Kd Tree

Cluster analysis method is one of the most analytical methods of data mining. The method will directly influence the result of clustering. This paper discusses the standard of k-mean clustering and analyzes the shortcomings of standard k-means such as k-means algorithm calculates distance of each data point from each cluster centre. Calculating this distance in each iteration makes the algorithm of low efficiency. This paper introduces an optimized algorithm which solves this problem. This is done by introducing a simple data structure to store some information in every iteration and used this information in next iteration. The introduced algorithm does not require calculating the distance of each data point from each cluster centre in each iteration due to which running time of algorithm is saved. Experimental results show that the improved algorithm can efficiently improve the speed of clustering and accuracy by reducing the computational complexity of standard k-means algorithm.

In this paper we address the problem of building an effi-cient database management system that allows querying for similar images. This system, which supports image-based queries on a database of photographs taken around the campus, helps the user to identify his/her ...

Efficient ray shooting algorithm is inherently required by many computer graphics algorithms, particularly in image synthesis. Practical ray shooting algorithms aiming at the average-case complexity use some underlying spatial data structure such as -tree. We show the new termi- nation criteria algorithm that improves the space and time complexity of the -tree construction. It provides efficient ray-shooting queries and does

Using image manipulation programs has become easier and more powerful than before. Due to such fact, detection of image forgeries has produced significant interest recently. Falsification of images can initiate dangerous legal concerns. Among the most extensively utilized approaches for image forgeries is copy-move forgery in which a section of the image is copied and duplicated in another location in the same image. A significant part of a digital image can be covered or added using this procedure. In this paper, we propose an accurate algorithm for copy-move forgery detection. A block-based approach is suggested that uses the KD-tree data structure and a simple yet efficient feature vector to detect the possible forgery. The results demonstrated in this work match state of the art methods while providing a significant speedup.

We describe a data structure for three-dimensional Nef complexes, algorithms for boolean operations on them, and our implementation of data structure and algorithms. Nef polyhedra were introduced by W. Nef in his seminal 1978 book on polyhedra. They are the closure of half-spaces under boolean operations and can represent non-manifold situations, open and closed boundaries, and mixed dimensional complexes. Our focus lies on the generality of the data structure, the completeness of the algorithms, and the exactness and efficiency of the implementation. In particular, all degeneracies are handled.

We describe a novel data structure for representing light transport called ray map. The ray map extends the concept of photon maps: it stores not only photon impacts but the whole photon paths. We demonstrate the utility of ray maps for global illumination by eliminating boundary bias and reducing topological bias of density estimation in global illumination. Thanks to the

We introduce a parallel algorithm to solve approximate and exact nearest neighbor queries on the GPU, exploiting its massively parallel processing power. Both data structure construction and nearest neighbor queries are performed on the GPU, avoiding memory copies from system memory to device memory. This algorithm achieves real-time performance, enabling its usage in dynamic scenarios, by minimizing the sorting comparisons

Many computer graphics rendering algorithms and techniques use ray tracing for generating natural and
photo-realistic images. Ray tracing is a method to convert 3D-modeles into 2D-high quality images by
complex computation. The millions of rays must be simulated and traced to create realistic image. A
method for reducing render time is acceleration structures. The kd-tree is the most commonly used in
accelerating ray tracing algorithms. This paper has focused on reducing render time. We propose tow
methods that are combined with ray tracing method for obtaining some pixel colour of image plane. Our
methods are linear algorithm and are faster than ray tracing method. Our results show that our methods
are at least 50% faster than spatial median approach for reasonably complex scenes with around 70k
polygons and about 0.2% quality degradation. In this article, we show that these proposal methods can be
combined with other ray tracing methods such as SAH to reduce render time.

In this article an interactive image information mining protocol is presented aiming at a computationally efficient pattern interpretation. The method operates on very high resolution (VHR) remote-sensing optical imagery and follows a modular approach. Images are projected onto a hierarchical image representation structure, the Max-Tree, which interfaces multi-dimensional features of the image components. Positive and negative samples are selected interactively from the image space and are translated into features describing best the targeted and non-desired patterns. Sourcing the feature entries into a hierarchical clustering algorithm, the kd-Tree, yields a structured representation that ensures fast classification. A classification is computed directly from the kd-Tree and is applied on the Max-Tree for accepting or rejecting image components. The complete process cycle is demonstrated on gigapixel-sized VHR satellite images and requires 3 min for building the Max-Tree, 30 min for hierarchical clustering and less than 10 s for each example based query.

Modeling audio signals via the long-term statistical distribu- tion of their local spectral features - often denoted as bag of frames (BOF) approach - is a popular and powerful method to describe audio content. While modeling the distribution of local spectral features by semi-parametric distributions (e.g. Gaussian Mixture Models) has been studied intensively, we investigate a non-para- metric variant based

Smooth surface extraction using partial differential equations (PDEs) is a well-known and widely used technique for visualizing volume data. Existing approaches operate on gridded data and mainly on regular structured grids. When considering unstructured point-based volume data where sample points do not form regular patterns nor are they connected in any form, one would typically resample the data over a grid prior to applying the known PDE-based methods. We propose an approach that directly extracts smooth surfaces from unstructured point-based volume data without prior resampling or mesh generation. When operating on unstructured data one needs to quickly derive neighborhood information. The respective information is retrieved by partitioning the 3D domain into cells using a kd-tree and operating on its cells. We exploit neighborhood information to estimate gradients and mean curvature at every sample point using a four-dimensional least-squares fitting approach. Gradients and me...

Building a model of large-scale terrain that can adequately handle uncertainty and incompleteness in a statistically sound way is a challenging problem. This work proposes the use of Gaussian processes as models of large-scale terrain. The proposed model naturally provides a multiresolution representation of space, incorporates and handles uncertainties aptly, and copes with incompleteness of sensory information. Gaussian process regression techniques are applied to estimate and interpolate (to fill gaps in occluded areas) elevation information across the field. The estimates obtained are the best linear unbiased estimates for the data under consideration. A single nonstationary (neural network) Gaussian process is shown to be powerful enough to model large and complex terrain, effectively handling issues relating to discontinuous data. A local approximation method based on a “moving window” methodology and implemented using k-dimensional (KD)-trees is also proposed. This enables the approach to handle extremely large data sets, thereby completely addressing its scalability issues. Experiments are performed on large-scale data sets taken from real mining applications. These data sets include sparse mine planning data, which are representative of a global positioning system–based survey, as well as dense laser scanner data taken at different mine sites. Further, extensive statistical performance evaluation and benchmarking of the technique has been performed through cross-validation experiments. They conclude that for dense and/or flat data, the proposed approach will perform very competitively with grid-based approaches using standard interpolation techniques and triangulated irregular networks using triangle-based interpolation techniques; for sparse and/or complex data, however, it would significantly outperform them. © 2009 Wiley Periodicals, Inc.

High-dimensional indexing has been very popularly used for performing similarity search over various data types such as multimedia (audio/image/video) databases, document collections, time-series data, sensor data and scientific databases. Because of the curse of dimensionality, it is already known that well-known data structures like kd-tree, R-tree, and M-tree suffer in their performance over high-dimensional data space which is inferior to a brute-force approach linear scan. In this paper, we focus on an approximate nearest neighbor search for two different types of queries: r-Range search and k-NN search. Adapting a novel concept of a ring structure, we define a new index structure MLR-Index (Multi-Layer Ring-based Index) in a metric space and propose time and space efficient algorithms with high accuracy. Evaluations through comprehensive experiments comparing with the best-known high-dimensional indexing method LSH show that our approach is faster for a similar accuracy, and shows higher accuracy for a similar response time than LSH.

Nowadays feature vector based similarity search is increasingly emerging in database systems. Consequently, many multidimensional data index techniques have been widely introduced to database researcher community. These index techniques are categorized into two main classes: SP (space partitioning)/KD-tree-based and DP (data partitioning)/R-tree-based. Recently, a hybrid index structure has been proposed. It combines both SP/KDtree-based and DP/R-tree-based techniques to form a new, more efficient index structure. However, weaknesses are still existing in techniques above. In this paper, we introduce a novel and flexible index structure for multidimensional data, the SH-tree (Super Hybrid tree). Theoretical analyses show that the SHtree is a good combination of both techniques with respect to both presentation and search algorithms. It overcomes the shortcomings and makes use of their positive aspects to facilitate efficient similarity searches.