Delaunay walk for fast nearest neighbor: accelerating correspondence matching for ICP

Abstract

Point set registration algorithms such as Iterative Closest Point (ICP) are commonly utilized in time-constrained environments like robotics. Finding the nearest neighbor of a point in a reference 3D point set is a common operation in ICP and frequently consumes at least 90% of the computation time. We introduce a novel approach to performing the distance-based nearest neighbor step based on Delaunay triangulation. This greedy algorithm finds the nearest neighbor of a query point by traversing the edges of the Delaunay triangulation created from a reference 3D point set. Our work integrates the Delaunay traversal into the correspondences search of ICP and exploits the iterative aspect of ICP by caching previous correspondences to expedite each iteration. An algorithmic analysis and comparison is conducted showing an order of magnitude speedup for both serial and vector processor implementation.

PatchFusion: Patch-based Nonrigid Tracking and Reconstruction of Deformable Objects using a Single RGB-D Sensor

“…However, it encounters challenges when dealing with complex geometries featuring low overlap or significant displacements, primarily due to the difficulty in finding reasonable correspondences via closest point search. Consequently, numerous ICP variants have been proposed to address these issues, including various designs concerning correspondence matching [17,18], objective functions [11,19], and robust kernels [20]. In the context of our system's rigid registration thread, we leverage geometric features such as normals and curvatures to enhance correspondence matching, as demonstrated in prior work [11].…”

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