Almost constant-time 3D nearest-neighbor lookup using implicit octrees

摘要

A recurring problem in 3D applications is nearest-neighbor lookups in 3D point clouds. In this work, a novel method for exact and approximate 3D nearest-neighbor lookups is proposed that allows lookup times that are, contrary to previous approaches, nearly independent of the distribution of data and query points, allowing to use the method in real-time scenarios. The lookup times of the proposed method outperform prior art sometimes by several orders of magnitude. This speedup is bought at the price of increased costs for creating the indexing structure, which, however, can typically be done in an offline phase. Additionally, an approximate variant of the method is proposed that significantly reduces the time required for data structure creation and further improves lookup times, outperforming all other methods and yielding almost constant lookup times. The method is based on a recursive spatial subdivision using an octree that uses the underlying Voronoi tessellation as splitting criteria, thus avoiding potentially expensive backtracking. The resulting octree is represented implicitly using a hash table, which allows finding the leaf node a query point belongs to with a runtime that is logarithmic in the tree depth. The method is also trivially extendable to 2D nearest neighbor lookups.