Abstract. Nearest-neighbor queries in high-dimensional space are of high importance in various applications, especially in content-based indexing of multimedia data. For an optimization of the query processing, accurate models for estimating the query processing costs are needed. In this paper, we propose a new cost model for nearest neighbor queries in high-dimensional space, which we apply to enhance the performance of high-dimensional index structures. The model is based on new insights into effects occurring in high-dimensional space and provides a closed formula for the processing costs of nearest neighbor queries depending on the dimensionality, the block size and the database size. From the wide range of possible applications of our model, we select two interesting samples: First, we use the model to prove the known linear complexity of the nearest neighbor search problem in high-dimensional space, and second, we provide a technique for optimizing the block size. For data of medium dimensionality, the optimized block size allows significant speed-ups of the query processing time when compared to traditional block sizes and to the linear scan. 1.

In nearest neighbor searching we are given a set of n data points in real d-dimensional space, R d , and the problem is to preprocess these points into a data structure, so that given a query point, the nearest data point to the query point can be reported eciently. Because data sets can be quite large, we are interested in data structures that use optimal O(dn) storage. Given the limitation of linear storage, the best known data structures suer from expected-case query times that grow exponentially in d. However, it is widely regarded in practice that data sets in high dimensional spaces tend to consist of clusters residing in much lower dimensional subspaces. This raises the question of whether data structures for nearest neighbor searching adapt to the presence of lower dimensional clustering, and further how performance varies when the clusters are aligned with the coordinate axes. We analyze the popular kd-tree data structure in the form of two variants based on a modication of the splitting method, which produces cells satisfy the basic packing properties needed for eciency without producing empty cells. We show that when data points are uniformly distributed on a k- dimensional hyperplane for k d, then expected number of leaves visited in such a kd-tree grows exponentially in k, but not in d. We show that the growth rate is even smaller still if the hyperplane is aligned with the coordinate axes. We present empirical studies to support our theoretical results. Keywords: Nearest neighbor searching, kd-trees, splitting methods, expected-case analysis, clustering. 1

We present a system for constructing 3D models of real-world objects with optically challenging surfaces. The system utilizes a new range imaging concept called multipeak range imaging, which stores multiple candidates of range measurements for each point on the object surface. The multiple measurements include the erroneous range data caused by various surface properties that are not ideal for structured-light range sensing. False measurements generated by spurious reflections are eliminated by applying a series of constraint tests. The constraint tests based on local surface and local sensor visibility are applied first to individual range images. The constraint tests based on global consistency of coordinates and visibility are then applied to all range images acquired from different viewpoints. We show the effectiveness of our method by constructing 3D models of five different optically challenging objects. To evaluate the performance of the constraint tests and to examine the effects of the parameters used in the constraint tests, we acquired the ground-truth data by painting those objects to suppress the surface-related properties that cause difficulties in range sensing. Experimental results indicate that our method significantly improves upon the traditional methods for constructing reliable 3D models of optically challenging objects.

The nearest neighbor problem is that of preprocessing a set P of n data points in R d so that, given any query point q, the closest point in P to q can be determined efficiently. In the chromatic nearest neighbor problem, each point of P is assigned a color, and the problem is to determine the color of the nearest point to the query point. More generally, given k 1, the problem is to determine the color occurring most frequently among the k nearest neighbors. The chromatic version of the nearest neighbor problem is used in many applications in pattern recognition and learning. In this paper we present a simple algorithm for solving the chromatic k nearest neighbor problem. We provide a query sensitive analysis, which shows that if the color classes form spatially well separated clusters (as often happens in practice), then queries can be answered quite efficiently. We also allow the user to specify an error bound ffl 0, and consider the same problem in the context of approximate ne...

Abstract—A method for the semi-automatic detection and visualization of defects in models of nematic liquid crystals (NLCs) is introduced; this method is suitable for unstructured models, a previously unsolved problem. The detected defects—also known as disclinations—are regions were the alignment of the liquid crystal rapidly changes over space; these defects play a large role in the physical behavior of the NLC substrate. Defect detection is based upon a measure of total angular change of crystal orientation (the director) over a node neighborhood via the use of a nearest neighbor path. Visualizations based upon the detection algorithm clearly identifies complete defect regions as opposed to incomplete visual descriptions provided by cutting-plane and isosurface approaches. The introduced techniques are currently in use by scientists studying the dynamics of defect change. Index Terms—scientific visualization, disclination, nematic liquid crystal, defects, unstructured grid, feature extraction 1

We present a modified photon mapping algorithm capable of running entirely on GPUs. Our implementation uses breadth-first photon tracing to distribute photons using the GPU. The photons are stored in a grid-based photon map that is constructed directly on the graphics hardware using one of two methods: the first method is a multipass technique that uses fragment programs to directly sort the photons into a compact grid. The second method uses a single rendering pass combining a vertex program and the stencil buffer to route photons to their respective grid cells, producing an approximate photon map. We also present an efficient method for locating the nearest photons in the grid, which makes it possible to compute an estimate of the radiance at any surface location in the scene. Finally, we describe a breadth-first stochastic ray tracer that uses the photon map to simulate full global illumination directly on the graphics hardware. Our implementation demonstrates that current graphics hardware is capable of fully simulating global illumination with progressive, interactive feedback to the user.

There are many nearest neighbor algorithms tailormade for ICP, but most of them require special input data like range images or triangle meshes. We focus on efficient nearest neighbor algorithms that do not impose this limitation, and thus can also be used with 3-D point sets generated by structure-frommotion techniques. We shortly present the evaluated algorithms and introduce the modifications we made to improve their efficiency. In particular, several enhancements to the well-known k-D tree algorithm are described. The first part of our performance analysis consists of experiments on synthetic point sets, whereas the second part features experiments with the ICP algorithm on real point sets. Both parts are completed by a thorough evaluation of the obtained results.

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Close collaboration with other scientific fields is seen as an important goal for the visualization community by leading researchers in visualization. Yet, engaging in a scientific collaboration can be challenging. Physical sciences, with its array of research directions, provide many exciting challenges for a visualization scientist which in turn create ample possibilities for collaboration. We present the first survey of its kind that provides a comprehensive view on existing work on visualization for the physical sciences. We introduce a novel classification scheme based on application area, data dimensionality and main challenge addressed and apply this classification scheme to each contribution from the literature. Our classification highlights mature areas in visualization for the physical sciences and suggests directions for future work. Our survey serves as a useful starting point for those interested in visualization for the physical sciences, namely astronomy, chemistry, earth sciences and physics. Categories and Subject Descriptors (according to ACM CCS): Utilities—Application packages

journal homepage: www.elsevier.com/locate/cviu Probabilistic cost model for nearest neighbor search in image retrieval q