decargroup/gnc-adapt

Graduated Nonconvexity and Adaptive Robust loss algorithm

GNC-ADAPT

This repository contains the MATLAB implementation of GNC (Graduated Non-Convexity) on ADAPT (Adaptive Loss) by Barron described in the following paper:

• K. Jung, T. Hitchcox, and J. R. Forbes. "An Adaptive Graudated Nonconvexity Loss Function for Robust Nonlinear Least-Squares Solutions," 2024. arXiv:2305.06869

@misc{Jung2023Adaptive,
      title={An Adaptive Graduated Nonconvexity Loss Function for Robust Nonlinear Least Squares Solutions}, 
      author={Kyungmin Jung and Thomas Hitchcox and James Richard Forbes},
      year={2024},
      eprint={2305.06869},
      archivePrefix={arXiv},
      primaryClass={cs.RO}
}

Quick-start

Open MATLAB and run

example.m

GNC-ADAPT Example

The code below demonstrates how to use GNC-ADAPT to solve a nonlinear least-squares problem. The example problem used here is a single rotation averaging problem. A user can modify the fields in problem_params to generate a problem with different parameters.

• N: number of measurements
• outlierRatio: the amount of outliers in the measurements
• noiseSigma: the standard deviation of the Gaussian noise in the measurements

A problem is then generated by executing

problem = SingleRotationAveragingProblem(problem_params);

The initial guess for the rotation matrix is generated by adding a random rotation to the ground truth rotation matrix.

initialNoise = 90; % degrees
rotAxis = normalize(randn(3, 1), 'norm');
rotAngle = deg2rad(initialNoise) * randn();
R_init = problem.R_gt * axang2rotm([rotAxis', rotAngle]);

Then, the problem is solved using the method of the user's choice (e.g., GNC-ADAPT).

results.gnc_adapt = problem.solve( ...
    'lossFunction', @gnc_adapt, ...
    'alphaStar', [], ...
    'R_init', R_init ...
);

The problem can be solved by other loss functions such as

Method	Function Handle	alphaStar
Cauchy	@cauchy	-
GM	@gm	-
ADAPT	@adapt	-
AMB	@amb	-
GNC-Cauchy	@gnc_adapt	0
GNC-GM	@gnc_adapt	-2
GNC-ADAPT	@gnc_adapt	-
GNC-AMB	@gnc_amb	-
GNC-TLS	@gnc_tls	-

The solve method has the following optional parameters:

• R_init: the initial guess for the rotation matrix
• lossFunction: a function handle to the loss function to be used
• inliers: a logical vector indicating the inliers
• maxIter: the maximum number of iterations
• tau: the noise bound parameter to estimate the optimal shape parameter
• costThreshold: the cost threshold to stop the iterations
• alphaStar: the value of optimal shape parameter when it is known
• verbose: a flag to print the progress of the algorithm

Acknowledgments

This work was partially funded by:

• Voyis Imaging Inc.
• Natural Sciences and Engineering Research Council of Canada (NSERC)
• McGill Engineering Doctoral Award (MEDA)

License

BSD License