Parallelized algorithms for rigid surface alignment on GPU

Alignment and registration of rigid surfaces is a fundamental computational geometric problem with applications ranging from medical imaging, automated target recognition, and robot navigation just to mention a few. The family of the iterative closest point (ICP) algorithms introduced by Chen and Medioni [YC] and Besl and McKey [PB92] and improved over the three decades that followed constitute a classical to the problem. However, with the advent of geometry acquisition technologies and applications they enable, it has become necessary to align in real time dense surfaces containing millions of points. The classical ICP algorithms, being essentially sequential procedures, are unable to address the need. In this study, we follow the recent work by Mitra et al. [NJM] considering ICP from the point of view of point-to-surface Euclidean distance map approximation. We propose a variant of a k-d tree data structure to store the approximation, and show its efficient parallelization on modern graphics processors. The flexibility of our implementation allows using different distance approximation schemes with controllable trade-off between accuracy and complexity. It also allows almost straightforward adaptation to richer transformation groups. Experimental evaluation of the proposed approaches on a state-of-the-art GPU on very large datasets containing around 10 ⁶ vertices shows real-time performance superior by up to three orders of magnitude compared to an efficient CPU-based version.