Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejection

09/18/2019
by   Heng Yang, et al.
19

Semidefinite Programming (SDP) and Sums-of-Squares (SOS) relaxations have led to certifiably optimal non-minimal solvers for several robotics and computer vision problems. However, most non-minimal solvers rely on least squares formulations, and, as a result, are brittle against outliers. While a standard approach to regain robustness against outliers is to use robust cost functions, the latter typically introduce other non-convexities, preventing the use of existing non-minimal solvers. In this paper, we enable the simultaneous use of non-minimal solvers and robust estimation by providing a general-purpose approach for robust global estimation, which can be applied to any problem where a non-minimal solver is available for the outlier-free case. To this end, we leverage the Black-Rangarajan duality between robust estimation and outlier processes (which has been traditionally applied to early vision problems), and show that graduated non-convexity (GNC) can be used in conjunction with non-minimal solvers to compute robust solutions, without requiring an initial guess. We demonstrate the resulting robust non-minimal solvers in applications, including point cloud and mesh registration, pose graph optimization, and image-based object pose estimation (also called shape alignment). Our solvers are robust to 70-80 specialized local solvers, and faster than specialized global solvers. We also extend the literature on non-minimal solvers by proposing a certifiably optimal SOS solver for shape alignment.

READ FULL TEXT

page 1

page 5

page 7

research
12/01/2022

Bayesian Heuristics for Robust Spatial Perception

Spatial perception is a key task in several robotics applications. In ge...
research
09/18/2022

A Decoupled and Linear Framework for Global Outlier Rejection over Planar Pose Graph

We propose a robust framework for the planar pose graph optimization con...
research
09/07/2021

Certifiable Outlier-Robust Geometric Perception: Exact Semidefinite Relaxations and Scalable Global Optimization

We propose the first general and scalable framework to design certifiabl...
research
04/04/2022

IMOT: General-Purpose, Fast and Robust Estimation for Spatial Perception Problems with Outliers

Spatial perception problems are the fundamental building blocks of robot...
research
07/29/2020

Outlier-Robust Estimation: Hardness, Minimally-Tuned Algorithms, and Applications

Nonlinear estimation in robotics and vision is typically plagued with ou...
research
06/24/2022

Optimal and Robust Category-level Perception: Object Pose and Shape Estimation from 2D and 3D Semantic Keypoints

We consider a category-level perception problem, where one is given 2D o...
research
04/16/2021

Optimal Pose and Shape Estimation for Category-level 3D Object Perception

We consider a category-level perception problem, where one is given 3D s...

Please sign up or login with your details

Forgot password? Click here to reset