A Certifiably Globally Optimal Solution to the Non-Minimal Relative Pose Problem

Abstract

Finding the relative pose between two calibrated views ranks among the most fundamental geometric vision problems. It therefore appears as somewhat a surprise that a globally optimal solver that minimizes a properly defined energy over non-minimal correspondence sets and in the original space of relative transformations has yet to be discovered. This, notably, is the contribution of the present paper. We formulate the problem as a Quadratically Constrained Quadratic Program (QCQP), which can be converted into a Semidefinite Program (SDP) using Shor's convex relaxation. While a theoretical proof for the tightness of this relaxation remains open, we prove through exhaustive validation on both simulated and real experiments that our approach always finds and certifies (a-posteriori) the global optimum of the cost function.