Convex Optimisation for Inverse Kinematics

TL;DR

This paper introduces a convex optimization method using semidefinite programming to solve inverse kinematics problems globally, overcoming local optima issues common in traditional local optimization techniques.

Contribution

The paper presents a novel convex relaxation approach for inverse kinematics, enabling polynomial-time solutions and improved accuracy over local methods.

Findings

Outperforms local optimization methods on real-world skeletons

Provides globally optimal solutions due to convex relaxation

Demonstrates efficiency and accuracy improvements

Abstract

We consider the problem of inverse kinematics (IK), where one wants to find the parameters of a given kinematic skeleton that best explain a set of observed 3D joint locations. The kinematic skeleton has a tree structure, where each node is a joint that has an associated geometric transformation that is propagated to all its child nodes. The IK problem has various applications in vision and graphics, for example for tracking or reconstructing articulated objects, such as human hands or bodies. Most commonly, the IK problem is tackled using local optimisation methods. A major downside of these approaches is that, due to the non-convex nature of the problem, such methods are prone to converge to unwanted local optima and therefore require a good initialisation. In this paper we propose a convex optimisation approach for the IK problem based on semidefinite programming, which admits a polynomial-time algorithm that globally solves (a relaxation of) the IK problem. Experimentally, we demonstrate that the proposed method significantly outperforms local optimisation methods using different real-world skeletons.