DeepAI AI Chat
Log In Sign Up

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

by   Heng Yang, et al.

We propose the first general and scalable framework to design certifiable algorithms for robust geometric perception in the presence of outliers. Our first contribution is to show that estimation using common robust costs, such as truncated least squares (TLS), maximum consensus, Geman-McClure, Tukey's biweight, among others, can be reformulated as polynomial optimization problems (POPs). By focusing on the TLS cost, our second contribution is to exploit sparsity in the POP and propose a sparse semidefinite programming (SDP) relaxation that is much smaller than the standard Lasserre's hierarchy while preserving exactness, i.e., the SDP recovers the optimizer of the nonconvex POP with an optimality certificate. Our third contribution is to solve the SDP relaxations at an unprecedented scale and accuracy by presenting STRIDE, a solver that blends global descent on the convex SDP with fast local search on the nonconvex POP. Our fourth contribution is an evaluation of the proposed framework on six geometric perception problems including single and multiple rotation averaging, point cloud and mesh registration, absolute pose estimation, and category-level object pose and shape estimation. Our experiments demonstrate that (i) our sparse SDP relaxation is exact with up to 60 real-time, STRIDE is up to 100 times faster than existing SDP solvers on medium-scale problems, and is the only solver that can solve large-scale SDPs with hundreds of thousands of constraints to high accuracy; (iii) STRIDE provides a safeguard to existing fast heuristics for robust estimation (e.g., RANSAC or Graduated Non-Convexity), i.e., it certifies global optimality if the heuristic estimates are optimal, or detects and allows escaping local optima when the heuristic estimates are suboptimal.


page 15

page 16

page 25

page 26

page 27

page 28


One Ring to Rule Them All: Certifiably Robust Geometric Perception with Outliers

We propose a general and practical framework to design certifiable algor...

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

Semidefinite Programming (SDP) and Sums-of-Squares (SOS) relaxations hav...

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

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

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...

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...

Accelerated Inference in Markov Random Fields via Smooth Riemannian Optimization

Markov Random Fields (MRFs) are a popular model for several pattern reco...

Dynamical Pose Estimation

We study the problem of aligning two sets of 3D geometric primitives giv...