint coefficients. Features: direct quartic construction, Newton refinement, bisector-based pose recovery.

Python Experiments (python/)

• fig_all_experiments.py — Scaling law validation, parameterization comparison, collinear analysis
• fig_geometry.py — 3D geometry formulation diagram
• fig_cylinder.py — Danger Cylinder geometric proof visualization

MATLAB Scripts (matlab/)

Condition number experiments, singularity verification, solver comparison benchmarks.

Citation

@article{luo2025p3p,
  title={From Qualitative to Quantitative: Geometric Degeneracy and Algebraic Conditioning in Minimal Pose Estimation},
  author={Luo, Peilin},
  journal={Journal of Mathematical Imaging and Vision},
  year={2025}
}