Fast k nearest neighbor search using GPU

Statistical measures coming from information theory represent interesting bases for image and video processing tasks such as image retrieval and video object tracking. For example, let us mention the entropy and the Kullback-Leibler divergence. Accurate estimation of these measures requires to adapt to the local sample density, especially if the data are high-dimensional. The k nearest neighbor (kNN) framework has been used to define efficient variable-bandwidth kernel-based estimators with such a locally adaptive property. Unfortunately, these estimators are computationally intensive since they rely on searching neighbors among large sets of d-dimensional vectors. This computational burden can be reduced by pre-structuring the data, e.g. using binary trees as proposed by the approximated nearest neighbor (ANN) library. Yet, the recent opening of graphics processing units (GPU) to general-purpose computation by means of the NVIDIA CUDA API offers the image and video processing community a powerful platform with parallel calculation capabilities. In this paper, we propose a CUDA implementation of the ldquobrute forcerdquo kNN search and we compare its performances to several CPU-based implementations including an equivalent brute force algorithm and ANN. We show a speed increase on synthetic and real data by up to one or two orders of magnitude depending on the data, with a quasi-linear behavior with respect to the data size in a given, practical range.