Fast and accurate surface alignment through an isometry-enforcing game

• We introduce a novel pipeline for rigid surface alignment based on Game Theory.
• The method allows to obtain accurate solutions without requiring an initial estimate.
• We propose simple descriptors designed to be fast and effective within our pipeline.
• We establish a relation between evolutionary stable states and optimal alignments.
• The technique is efficient and outperforms the state of the art.

Surface registration is often performed as a two step process. A feature matching scheme is first adopted to find a coarse initial alignment between two meshes. Subsequently, a refinement step, which usually operates in the space of rigid motions, is applied to reach an optimal registration with respect to pointwise distances between overlapping areas. In this paper we propose a novel technique that allows to obtain an accurate surface registration in a single step, without the need for an initial motion estimation. The main idea of our approach is to cast the selection of correspondences between points on the surfaces in a game-theoretic framework, where a natural selection process allows matching points that satisfy a mutual rigidity constraint to thrive, eliminating all the other correspondences. This process yields a very robust inlier selection scheme that does not depend on any particular technique for selecting the initial strategies as it relies only on the global geometric compatibility between correspondences. The practical effectiveness of the approach is confirmed by an extensive set of experiments and comparisons with state-of-the-art techniques.