Dynamical Pose Estimation

TL;DR

This paper introduces DAMP, a novel physics-inspired algorithm for 3D primitive alignment that unifies multiple perception tasks and guarantees convergence in several cases, demonstrating strong empirical performance.

Contribution

The paper unifies five perception problems under a primitive alignment framework and proposes DAMP, a practical dynamical system-based algorithm with proven global convergence in certain scenarios.

Findings

DAMP converges to the global optimum in point cloud registration and related problems.

DAMP reliably escapes local minima in 2D-3D correspondence problems.

Theoretical analysis confirms local stability and convergence of DAMP in specific cases.

Abstract

We study the problem of aligning two sets of 3D geometric primitives given known correspondences. Our first contribution is to show that this primitive alignment framework unifies five perception problems including point cloud registration, primitive (mesh) registration, category-level 3D registration, absolution pose estimation (APE), and category-level APE. Our second contribution is to propose DynAMical Pose estimation (DAMP), the first general and practical algorithm to solve primitive alignment problem by simulating rigid body dynamics arising from virtual springs and damping, where the springs span the shortest distances between corresponding primitives. We evaluate DAMP in simulated and real datasets across all five problems, and demonstrate (i) DAMP always converges to the globally optimal solution in the first three problems with 3D-3D correspondences; (ii) although DAMP sometimes converges to suboptimal solutions in the last two problems with 2D-3D correspondences, using a scheme for escaping local minima, DAMP always succeeds. Our third contribution is to demystify the surprising empirical performance of DAMP and formally prove a global convergence result in the case of point cloud registration by charactering local stability of the equilibrium points of the underlying dynamical system.