Accelerated Parametric Chamfer Alignment Using a Parallel, Pipelined GPU Realization

Parametric chamfer alignment (PChA) is commonly employed for aligning an observed set of points with a corresponding set of reference points. PChA estimates optimal geometric transformation parameters that minimize an objective function formulated as the sum of the squared distances from each transformed observed point to its closest reference point. A distance transform enables efficient computation of the (squared) distances and the objective function minimization is commonly performed via the Levenberg-Marquardt (LM) non-linear least squares iterative optimization algorithm. The pointwise computations of the objective function, gradient, and Hessian approximation required for the LM iterations make PChA computationally demanding for large scale data sets. We propose an acceleration of the PChA via a parallelized and pipelined realization that is particularly wellsuited for large scale data sets and for modern GPU architectures. Specifically, we partition the observed points among the GPU blocks and decompose the expensive LM calculations in correspondence with the GPU’s single instruction multiple thread (SIMT) architecture to significantly speed-up this bottleneck step for PChA on large-scale datasets. Additionally, by re-ordering computations, we propose a novel pipelining of the LM algorithm that offers further speed-up by exploiting the low arithmetic latency of the GPU compared with its high global memory access latency. Results obtained on two different platforms for both 2D and 3D large-scale point data sets from our ongoing research demonstrate that the proposed PChA GPU implementation provides a significant speed-up over its single CPU counterpart.