Abstract
Point set registration under affine transformation is an important problem in computer vision because not only it has many direct applications, but it is also often used as an initial step for non-rigid registration. This problem is challenging when no correspondences between the two point sets are known, and most existing methods start from an initial pose and find a local optimal transformation. This paper presents a deterministic global optimization method for affine point set registration, which is called GO-APSR. We model the two sets to be registered with Gaussian Mixture Models (GMMs) and minimize the L2 distance between the two GMMs under affine transformation. Branch-and-Bound (BnB) is employed to search the transformation parameter space, and we propose a convex quadratic function as the under-estimator of the objective function in each branch. Therefore, calculation of the lower bound in each branch is casted into a bound-constrained convex quadratic programming problem, which can be solved globally and efficiently. Experiment results verify the global optimality of the proposed method and its robustness to noise and outliers. Furthermore, it works very well in the challenging partially-overlap scenarios.
Highlights
Point set registration, which finds a spatial transformation to align two point sets, is widely used in computer vision, pattern recognition, and medical image analysis
EXPERIMENT RESULTS we evaluate the performance of the proposed algorithm GO-APSR and compare it against state-of-the-art affine point set registration methods APM [15] and CPD [28] on both synthetic and real data
The algorithm GO-APSR was implemented with MATLAB, the code of APM is from http://www4.comp.polyu.edu.hk/ cslzhang/APM.html, and the code of CPD is from www.pudn.com
Summary
Point set registration, which finds a spatial transformation to align two point sets, is widely used in computer vision, pattern recognition, and medical image analysis. The idea of soft correspondence exists in new alignment criterions based on the probability distribution constructed from the original point sets, e.g., Kernel Correlation [12] and Gaussian Mixture Models (GMMs) [13], [14] These probability distribution based alignment criterions are robust to noise and outliers, and can provide a larger convergence basin than ICP, but a good initial transformation is still needed. There has been a surge of solving point set registration problem globally by using Branch-and-Bound (BnB) optimization framework without prior information on correspondence or transformation. Most of these approaches focus on rigid registration. BnB framework is used to minimize the cost function, and we derive a quadratic lower bound function to the cost function in every branch, so that finding the lower bound in each branch is casted into a bound-constrained convex Quadratic Programming (QP) problem, which can be globally optimized quickly
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