Simple GNC

Heavy outliers, noisy correspondences, and a compact registration benchmark in one self-contained tutorial.
This repository compares Least Squares, RANSAC, GNC-GM, and GNC-TLS on classic Stanford 3D scan data.

Overview

This repository is a small but complete tutorial on outlier-robust point cloud registration. The main script, simple_gnc_pcr.py, takes a .ply point cloud, applies a random rigid transform, injects inlier noise and extreme outliers, and then compares several pose estimators under the same synthetic correspondence set.

The goal is simple:

• show how quickly naive least squares breaks under heavy outlier corruption
• compare minimal solvers such as RANSAC against non-minimal robust estimators
• visualize correspondences and registration results in a way that is easy to explain in a talk, class, or GitHub project page
• keep the code path short enough that the full experiment can be read in one sitting

Highlights

• Single-file experiment pipeline in simple_gnc_pcr.py
• Random SE(3) perturbation plus Monte Carlo evaluation over 30 runs
• Truncated Gaussian inlier noise and uniformly sampled spherical outliers
• Side-by-side comparison of LS, RANSAC1K, RANSAC10K, GNC-GM, and GNC-TLS
• Ready-to-use Stanford Bunny, Armadillo, Dragon, and Happy Buddha assets included in the repository

Companion Reading

If you want the theory behind the code, I also wrote a short blog series on GNC and robust estimation:

• Graduated Non-Convexity (1): motivation for robust estimation, why outliers break plain least squares, and why non-convex robust costs create local minimum issues
• Graduated Non-Convexity (2): a walkthrough of Black-Rangarajan duality and the weighted least-squares view of robust kernels
• Graduated Non-Convexity (3): the actual GNC algorithm, mu continuation, and how GNC-GM is turned into a practical solver

The posts are a more theory-first companion to this repository, while the code here is meant to stay compact and experiment-focused.

Polynomial Toy Example

GT	LS	RANSAC-1K	RANSAC-10K	GNC-TLS

Result Gallery

Corr	RANSAC	GNC-GM	GNC-TLS
Armadillo
Bunny
Dragon

The misc/ folder also contains the animated GNC-TLS trajectory and additional presentation-style figures.

What The Script Does

simple_gnc_pcr.py follows the pipeline below:

1. Load a .ply point cloud and normalize it to a consistent scale.
2. Sample a random rotation and translation to create a target point cloud.
3. Generate synthetic correspondences from ground-truth pairs.
4. Add truncated Gaussian noise to inliers.
5. Replace a large fraction of target correspondences with uniformly sampled outliers inside a sphere.
6. Estimate the rigid transform with multiple solvers.
7. Measure translation and rotation error over repeated Monte Carlo trials.
8. Save box-style RMSE summaries as translation_rmse.png and rotation_rmse.png.

Methods Compared

• LS: vanilla least-squares alignment using Horn's method
• RANSAC1K: minimal-set RANSAC with 1,000 iterations
• RANSAC10K: minimal-set RANSAC with 10,000 iterations
• GNC-GM: Graduated Non-Convexity with the Geman-McClure penalty
• GNC-TLS: Graduated Non-Convexity with a truncated least-squares penalty

Quick Start

Install the Python dependencies:

pip install numpy open3d pandas seaborn matplotlib tqdm

Run the tutorial on one of the bundled point clouds:

python simple_gnc_pcr.py \
  --ply bunny/reconstruction/bun_zipper_res4.ply \
  --noise_std 0.01 \
  --outlier_ratio 0.99 \
  --voxel 0.03

You can also try other included assets:

python simple_gnc_pcr.py --ply Armadillo_scans/Armadillo.ply --noise_std 0.01 --outlier_ratio 0.95 --voxel 0.03 --visualize
python simple_gnc_pcr.py --ply dragon_recon/dragon_vrip_res4.ply --noise_std 0.01 --outlier_ratio 0.99 --voxel 0.03
python simple_gnc_pcr.py --ply happy_recon/happy_vrip_res4.ply --noise_std 0.01 --outlier_ratio 0.99 --voxel 0.03

Command-Line Options

Option	Description	Default
--ply	Path to the input .ply point cloud	required
--noise_std	Standard deviation of Gaussian inlier noise	0.01
--outlier_ratio	Fraction of correspondences replaced by outliers	0.99
--voxel	Voxel size used for downsampling	0.03
--visualize	Open Open3D windows for correspondences and registration results	off