Abstract
The registration of 3D models by a Euclidean transformation is a fundamental task at the core of many application in computer vision. This problem is non-convex due to
the presence of rotational constraints, making traditional
local optimization methods prone to getting stuck in local minima. This paper addresses finding the globally optimal transformation in various 3D registration problems
by a unified formulation that integrates common geometric
registration modalities (namely point-to-point, point-to-line
and point-to-plane). This formulation renders the optimization problem independent of both the number and nature of
the correspondences.
The main novelty of our proposal is the introduction of a
strengthened Lagrangian dual relaxation for this problem,
which surpasses previous similar approaches [32] in effectiveness. In fact, even though with no theoretical guarantees, exhaustive empirical evaluation in both synthetic and
real experiments always resulted on a tight relaxation that
allowed to recover a guaranteed globally optimal solution
by exploiting duality theory.
Thus, our approach allows for effectively solving the 3D
registration with global optimality guarantees while running at a fraction of the time for the state-of-the-art alternative [34], based on a more computationally intensive
Branch and Bound method