The rkd-Tree : An Improved kd-Tree for Fast n-Closest Point Queries in Large Point Sets

The kd-tree is used in various applications, such as photon simulation with photon maps, or normal estimation in point sets for reconstruction, in order to perform fast n-closest neighbour searches in huge, static data sets of point sets of arbitrary dimensions. In a number of cases, where lower dimensional point sets are embedded in higher dimensional spaces, it has been shown that the vantage point tree (vp-tree) can significantly outperform the kd-tree. In this paper we introduce the rkd-tree, a modified version of the kd-tree that applies ideas from the vp-tree to the kd-tree. This improved kd-tree version is shown to outperform both the kd-tree and the vp-tree in a number of artificial and real test-cases.