Fast Nearest Neighbor Search using Approximate Cached k-d tree

We introduce a fast Nearest Neighbor Search (NNS) algorithm using an Approximate Cached k-d tree (ACk-d tree) structure for low dimensional data sets. The search process of the standard k-d tree starts from the root node and employs a tentative back-tracking search. In contrast, the proposed method begins to search at the appropriate leaf node (cached node) and applies a depth-first nontentative search. This method improves searching speed, with tradeoff of the searching accuracy. To get a proper starting node, the proposed method is based on two properties: i) The i_th query point is likely to be close to the (i-1)_th query point, ii) The i_th query point is likely to be close to the i_th model point. These properties are rather right, in case of practical 3D point sets which are consecutively acquired from 3D point sensors (e.g. a stereo camera, the Kinect sensor, and LIDAR). Results show that the search time of the proposed method is superior to other variants of k-d tree for practical point data sets.