2The recent improvements of graphics processing units (GPU) offer to the computer vision community a powerful processing platform. Indeed, a lot of highlyparallelizable computer vision problems can be significantly accelerated using GPU architecture. Among these algorithms, the k nearest neighbor search (KNN) is a well-known problem linked with many applications such as classification, estimation of statistical properties, etc. The main drawback of this task lies in its computation burden, as it grows polynomially with the data size. In this paper, we show that the use of the NVIDIA CUDA API accelerates the search for the KNN up to a factor of 120. IntroductionA graphics processing unit (also called GPU) is a dedicated graphics rendering device for a personal computer, workstation, or game console. GPU is highly specialized for parallel computing. The recent improvements of GPUs offer a powerful processing platform for both graphics and non-graphics applications. Indeed, a large proportion of computer vision algorithms are parallelizable and can greatly be accelerated using GPU. The use of GPU was, uptil recently, not easy for nongraphics applications. The introduction of the NVIDIA CUDA (Compute Unified Device Architecture) brought, through a C-based API, an easy way to take advantage of the high performance of GPUs for parallel computing. The k nearest neighbor search problem (KNN) is encountered in many different fields. In statistics, one of the first density estimate [LQ65] was indeed formulated as a k nearest neighbor problem. It has since appeared in many applications such as KNN-based classification [Das91, SDI06] and image filtering [Yar85]. More recently, some effective estimates of high-dimensional statistical measures have been proposed [KL87]. These works have some computer vision applications [BWD + 06, GBDB07]. The KNN search is usually slow because it is a heavy process. The computation of the distance between two points requires many basic operations. The resolution of the KNN search polynomially grows with the size of the point sets. In this paper, we show how GPU can accelerate the process of the KNN search using NVIDIA CUDA. Our CUDA implementation is up to 120 times faster than a similar C implementation. Moreover, we show that the space dimension has a negligible impact on the computation time for the CUDA implementation contrary to the C implementation. These two improvements allow to (1) decrease the time of computation, (2) reduce the size restriction generally necessary to solve KNN in a reasonable time. 0.2. K NEAREST NEIGHBORS SEARCH 3 0.2 k Nearest Neighbors Search Problem definitionLet R = {r 1 , r 2 , · · · , r m } be a set of m reference points in a d dimensional space, and let Q = {q 1 , q 2 , · · · , q n } be a set of n query points in the same space. The k nearest neighbor search problem consists in searching the k nearest neighbors of each query point q i ∈ Q in the reference set R given a specific distance. Commonly, the Euclidean or the Manhattan distance is used but any othe...

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This paper presents a new variational method for the segmentation of a moving object against a still background, over a sequence of [two-dimensional or three-dimensional (3-D)] image frames. The method is illustrated in application to myocardial gated single photon emission computed tomography (SPECT) data, and incorporates a level set framework to handle topological changes while providing closed boundaries. The key innovation is the introduction of a geometrical constraint into the derivation of the Euler-Lagrange equations, such that the segmentation of each individual frame can be interpreted as a closed boundary of an object (an isolevel of a set of hyper-surfaces) while integrating information over the entire sequence. This results in the definition of an evolution velocity normal to the object boundary. Applying this method to 3-D myocardial gated SPECT sequences, the left ventricle endocardial and epicardial limits can be computed in each frame. This space-time segmentation method was tested on simulated and clinical 3-D myocardial gated SPECT sequences and the corresponding ejection fractions were computed.