dev10110 / GraduatedNonConvexity.jl

A lightweight pure-julia library to perform outlier-robust least-squares optimization using Graduated NonConvexity

GraduatedNonConvexity

Quickstart

Suppose we are given data x, y

data = (x, y)

Suppose the model to fit is y = x * m, where we want to find m.

Implement a weighted least squares solver

function solver(w, data)
  # implement your weighted least squares optimizer
  # w is a N-vector of weights 
end

and a function to calculate the residuals

function residuals(c, data)
  # implement a function that returns the residuals for each data point given the candidate solution m
  # should return a N-vector of residuals
end

define maximum residual of inliers

c = 0.2

Solve using GNC

using GraduatedNonConvexity
m_gm = GNC_GM(N, data, solver, residuals, c) # or
m_tls = GNC_TLS(N, data, solver, residuals, c)

Complete Example

see examples/1d.jl

Documentation

Citation

This package is a re-implementation of

H. Yang, P. Antonante, V. Tzoumas, and L. Carlone,“Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection”,IEEE Robotics and Automation Letters (RA-L), 2020

The author's original implementatation is available at https://github.com/MIT-SPARK/GNC-and-ADAPT