  In many applications, the demand arises for algorithms capable of aligning
partially overlapping point sets while remaining invariant to the corresponding
transformations. This research presents a method designed to meet such
requirements through minimization of the objective function of the robust point
matching (RPM) algorithm. First, we show that the RPM objective is a cubic
polynomial. Then, through variable substitution, we transform the RPM objective
to a quadratic function. Leveraging the convex envelope of bilinear monomials,
we proceed to relax the resulting objective function, thus obtaining a lower
bound problem that can be conveniently decomposed into distinct linear
assignment and low-dimensional convex quadratic program components, both
amenable to efficient optimization. Furthermore, a branch-and-bound (BnB)
algorithm is devised, which solely branches over the transformation parameters,
thereby boosting convergence rate. Empirical evaluations demonstrate better
robustness of the proposed methodology against non-rigid deformation,
positional noise, and outliers, particularly in scenarios where outliers remain
distinct from inliers, when compared with prevailing state-of-the-art
approaches.
