Quadtree Data Structure Research Articles

A conservative discretization of the Poisson–Nernst–Planck equations on adaptive Cartesian grids

In this paper we present a novel hybrid finite-difference/finite-volume method for the numerical solution of the nonlinear Poisson–Nernst–Planck (PNP) equations on irregular domains. The method is described in two spatial dimensions but can be extended to three dimensional problems as well. The boundary of the irregular domain is represented implicitly via the zero level set of a signed distance function and quadtree data structures are used to systematically generate adaptive grids needed to accurately capture the electric double layer near the boundary. To handle the nonlinearity in the PNP equations efficiently, a semi-implicit time integration method is utilized. An important feature of our method is that total number of ions in the system is conserved by carefully imposing the boundary conditions, by utilizing a conservative discretization of the diffusive and, more importantly, the nonlinear migrative flux term. Several numerical experiments are conducted which illustrate that the presented method is first-order accurate in time and second-order accurate in space. Moreover, these tests explicitly indicate that the algorithm is also conservative. Finally we illustrate the applicability of our method in the study of the charging dynamics of porous supercapacitors.

폭발현상 해석을 위한 적응적 요소망 생성

Computer simulation with FEM is very useful to analyze hypervelocity impact phenomena that are tremendously expensive or otherwise too impractical to analyze experimentally. Shock physics can be efficiently handled by mesh adaptation which allows finite element mesh to be locally optimized to resolve moving shock wave in explosion. In this paper, an adaptive meshing technique based upon quadtree data structure was applied to resolve ballistic impact phenomena. The technique can adaptively refine a mesh in the neighborhood of a shock and coarsen the mesh for the smooth flow behind the shock according to a criterion. The criterion for refinement and coarsening is based upon the standard deviation of the gradient of shock pressure on the associated field. Shock simulation starts with the rough mesh of the pressure field and mesh density is increased locally under the criterion at each time step. The results show that the mesh adaptation enables to minimize the global computation error of FEM and to increase storage and computational saving compared to the fixed resolution of the conventional static mesh approach.

Ontology-based topological representation of remote-sensing images

This article proposes an ontology-based topological representation of remote-sensing images. Semantics, especially related to the topological relationships between the objects represented, are not explicit in remote-sensing images and this fact limits spatial analysis. Our aim is to provide an explicit ontological definition of the topological relations between objects in the image using the Quadtree data structure for spatial indexing. This structure is explicitly defined in an ontology allowing the automatic interpretation of the representations obtained, taking into account the topological relations and increasing the spatial analytical capabilities. This representation has been validated by a case study of semantic retrieval based on the normalized difference vegetation index (NDVI), taking into account the topological relations between NDVI regions in images. In the experiments, we compare the effectiveness of results from eight queries using four traditional supervised image classification algorithms and the proposal representation. The experimental results show the feasibility of the proposal, supporting the concept of the image retrieval process providing a semantic complement to remote-sensing images. The proposed representation contributes to incorporation of semantics into geographical data, especially to remote-sensing images, and it can be used to develop applications in the Geospatial Semantic Web.

무인지상차량의 전역경로계획을 위한 지형정보 분석 시스템

In this paper, we proposed a system that efficiently provides support maps which includes the grid based terrain analysis information. To do this, we use the FDB which is defined as a GIS database that contains features with attributes attached to the features. The FDB is composed of a number of features and feature classes. In order to create support maps, it is necessary to classify feature classes that are associated with each support map and to search them in a grid map. The proposed system use a ontology model to classify semantically feature classes and the quad-tree data structure to find them in a grid map quickly. Therefore, our system is expected to be utilized for global path planning of UGV. In this paper, we show the possibility through an experimental implementation.

Real-time generalization of point data in mobile and web mapping using quadtrees

With a focus on mobile and web mapping, we propose several algorithms for on-the-fly generalization of point data, such as points of interest (POIs) or large point collections. In order to achieve real-time performance, we use a quadtree data structure. With their hierarchical subdivision structure and progressive levels of detail, indices of the quadtree family lend themselves as auxiliary data structures to support algorithms for generalization operations, including selection, simplification, aggregation, and displacement of point data. The spatial index can further be used to generate several local and global measures that can then serve to make educated guesses on the density and proximity of points across map scales, and thus enable control of the operation of the generalization algorithms. An implementation of the proposed algorithms has shown that, and thanks to the quadtree index, real-time performance can be achieved even for large point sets. Furthermore, the quadtree data structure can be extended into a caching structure, which can be used to store pre-computed generalizations; thus, a desired level of detail (LOD) can simply be retrieved from cache.

Variable Resolution Search with Quadrotors: Theory and Practice

This paper presents a variable resolution framework for autonomously searching stationary targets in a bounded area. Theoretical formulations are also described for using a probabilistic quadtree data structure, which incorporates imperfect Bayesian (false positive and false negative) detections and informs the searcher's route based on optimizing information gain. Live‐fly field experimentation results using a quadrotor unmanned aerial vehicle validate the proposed methodologies and demonstrate an integrated system with autonomous control and embedded object detection for probabilistic search in realistic operational settings. Lessons learned from these field trials include characterization of altitude‐dependent detection performance, and we also present a benchmark data set of outdoor aerial imagery for search and detection applications.

KSR-Quadtree: an Intelligent Knowledge Storage and Retrieval Using Quadtree Structure

The size of the data in modern applications grows at an increasing rate. The voluminous database stored in direct access storage device requires more number of disk accesses and the database requires rescanning due to frequent updates. This leads to increased retrieval time. Also, the information retrieved from repository of data cannot guide decision-makers or management to make correct decisions as humans. In this paper, we propose a Knowledge Based System which converts the existing database into Quad tree. Here, the quad trees are used in arriving at decisions on what kind of plants can be that grown in soil based on the domain information (edaphology-soil characteristics) given by the user. The domain information that is stored as an application database is converted into a knowledge base using the dynamic quad-tree data structure. This system is designed with two phases namely, (1) Knowledge storage (as quad-tree) and (2) Effective knowledge retrieval. In the first phase, the records from the database are converted into 2Dpoints and store the point recursively in a two-dimensional space with four recursive quadrants. In the second phase, knowledge retrieval is done with the help of the constructed knowledge base (XML architecture). This system transforms the voluminous database storage into a file thereby reducing the number of disk access and retrieval time. The rescanning of Database is also avoided and supports the edaphologists in making right decisions.

Mathematical Morphology for Applications to Sensor Networks

Morphological image processing is a type of processing based on the theory of mathematical morphology, by which the spatial forms or the structures of objects in an image are modified. This objects-oriented image processing is advantageous for a sensor to make a decision, although is not good enough for visual aesthetics (or entertainment) purposes. Therefore, morphological image processing is suitable for sensing applications. It is noted that there are two special features associated with the video sensor networks: 1) limited resource and 2) the nonvisual aesthetics (or not for entertainment) purpose. Therefore, an approach of particular image processing on the sensor network is proposed in this paper. In this approach, the image is compressed using the quad tree data structure and is also processed in this structure using morphological operations to achieve the sensing purpose. Both the speed and the compression efficiencies of this proposed approach are verified from the sensor's perspective in our experiments.

Development of a 2-D flow solver on unstructured and adaptive Cartesian meshes

A two-dimensional flow solver using mixed grids has been developed for accurate and efficient simulation of steady and unsteady flow fields. The flow solver was cast to accommodate two different topologies of computational meshes: unstructured triangular meshes in the near-body region such that complex geometric configurations can be easily modeled, while unstructured adaptive Cartesian meshes are utilized in the off-body region to resolve the flow more accurately with less numerical dissipation by adopting a spatially high-order accurate scheme and solution-adaptive mesh refinement technique. The unstructured adaptive Cartesian meshes can be generated auto- matically and allow to handle data efficiently via quad-tree data structures. A chimera mesh approach has been employed to link the two flow regimes adopting each mesh topology. A second-order accurate vertex-centered scheme and a 3 rd - or 5 th - order accurate cell- centered WENO scheme has been utilized in the near-body region and in the off-body region, respectively. Validations were made for the unsteady inviscid vortex convection and the steady and unsteady turbulent flows over an NACA0012 airfoil, and the results were compared with other computational and experimental results.

Hierarchical Salient Point Selection for image retrieval

Salient point detection in images is very useful for image processing applications like image compression, object detection and object recognition. It is also frequently used to represent local properties of the image in content-based image retrieval (CBIR). Many research results focused on finding the most salient points in the image. However, the large number of salient points and continuous point sets are still the problems. Based on the saliency values from wavelet-based methods, this paper presents a hierarchical algorithm for selecting the most salient points such that they cannot only give a satisfying representation of an image, but also make the image retrieval systems more efficiently. Under a top–down approach from quadtree data structure, the algorithm keeps the most salient points in each quadrant according to the percentage of saliency values in the whole image. The performance of the proposed method was evaluated with the spreading measure and retrieval rate from a CBIR system. In this experiment, it shows that our method is robust and the extracted salient points provide efficient retrieval performance comparing with two wavelet-based point detectors.

Field D* path-finding on weighted triangulated and tetrahedral meshes

Classic shortest path algorithms operate on graphs, which are suitable for problems that can be represented by weighted nodes or edges. Finding a shortest path through a set of weighted regions is more difficult and only approximate solutions tend to scale well. The Field D* algorithm efficiently calculates an approximate, interpolated shortest path through a set of weighted regions and was designed for navigating robots through terrains with varying characteristics. Field D* operates on unit grid or quad-tree data structures, which require high resolutions to accurately model the boundaries of irregular world structures. In this paper, we extend the Field D* cost functions to 2D triangulations and 3D tetrahedral meshes: structures which model polygonal world structures more accurately. Since robots typically have limited resources available for computation and storage, we pay particular attention to computation and storage overheads when detailing our extensions. We begin by providing analytic solutions to the minimum of each cost function for 2D triangles and 3D tetrahedra. Our triangle implementation provides a 50 % improvement in performance over an existing triangle implementation. While our 3D extension to tetrahedra is the first full analytic extension of Field D* to 3D, previous work only provided an approximate minimization for a single cost function on a 3D cube with unit lengths. Each cost function is expressed in terms of a general function whose characteristics can be exploited to reduce the calculations required to find a minimum. These characteristics can also be exploited to cache the majority of cost functions, producing a speedup of up to 28 % in the 3D tetrahedral case. We demonstrate that, in environments composed of non-grid aligned data, Multi-resolution quad-tree Field D* requires an order of magnitude more faces and between 15 and 20 times more node expansions, to produce a path of similar cost to one produced by a triangle implementation of Field D* on a lower resolution triangulation. We provide examples of 3D pathing through models of complex topology, including pathing through anatomical structures extracted from a medical data set. To summarise, this paper details a robust and efficient extension of Field D* pathing to data sets represented by weighted triangles and tetrahedra, and also provides empirical data which demonstrates the reduction in storage and computation costs that accrue when one chooses such a representation over the more commonly used quad-tree and grid-based alternatives.

A high-performance web-based information system for publishing large-scale species range maps in support of biodiversity studies

Functionality, performance and scalability are critical to Web-based information systems for publishing and disseminating large-scale species distribution data. Existing systems do not support dynamic spatial window queries on large-scale species range maps that are important to compute alpha and beta diversities for biodiversity analysis and modeling. In this study, we have developed a main-memory based novel quadtree data structure to represent large-scale species range maps and support dynamic spatial window queries to retrieve a list of species and their area sizes within a query window efficiently. Using the NatureServe's 4000+ bird species range maps, experiment results have shown that the memory footprint of the proposed quadtree data structure representing the range maps of all the species is about 1/6 of the quadtree derived by combining individual quadtrees each representing a species range map. The experiment results have also demonstrated that the query response times of our main-memory spatial database are well below a fraction of a second for query windows as large as 10×10°, which are 2–3 orders better than using a typical disk-resident spatial database system.

A local level-set method using a hash table data structure

We present a local level-set method based on the hash table data structure, which allows the storage of only a band of grid points adjacent to the interface while providing an O(1) access to the data. We discuss the details of the construction of the hash table data structure as well as the advection and reinitialization schemes used for our implementation of the level-set method. We propose two dimensional numerical examples and compare the results to those obtained with a quadtree data structure. Our study indicates that the method is straightforward to implement but suffers from limitations that make it less efficient than the quadtree data structure.

Revision of wFMM – A Wideband Fast Multipole Method for the two-dimensional complex Helmholtz equation

The Wideband Fast Multipole Method for the two-dimensional complex Helmholtz equation program is updated. The new version uses significantly less memory than the original version and uses almost constant memory for all the wavenumbers k when the number of particles is given. The CPU time is also improved slightly. Additionally, the memory leak problems and errors from external variables when it is used in an iterative solver are fixed. The new version wFMM and other useful codes are available from the website http://fastmultipole.org/.

Quadrilateral meshes with provable angle bounds

In this paper, we present an algorithm that utilizes a quadtree data structure to construct a quadrilateral mesh for a simple polygonal region in which no newly created angle is smaller than $${{18.43}}^{\circ} ({=}\hbox{arctan}(\frac{1}{3}))$$ or greater than $${{171.86}}^{\circ} ({=}{{135}}^{\circ} + 2\hbox{arctan}(\frac{1}{3}))$$ . This is the first known result, to the best of our knowledge, on a direct quadrilateral mesh generation algorithm with a provable guarantee on the angles.

Distributed data organization and parallel data retrieval methods for huge laser scanner point clouds

This paper proposes a novel method for distributed data organization and parallel data retrieval from huge volume point clouds generated by airborne Light Detection and Ranging (LiDAR) technology under a cluster computing environment, in order to allow fast analysis, processing, and visualization of the point clouds within a given area. The proposed method is suitable for both grid and quadtree data structures. As for distribution strategy, cross distribution of the dataset would be more efficient than serial distribution in terms of non-redundant datasets, since a dataset is more uniformly distributed in the former arrangement. However, redundant datasets are necessary in order to meet the frequent need of input and output operations in multi-client scenarios: the first copy would be distributed by a cross distribution strategy while the second (and later) would be distributed by an iterated exchanging distribution strategy. Such a distribution strategy would distribute datasets more uniformly to each data server. In data retrieval, a greedy algorithm is used to allocate the query task to a data server, where the computing load is lightest if the data block needing to be retrieved is stored among multiple data servers. Experiments show that the method proposed in this paper can satisfy the demands of frequent and fast data query.

Framed-quadtree path planning for an underwater vehicle with the task of tracking a moving target

An autonomous underwater vehicle (AUV) must use an algorithm to plan its path to distant, mobile offshore objects. Because of the uneven distribution of obstacles in the real world, the efficiency of the algorithm decreases if the global environment is represented by regular grids with all of them at the highest resolution. The framed quadtree data structure is able to more efficiently represent the environment. When planning the path, the dynamic object is expressed instead as several static objects which are used by the path planner to update the path. By taking account of the characteristics of the framed quadtree, objects can be projected on the frame nodes to increase the precision of the path. Analysis and simulations showed the proposed planner could increase efficiency while improving the ability of the AUV to follow an object.

Corpus callosum MR image classification

An approach to classifying magnetic resonance (MR) image data is described. The specific application is the classification of MRI scan data according to the nature of the corpus callosum, however the approach has more general applicability. A variation of the “spectral segmentation with multi-scale graph decomposition” mechanism is introduced. The result of the segmentation is stored in a quad-tree data structure to which a weighted variation (also developed by the authors) of the gSpan algorithm is applied to identify frequent sub-trees. As a result the images are expressed as a set frequent sub-trees. There may be a great many of these and thus a decision tree based feature reduction technique is applied before classification takes place. The results show that the proposed approach performs both efficiently and effectively, obtaining a classification accuracy of over 95% in the case of the given application.

Finite-element analysis of thermal-induced stresses around a cased injection well

Injection of surface fluids (sea water, CO2, steam) into hydrocarbon reservoirs induces thermal stresses in the wellbore structures and in the near-well area. These stresses may endanger the integrity of the casing, the cement and the surrounding formation. Therefore, an accurate assessment of injection-induced thermal stresses and the associated risk of failure are of utmost importance for a safe and environmentally secure oil production. A coupled finite-element model has been developed and tested as a tool for assessing the probability and extent of failure caused by thermal-induced stresses around a cased wellbore. A feature of the model is an option for an automatic mesh refinement using Nikishkov elements and a quad-tree data structure. The refinement is automatically provided in the regions of rapid change of the nodal variables (displacements, temperature).

A Constant-Time Algorithm for Finding Neighbors in Quadtrees

Quadtrees and linear quadtrees are well-known hierarchical data structures to represent square images of size 2(r) x 2(r). Finding the neighbors of a specific leaf node is a fundamental operation for many algorithms that manipulate quadtree data structures. In quadtrees, finding neighbors takes O(r) computational time for the worst case, where r is the resolution (or height) of a given quadtree. Schrack [1] proposed a constant-time algorithm for finding equal-sized neighbors in linear quadtrees. His algorithm calculates the location codes of equal-sized neighbors; it says nothing, however, about their existence. To ensure their existence, additional checking of the location codes is needed, which usually takes O(r) computational time. In this paper, a new algorithm to find the neighbors of a given leaf node in a quadtree is proposed which requires just O(1) (i.e., constant) computational time for the worst case. Moreover, the algorithm takes no notice of the existence or nonexistence of neighbors. Thus, no additional checking is needed. The new algorithm will greatly reduce the computational complexities of almost all algorithms based on quadtrees.