K-dimensional Tree Research Articles

Fast and accurate solution of inverse problem in optical scatterometry using heuristic search and robust correction

Library search is one of the most commonly used methods in optical scatterometry, which consists of the beforehand construction of a signature library and the grid search. The efficiency of existing search algorithms such as k-dimensional tree method and locality-sensitive hashing heavily depends on the size of the signature library and usually is inversely proportional to the library scale. Additionally, since the two-norm based objective function is quite sensitive to the outliers, the abnormally distributed measurement errors will bias the solution of the traditional chi-square or maximum likelihood function. In the present paper, the authors propose a heuristic search algorithm and a robust correction method to realize the fast library search and to achieve the more accurate results, respectively. Instead of searching in the signature library, the authors perform the search procedure in an extra constructed Jacobian library using the principle of gradient-based iteration algorithms, by which the fast search speed can be achieved for an arbitrary scale library. After the search, a robust correction procedure is performed on the basis of the searched optimal parameter set to obtain the more accurate results. Simulations and experiments performed on an etched silicon grating have demonstrated the feasibility of the proposed heuristic search algorithm and robust correction method.

Automatic Leaf Recognition from a Big Hierarchical Image Database

Automatic plant recognition has become a research focus and received more and more attentions recently. However, existing methods usually only focused on leaf recognition from small databases that usually only contain no more than hundreds of species, and none of them reported a stable performance in either recognition accuracy or recognition speed when compared with a big image database. In this paper, we present a novel method for leaf recognition from a big hierarchical image database. Unlike the existing approaches, our method combines the textural gradient histogram with the shape context to form a more distinctive feature for leaf recognition. To achieve efficient leaf image retrieval, we divided the big database into a set of subsets based on mean-shift clustering on the extracted features and build hierarchical k-dimensional trees (KD-trees) to index each cluster in parallel. Finally, the proposed parallel indexing and searching schemes are implemented with MapReduce architectures. Our method is evaluated with extensive experiments on different databases with different sizes. Comparisons to state-of-the-art techniques were also conducted to validate the proposed method. Both visual results and statistical results are shown to demonstrate its effectiveness.

3D Ear Segmentation and Classification Through Indexing

Current growth trends in different biometrics applications present challenges to researchers. To address these challenges, we need new data storage and retrieval techniques to make the recognition process time efficient. This paper presents a system for time efficient 3D ear biometrics from a large biometrics database. The proposed system has two components that are primarily responsible for: 1) automatic 3D ear segmentation and 2) hierarchical categorization of the 3D ear database using the shape information and surface depth information, respectively. We use an active contour algorithm along with a tree-structured graph to segment the ear region from the 3D profile images. The segmented 3D ear database is then categorized based on the geometrical feature values, computed from the ear shape, into oval, round, rectangular, and triangular categories. For the categorization based on the depth information, the feature space is partitioned using tree-based indexing techniques. We used indexing techniques with balanced split (k-dimensional (KD) tree) and unbalanced split (pyramid tree) data structures to categorize the database separately and then compared their retrieval efficiency. Experiments are conducted to compare the average computation time per query when performing recognition through hierarchical categorization with the average computation time when recognition is based on sequential search. Experimental results without indexing conducted on the University of Notre Dame Collection J2 data set yielded a rank-one recognition rate of 98.5%. We applied the indexing technique to compute the rank-one recognition accuracy with a 10%–50% search space reduction using a 10% step size. With 10%, 20%, 30%, 40%, and 50% search space reduction the rank-one recognition accuracy gracefully degrades to 96.87%, 96.14%, 95.18%, 94.21%, and 93.49%, respectively, while performing nearly 3, 3.3, 4, 4.2, and 5 times faster than the state-of-the-art technique that uses sequential search.

Fuzzy Control Simultaneous Localization and Mapping Strategy Based on Iterative Closest Point and k-Dimensional Tree Algorithms

Fuzzy Control Simultaneous Localization and Mapping Strategy Based on Iterative Closest Point and k-Dimensional Tree Algorithms

Midsagittal plane extraction from brain images based on 3D SIFT

Midsagittal plane (MSP) extraction from 3D brain images is considered as a promising technique for human brain symmetry analysis. In this paper, we present a fast and robust MSP extraction method based on 3D scale-invariant feature transform (SIFT). Unlike the existing brain MSP extraction methods, which mainly rely on the gray similarity, 3D edge registration or parameterized surface matching to determine the fissure plane, our proposed method is based on distinctive 3D SIFT features, in which the fissure plane is determined by parallel 3D SIFT matching and iterative least-median of squares plane regression. By considering the relative scales, orientations and flipped descriptors between two 3D SIFT features, we propose a novel metric to measure the symmetry magnitude for 3D SIFT features. By clustering and indexing the extracted SIFT features using a k-dimensional tree (KD-tree) implemented on graphics processing units, we can match multiple pairs of 3D SIFT features in parallel and solve the optimal MSP on-the-fly. The proposed method is evaluated by synthetic and in vivo datasets, of normal and pathological cases, and validated by comparisons with the state-of-the-art methods. Experimental results demonstrated that our method has achieved a real-time performance with better accuracy yielding an average yaw angle error below 0.91° and an average roll angle error no more than 0.89°.

基于字典描述向量的实时图像配准

As traditional description vector calculation method used in image registration is too complex, time consuming and taking up more memory, a novel dictionary based local feature description algorithm was proposed. The K-singular Value Decomposition( KSVD ) method was used to generate dictionary and the feature descriptor was obtained by comparing the similarity between feature point region in images and elements in the dictionary. By above, the description vector generation algorithm was simplified and a higher feature matching speed was obtained. The matching process could be carried out by using randomized KD(k-dimension)tree algorithm. Then, the Random Sample Consensus (RANSAC) was used to choose the correct matching pairs. Finally, the transform parameters were estimated by using the least square method and the space geometric transformation of two images to be registrated was obtained. Results from experiments show that the proposed method reduces the description vector storage space, speeds up the feature matching and implements the registration process in real time.

SR-NBS: A fast sparse representation based N-best class selector for robust phoneme classification

Although exemplar based approaches have shown good accuracy in classification problems, some limitations are observed in the accuracy of exemplar based automatic speech recognition (ASR) applications. The main limitation of these algorithms is their high computational complexity which makes them difficult to extend to ASR applications. In this paper, an N-best class selector is introduced based on sparse representation (SR) and a tree search strategy. In this approach, the classification is fulfilled in three steps. At first, the set of similar training samples for the specific test sample is selected by k-dimensional (KD) tree search algorithm. Then, an SR based N-best class selector is used to limit the classification among certain classes. This makes the classifier adapt to each test sample and reduces the empirical risk. Finally, a well known low error rate classifier is trained by the selected exemplar samples and the trained classifier is employed to classify among the candidate classes. The algorithm is applied to phoneme classification and it is compared with some well-known phoneme classifiers according to accuracy and complexity issues. By this approach, we obtain competitive classification rate with promising computational complexity in comparison with the state of the art phoneme classifiers in clean and well known acoustic noisy environments which causes this approach become a suitable candidate for ASR applications.

Local feature based retrieval approach for iris biometrics

This paper proposes an efficient retrieval approach for iris using local features. The features are extracted from segmented iris image using scale invariant feature transform (SIFT). The keypoint descriptors extracted from SIFT are clustered into m groups using k-means. The idea is to perform indexing of keypoints based on descriptor property. During database indexing phase, k-d tree k-dimensional tree is constructed for each cluster center taken from N iris images. Thus for m clusters, m such k-d trees are generated denoted as t i , where 1 ? i ? m. During the retrieval phase, the keypoint descriptors from probe iris image are clustered into m groups and ith cluster center is used to traverse corresponding t i for searching. k nearest neighbor approach is used, which finds p neighbors from each tree (t i ) that falls within certain radius r centered on the probe point in k-dimensional space. Finally, p neighbors from m trees are combined using union operation and top S matches (S ⊆ (m× p)) corresponding to query iris image are retrieved. The proposed approach has been tested on publicly available databases and outperforms the existing approaches in terms of speed and accuracy.

Tree-based Indexing for DHT-based P2P Systems

Nowadays, DHT-based P2P technology is used as a basis in many wide spread applications because of its scalability, robustness, and load balance. Many applications, including file sharing, communication and live video streaming are in a large distributed network environment. For an efficient and effective search in large data repositories, complex query processing becomes a major issue for DHT. Towards the goal of supporting complex queries in DHT-based P2P systems, this paper focuses on the usage of k-dimensional tree to build a tree-based index. The proposed index is built without modifying the structure of the overlay network. In this paper, the load balancing among peers is also considered according to the usage of kd-tree. Therefore the performance of kd-tree is studied and show that how it can affect the proposed index over P2P network. In this paper, PlanetSim simulator is used to implement the proposed index and evaluate the performance of the index by using various metrics.

A Fast Approach to Clustering Datasets using DBSCAN and Pruning Algorithms

Among the various clustering algorithms, DBSCAN is an effective clustering algorithm used in many applications. It has various advantages like no a priori assumption needed about the number of clusters, can find arbitrarily shaped clusters and can perform well even in the presence of outliers. However, the performance is seriously affected when the dataset size becomes large. Moreover, the selection of the two input parameters, Eps and MinPts, has a great impact on the clustering performance. To solve these two problems, this paper modifies the traditional DBSCAN algorithm in two manners. The first method uses K-dimensional tree instead of the traditional R-tree algorithm while the second method includes a locally sensitive hash procedure to speed up the process of clustering and increase the efficiency of clustering. The algorithms use a k-distance graph method to automatically calculate Eps and MinPts. Experimental results show that both the algorithms are efficient in terms of scalability and speeds up the clustering process in an efficient manner.

Enhanced 3-D Modeling for Landmark Image Classification

Landmark image classification is a challenging task due to the various circumstances, e.g., illumination, viewpoint, zoom in/out and occlusion under which landmark images are taken. Most existing approaches utilize features extracted from the whole image including both landmark and non-landmark areas. However, non-landmark areas introduce redundant and noisy information. In this paper, we propose a novel approach to improve landmark image classification consisting of three steps. First, an attention-based 3-D reconstruction method is proposed to reconstruct sparse 3-D landmark models. Second, the sparse 3-D models are projected onto iconic images in order to identify images of the hot regions. For a landmark, hot regions are parts of a landmark which attract photographers' attention and are popularly captured in photos. These hot region images are later used to enhance reconstructed sparse 3-D models. Third, the landmark regions are obtained through mapping the enhanced 3-D models to landmark images. A k-dimensional tree (kd-tree) is then constructed for each landmark based on scale invariant feature transform (SIFT) features extracted from the landmark area to classify unlabeled images into pre-defined landmark categories. The proposed method is evaluated using 291 661 images of 51 landmarks. Experiments of comparison indicate that our method outperforms bag-of-words (BoW) based approach 18.5% and method of spatial-pyramid-matching using sparse-coding (ScSPM) 8.4%.

Implementation aspects of sequential Gaussian simulation on irregular points

The increasing use of unstructured grids for reservoir modeling motivates the development of geostatistical techniques to populate them with properties such as facies proportions, porosity and permeability. Unstructured grids are often populated by upscaling high-resolution regular grid models, but the size of the regular grid becomes unreasonably large to ensure that there is sufficient resolution for small unstructured grid elements. The properties could be modeled directly on the unstructured grid, which leads to an irregular configuration of points in the three-dimensional reservoir volume. Current implementations of Gaussian simulation for geostatistics are for regular grids. This paper addresses important implementation details involved in adapting sequential Gaussian simulation to populate irregular point configurations including general storage and computation issues, generating random paths for improved long range variogram reproduction, and search strategies including the superblock search and the k-dimensional tree. An efficient algorithm for computing the variogram of very large irregular point sets is developed for model checking.

Contrast enhancement of images using Partitioned Iterated Function Systems

A new algorithm for the contrast enhancement of images, based on the theory of Partitioned Iterated Function System (PIFS), is presented. A PIFS consists of contractive transformations, such that the original image is the fixed point of the union of these transformations. Each transformation involves the contractive affine spatial transform of a square block, as well as the linear transform of the gray levels of its pixels. The transformation of the gray levels is determined by two parameters which adjust the brightness and the contrast of the transformed block. The PIFS is used in order to create a lowpass version of the original image. The contrast-enhanced image is obtained by adding the difference of the original image with its lowpass version, to the original image itself. The proposed algorithm uses a predefined constant value for the contrast parameter, whereas, the parameters of the affine spatial transform, as well as the parameter adjusting the brightness, are calculated using k-dimensional trees. The lowpass version of the original image is obtained applying the PIFS on the original image repeatedly while using a value for the contrast parameter that is lower than the predefined one. Quantitative and qualitative results stress the superior performance of the proposed contrast enhancement algorithm against four other widely used contrast enhancement methods; namely, linear and nonlinear unsharp masking, Contrast Limited Adaptive Histogram Equalization and Local Range Modification.

거대 구조물의 유체-구조 연계 해석을 위한 효과적인 보간기법에 대한 연구

Generally, the events in nature have multi-disciplinary characteristics. To solve this problems, these days loosely coupled methods are widely applied because of advantage of solvers which are already developed and well proved. Those solvers use different mesh system, so transformation and mapping of data are vital in the field of fluid-structure interaction(FSI). In this paper, the interpolation of deformation which is used globally and compactly supported radial basis functions(RBF), and mapping of force which use principle of virtual work are examined for computing time and accuracy to compare ability with simple 3-D problem. As the results, interpolation scheme of compactly supported radial basis functions are useful to interpolation and mapping for large-scale airplane in FSI with a k-dimensional tree(kd-tree) which is a space-partitioning data structure for organizing points in a k-dimensional space.

Improved particle fusing geometric relation between particles in FastSLAM

SUMMARYFastSLAM is a framework for simultaneous localization and mapping using a Rao-Blackwellized particle filter (RBPF). But, FastSLAM is known to degenerate over time due to the loss of particle diversity, mainly caused by the particle depletion problem in resampling phase. In this work, improved particle filter using geometric relation between particles is proposed to restrain particle depletion and to reduce estimation errors and error variances. It uses a KD tree (k-dimensional tree) to derive geometric relation among particles and filters particles with importance weight conditions for resampling. Compared to the original particle filter used in FastSLAM, this technique showed less estimation error with lower error standard deviation in computer simulations.

3D registration of human face using evolutionary computation and Kriging interpolation

This paper proposes a fast and robust 3D human face geometric data registration strategy dedicated for image-guided medical applications. The registration scheme is composed of a coarse transformation stage and a fine-tuning stage. In the first stage, fuzzy c-mean is used to reduce the data amount of template 3D image, and evolutionary computation is implemented to find optimal initial pose for the Iterative Closest Point plus k-dimensional (KD) tree scheme. In the second stage, the huge reference image data are replaced by a Kriging model. The time-consuming search for corresponding points in evaluating the degree of misalignment is substituted by projecting the points in the template image onto the model. To illustrate the validity and applicability of the proposed approach, a problem composed of 174 635 points reference image and an 11 280 points template image is demonstrated. Computational results show that our approach accelerates the registration process from 1361.28 seconds to 432.85 seconds when compared with the conventional ICP plus K-D tree scheme, while the average misalignment reduces from 11.35 mm to 2.33 mm.

Support vector machines and kd-tree for separating quasars from large survey data bases

We compare the performance of two automated classification algorithms, k-dimensional tree (kd-tree) and support vector machines (SVMs), to separate quasars from stars in the data bases of the Sloan Digital Sky Survey (SDSS) and the Two-Micron All Sky Survey (2MASS) catalogues. The two algorithms are trained on subsets of SDSS and 2MASS objects whose nature is known via spectroscopy. We choose different attribute combination as input patterns to train the classifier using photometric data only and present the classification results obtained by these two methods. Performance metrics, such as precision and recall, true positive rate and true negative rate, F-measure, G-mean and Weighted Accuracy, are computed to evaluate the performance of the two algorithms. The study shows that both kd-tree and SVMs are effective automated algorithms to classify point sources. SVMs show slightly higher accuracy, but kd-tree requires less computation time. Given different input patterns based on various parameters (e.g. magnitudes, colour information), we conclude that both kd-tree and SVMs show better performance with fewer features. What is more, our results also indicate that the accuracy using the four colours (u−g, g−r, r−i and i−z) and r magnitude based on SDSS model magnitudes adds up to the highest value. The classifiers trained by kd-tree and SVMs can be used to solve the automated classification problems faced by the virtual observatory (VO); moreover, they can all be applied for the photometric preselection of quasar candidates for large survey projects in order to optimise the efficiency of telescopes.

ON NUMBER OF WAYS TO SHELL THE k-DIMENSIONAL TREES

Which spheres are shellable?[2]. We present one of them which is the k-tree with n-labeled vertices. We found that the number of ways to shell the k-dimensional trees on n-labeled vertices is

Adaptive DOA Estimation Using a Database of PARCOR Coefficients

An adaptive direction-of-arrival (DOA) tracking method based upon a linear predictive model is developed. This method estimates the DOA by using a database that stores PARCOR coefficients as key attributes and the corresponding DOAs as non-key attributes. The k-dimensional digital search tree is used as the data structure to allow efficient multidimensional searching. The nearest neighbour to the current PARCOR coefficient is retrieved from the database, and the corresponding DOA is regarded as the estimate. The processing speed is very fast since the DOA estimation is obtained by the multidimensional searching. Simulations are performed to show the effectiveness of the proposed method.

Intersections with random geometric objects

We present a systematic study of the expected complexity of the intersection of geometric objects. We first study the expected size of the intersection between a random Voronoi diagram and a generic geometric object that consists of a finite collection of line segments in the plane. Using this result, we explore the intersection complexity of a random Voronoi diagram with the following target objects which may or may not be random: a line segment, a Voronoi diagram, a minimum spanning tree, a Gabriel graph, a relative neighborhood graph, a Hamiltonian circuit, a furthest point Voronoi diagram, a convex hull, a k-dimensional tree, and a rectangular grid.