A hashing strategy for efficient k-nearest neighbors computation

The problem of k-nearest neighbors computation within a 3D data set is frequently encountered in computer graphics. Applications include the technique of photon-map rendering where the closest photons to a given one have to be identified and the segmentation phase within a reverse engineering process. We present a new algorithm for k-nearest neighbors computation based on median subdivision and a hashing strategy. The major advantage of our hashing function is that bounds can be established that limit the number of points to be inspected during the search process. Estimates for the asymptotic complexity of our search method are given. Finally we compare our algorithm with a different search strategy based on KD-Trees.