Efficient Pruning LMI Conditions for Branch-and-Prune Rank and Chirality-Constrained Estimation of the Dual Absolute Quadric

Abstract

We present a new globally optimal algorithm for self-calibrating a moving camera with constant parameters. Our method aims at estimating the Dual Absolute Quadric (DAQ) under the rank-3 and, optionally, camera centers chirality constraints. We employ the Branch-and-Prune paradigm and explore the space of only 5 parameters. Pruning in our method relies on solving Linear Matrix Inequality (LMI) feasibility and Generalized Eigenvalue (GEV) problems that solely depend upon the entries of the DAQ. These LMI and GEV problems are used to rule out branches in the search tree in which a quadric not satisfying the rank and chirality conditions on camera centers is guaranteed not to exist. The chirality LMI conditions are obtained by relying on the mild assumption that the camera undergoes a rotation of no more than 90 between consecutive views. Furthermore, our method does not rely on calculating bounds on any particular cost function and hence can virtually optimize any objective while achieving global optimality in a very competitive running-time.