Quadtree Data Structure Research Articles

Elaborating and performing optimization approaches for web-based 3D spatial analysis of 3D city models

ABSTRACT Three-dimensional (3D) geographic information systems (GIS) are vital for urban planning and architectural design, enabling detailed visualization and analysis of urban landscapes. However, the growing size of 3D city data and the transition to web environments cause performance challenges for real-time applications. This study addresses the need for optimizing 3D spatial analyses for the web using Quadtree data structures and multiprocessing tools. Optimization scenarios based on data size and hardware configurations are evaluated, and the best hosting plans for GIS applications on cloud services are also considered.

A non-uniform quadtree map building method including dead-end semantics extraction

To reduce the complexity of large-scene high-resolution maps while using the dead-end information distributed in the unmanned vehicle driving environment, we propose a novel non-uniform quadtree map-building method including dead-end semantic information extraction. By utilizing quadtree data structures, submaps and a positive-order tree depth organization approach, our proposed map can adapt to the large-scale high-resolution requirement and expand more easily to larger environments. To verify the practicality of our proposed map, we have successfully implemented map matching and path planning in real environments. Additionally, we effectively extract the dead-end semantic information that widely distributes in the environment, which can help unmanned vehicles avoid collisions and improve the search efficiency of the planning procedure. We evaluate our method with KITTI datasets, CARLA Simulator, and our self-collected real-world datasets. The experimental results show that our proposed method significantly reduces the complexity of large-scale high-resolution maps, effectively extracts dead-end semantic information, and has good practicality in real environments. The implementation of our method is released here: https://github.com/biter0088/Non-uniform-quadtree-map.

A ROUTE PLANNING METHOD FOR COASTAL NAVIGATION OF SMALL SHIPS

This study proposes route planning considering the characteristics of small ships sailing on coasts. An electronic chart based on the S-57 standard object and attributes catalogue was used. A Quadtree data structure was used for modelling an environment for route planning. The main idea of Hierarchical Pathfinding A* (HPA*) was adapted to our route planning algorithm. The route planning method proposed in this study can find route for small ships within a short time that the users can understand. In addition, it consumes little computer resources so that there is no difficulty in operating it on the computer of the small ships. In addition, the program was verified by conducting route planning tests in various areas along the coastal areas of Korea.

A Local Adaptive Mesh Refinement for JFO Cavitation Model on Cartesian Meshes

Nonuniform mesh is beneficial to reduce computational cost and improve the resolution of the interest area. In the paper, a cell-based adaptive mesh refinement (AMR) method was developed for bearing cavitation simulation. The bearing mesh can be optimized by local refinement and coarsening, allowing for a reasonable solution with special purpose. The AMR algorithm was constructed based on a quadtree data structure with a Z-order filling curve managing cells. The hybrids of interpolation schemes on hanging nodes were applied. A cell matching method was used to handle periodic boundary conditions. The difference schemes at the nonuniform mesh for the universal Reynolds equation were derived. Ausas’ cavitation algorithm was integrated into the AMR algorithm. The Richardson extrapolation method was employed as an a posteriori error estimation to guide the areas where they need to be refined. The cases of a journal bearing and a thrust bearing were studied. The results showed that the AMR method provided nearly the same accuracy results compared with the uniform mesh, while the number of mesh was reduced to 50–60% of the number of the uniform mesh. The computational efficiency was effectively improved. The AMR method is suggested to be a potential tool for bearing cavitation simulation.

Compression of Monochromatic and Multicolored Image with Neural Network

Nowadays we have so much images provided by different types of machines, while we need to store them or transfer to other devices or via internet, we need to compress them because the images usually have large amount of size. Compressing them reduces time for transferring files. The compression can be done with different methods and software in order to reduce their capacity expressed in megabytes as much as tens of hundreds of gigabytes for more files. It is well known that the speed of information transmission depends mainly on its quantity or the capacity of the information package. Image compression is a very important task for data transfer and data storage, especially nowadays because of the development of many image acquisition devices. If there is no compression technique used on these data, they may occupy immense space of memory, or render difficult data transmission. Artificial Neural Networks (ANN) have demonstrated good capacities for lossy image compression. The ANN algorithm we investigate is BEP-SOFM, which uses a Backward Error Propagation algorithm to quickly obtain the initial weights, and then these weights are used to speed up the training time required by the Self-Organizing Feature Map algorithm. In order to obtain these initial weights with the BEP algorithm, we analyze the hierarchical approach, which consists in preparing the image to compress using the quadtree data structure by segmenting the image into blocks of different sizes. Small blocks are used to represent image areas with large-scale details, while the larger ones represent the areas that have a small number of observed details. Tests demonstrate that the approach of quadtree segmentation quickly leads to the initial weights using the BEP algorithm.

Adaptive Extraction and Refinement of Marine Lanes from Crowdsourced Trajectory Data

Crowdsourced trajectory data of ships provide the opportunity for extracting marine lane information. However, extracting useful knowledge from massive amounts of trajectory data is a challenging problem. Trajectory data collected from crowdsourcing can be extremely diverse in different areas and its quality might be very low. Moreover, the density distribution of the crowdsourced trajectory points is quite uneven in different areas. Furthermore, it is necessary to extract marine lanes with high extraction precision in offshore and nearshore water areas, but extraction precision can be lower in the open sea. We propose an adaptive approach for marine lane extraction and refinement based on grid merging and filtering to meet the challenges. In this paper, after pre-processing and clustering the trajectory data based on the density value of grids with a parallel GeoHash encoding algorithm, we propose a parallel grid merging and filtering algorithm based on a QuadTree data structure. The algorithm performs grid merging on the simplified grid data according to the density value of grid, then filters the merged grid data based on a local sliding window mechanism to get the marine lane grid data. Applying the Delaunay Triangulation on the marine lane grid data, the marine lane boundary information can be extracted with adaptive extraction precision. Experimental results show that the proposed approach can extract marine lanes with high extraction precision in offshore and nearshore water area and low extraction precision in open sea area.

Parallel Demodulation Algorithm for processing independent windows of a fringe patterns using Simulating Annealing

We present a method for demodulating fringe patterns, which uses Simulated Annealing algorithm by setting an objective function and is capable of recovering the phase map without using an unwrapping algorithm. This method is based on the window fringe pattern demodulation method and introduces a recursive algorithm that performs an automatic partitioning of the pattern of fringes using a quad tree data structure and limiting each partition to a maximum number of fringes. The phase is approximated by means of a parametric estimation of a polynomial of the n-th degree in each window, independently, which facilitates parallel implementation, and ultimately, a gain in speed. The computer simulation and the experimental results have demonstrated that this method is able to recover the phase map in complex interferograms with results comparable to those obtained with soft computing techniques that address this problem ( Independent Windows Using a Genetic Algorithm), in terms of to quality, furthermore, our method employs parallel implementation, which makes the demodulation process more agile.

Displacement and visualization of point symbols based on spatial distribution characteristics

Abstract. In WEB2.0 environment, the number of map-based mashups which display user-led POI data keeps increasing. When the cartographic processing of these map mashups is lacking, the display of the POI data showed on the maps are quite unsatisfactory because of the overlapping of symbols.At present, some widely used methods commonly use selection and simplification operations based on a quadtree data structure, which can get a good result in the small and medium scales in which users mainly focus on the distribution characteristics and the density difference of POI, but will lose a lot of information in the large scales in which users mainly focus on the specific location and detailed information of the data. For example, two hotels with the same size will retain only one symbol after using selection or simplification operation although in the large scale if they are adjacent to each other, which will bring trouble to users when using maps. Displacement is a suitable operation to deal with this situation, however, current displacement methods face the problems of symbol position drift and nevertheless the loss of information in high-density areas.In order to address these problems, this paper proposes a real-time POI visualization algorithm combining the characteristics of traditional quadtree data structure and the advantages of an improved displacement operator.

Fast video encoding based on random forests

Machine learning approaches have been increasingly used to reduce the high computational complexity of high-efficiency video coding (HEVC), as this is a major limiting factor for real-time implementations, due to the decision process required to find optimal coding modes and partition sizes for the quad-tree data structures defined by the standard. This paper proposes a systematic approach to reduce the computational complexity of HEVC based on an ensemble of online and offline Random Forests classifiers. A reduced set of features for training the Random Forests classifier is proposed, based on the rankings obtained from information gain and a wrapper-based approach. The best model parameters are also obtained through a consistent and generalizable method. The proposed Random Forests classifier is used to model the coding unit and transform unit-splitting decision and the SKIP-mode prediction, as binary classification problems, taking advantage from the combination of online and offline approaches, which adapts better to the dynamic characteristics of video content. Experimental results show that, on average, the proposed approach reduces the computational complexity of HEVC by 62.64% for the random access (RA) profile and 54.57% for the low-delay (LD) main profile, with an increase in BD-Rate of 2.58% for RA and 2.97% for LD, respectively. These results outperform the previous works also using ensemble classifiers for the same purpose.

Aerial Camera Network for Observing Moving Targets

This paper considers a network of camera-equipped quad-rotors (aerial cameras) as aerial camera network (ACN) where each aerial camera is smart in the sense that it is mobile and can process, store, and wirelessly communicate information. This paper then presents an algorithm for decentralized and cooperative motion planning of these aerial cameras in 3-D environment to observe multiple targets moving on the ground. The proposed algorithm enables the ACN to observe targets from different elevations with the objective of jointly maximizing duration and quality (resolution) of observation for each target. This multi-scale observation depends on the field-of-view (FOV) of aerial camera and the quality of observation depends on the elevation and/or zoom level of aerial camera. The algorithm uses a quad-tree data structure to model not only the discrete movement decisions of aerial cameras in a 3-D environment but also the variations in the FOVs and qualities of observations. The use of artificial forces in the algorithm allows the aerial cameras to avoid collisions and to share the workload of assigning locations and targets to themselves. Simulation results present the effectiveness and performance evaluation of the proposed algorithm by comparison with the existing approaches of multi-target cooperative observation.

Strength distribution of large unidirectional composite patches with realistic load sharing.

Monte Carlo simulations of the failure of unidirectional fiber composites in a plane transverse to the fiber direction are performed on much larger patches than in previous works, assuming a realistic load redistribution scheme from broken to intact fibers. Computational effort involved in these simulations is substantially reduced using an algorithm based on the quadtree data structure. The empirical strength distribution obtained from the simulations has a weak-link character, regardless of the variability in fiber strengths. The empirical strength distribution is well captured by a probabilistic model based on the growth of a tight cluster of fiber breaks. It is also well captured by regarding composite patch failure as the failure of the weakest equal load-sharing bundle of a certain size, following Curtin [Phys. Rev. Lett. 80, 1445 (1998)PRLTAO0031-900710.1103/PhysRevLett.80.1445]. The approximate coincidence of these two predictions identifies the dominant failure mechanism underlying Curtin's empirical scaling relationship.

Enhanced Map-Matching Algorithm with a Hidden Markov Model for Mobile Phone Positioning

Numerous map-matching techniques have been developed to improve positioning, using Global Positioning System (GPS) data and other sensors. However, most existing map-matching algorithms process GPS data with high sampling rates, to achieve a higher correct rate and strong universality. This paper introduces a novel map-matching algorithm based on a hidden Markov model (HMM) for GPS positioning and mobile phone positioning with a low sampling rate. The HMM is a statistical model well known for providing solutions to temporal recognition applications such as text and speech recognition. In this work, the hidden Markov chain model was built to establish a map-matching process, using the geometric data, the topologies matrix of road links in road network and refined quad-tree data structure. HMM-based map-matching exploits the Viterbi algorithm to find the optimized road link sequence. The sequence consists of hidden states in the HMM model. The HMM-based map-matching algorithm is validated on a vehicle trajectory using GPS and mobile phone data. The results show a significant improvement in mobile phone positioning and high and low sampling of GPS data.

Variable-scale maps in real-time generalisation using a quadtree data structure and space deforming algorithms

ABSTRACTVariable-scale maps have been advocated by several authors in the context of mobile cartography. In the literature on real-time map generalisation, however, corresponding methods that resolve cartographic conflicts by deformation of the underlying map space together with the map foreground, are underrepresented. This paper demonstrates how the concept of a malleable space can be applied as a part of the generalisation process and incorporated into the overall methodology of point generalisation. Two different algorithms are used, a density-equalising cartogram algorithm and Laplacian smoothing. Both methods work in real-time and are datadriven. In addition, they allow for a parameterisation in combi-nation with a quadtree data structure, as well as a combination with 'classic' generalisation operators (e.g. selection, aggregation, displacement) based on the quadtree. The quadtree serves both as a spatial index for fast retrieval and search of points, and as a density estimator to inform generalisation operators. The use of the quadtree as a common spatial index provides a tool to combine variable-scale maps with classic generalisation. A combination of the two allows, at small map scales, the maintenance of detail in dense areas and data reduction in sparse areas. Additionally, it facilitates building a modular workflow for real-time map generalisation.

Efficient manifold-preserving edit propagation using quad-tree data structures

In this paper, we propose an edit propagation algorithm using quad-tree data structures for image manipulation. First, we use a quad-tree to adaptively group all pixels into clusters. Then, we build a manifold-preserving propagation function based on clusters using locally linear embedding for improved distance. Moreover, we employ an adaptive weight function built on cell corners instead of individual pixels. Because the number of corners is smaller than the number of individual pixels, it results in runtime performance improvement. Finally, the edits of all pixels can be computed by interpolating the edits solved from the clusters. Compared with previous approaches, our method requires less time without sacrificing the visualization quality. Experimental results demonstrate two applications of our algorithm: grayscale image colorization and color image recoloring.

Speeding Up A* Search on Visibility Graphs Defined Over Quadtrees to Enable Long Distance Path Planning for Unmanned Surface Vehicles

We introduce an algorithm for long distance path planning in complex marine environments. The available free space in marine environments changes over time as a result of tides, environmental restrictions, and weather. As a result of these considerations, the free space region in marine environments needs to be dynamically generated and updated. The approach presented in this paper demonstrates that it is feasible to compute optimal paths using A* search on visibility graphs defined over quadtrees. Our algorithm exploits quadtree data structures for efficiently computing tangent edges in visibility graphs. We have developed an admissible heuristic that accounts for large islands while estimating the cost-to-go and provides a better lower bound than the Euclidean distance-based heuristic. During the search over visibility graphs, the branching factor of A* can be large due to the large size of the region. We introduce the idea of focusing the search by limiting the child nodes to be in certain regions of the workspace. Our results show that focusing the search significantly improves the computational efficiency without any noticeable degradation in path quality. We have also developed a method to estimate bounds on how far the computed path can be from the optimal path when methods for focusing the search are utilized for speeding up the computation.

Fast, Adaptive, High-Order Accurate Discretization of the Lippmann--Schwinger Equation in Two Dimensions

We present a fast direct solver for two-dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered field using a volume potential whose kernel is the outgoing Green's function for the exterior domain. Inserting this representation into the governing partial differential equation, we obtain an integral equation of Lippmann--Schwinger type. The principal contribution here is the development of an automatically adaptive, high-order accurate discretization based on a quad-tree data structure which provides rapid access to arbitrary elements of the discretized system matrix. This permits the straightforward application of state-of-the-art algorithms for constructing compressed versions of the solution operator. These solvers typically require $O(N^{3/2})$ work, where $N$ denotes the number of degrees of freedom. We demonstrate the performance of the method for a variety of problems in both low and high frequency regimes.

Dynamic fracture simulations using the scaled boundary finite element method on hybrid polygon–quadtree meshes

In this paper, we present an efficient computational procedure to model dynamic fracture within the framework of the scaled boundary finite element method (SBFEM). A quadtree data structure is used to discretise the domain, and 2:1 ratio between the cells is maintained. This limits the number of patterns in the quadtree decomposition and allows for efficient computation of the system matrices. The regions close to the boundary are discretised with arbitrary sided polygons so as to facilitate accurate modelling of the curved boundaries. The stiffness and the mass matrix over all the cells are computed by the SBFEM. Moreover, the semi-analytical nature of the SBFEM enables accurate modelling of the asymptotic stress fields in the vicinity of the crack tip. An efficient remeshing algorithm that combines the quadtree decomposition with simple Boolean operations is proposed to model the crack propagation. The remeshing is restricted only to a small region in the vicinity of the crack tip. The efficiency and the convergence properties of the proposed framework are demonstrated with a few benchmark problems.

Image Restoration Based on Quadtree Data Structures

This paper investigates the problem of image restoration when the image is corrupted by Pepper-and-salt noise and proposes a new restoration algorithm based on quadtree data structures. The crucial parts of the algorithm are picking noise and fuzzy estimation, so that unlike some other usual denoising methods, it avoids blurring and averaging edges and non-noise pixels. This paper describes, analyzes and compares several methods and results of removing noise from image. Experimental results indicate that the new algorithm proposed by this paper is superior.

Adaptive Gradient-Augmented Level Set Method with Multiresolution Error Estimation

A space-time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Hermite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic quadtree data structures. For adaptive time integration, an embedded Runge-Kutta method is employed. The precision of the new fully adaptive method is analysed and speed up of CPU time and memory compression with respect to the uniform grid discretization are reported.

A parallel LEGION algorithm and cell-based architecture for real time split and merge video segmentation

Split and merge segmentation is a popular region-based segmentation scheme for its robustness and computational efficiency. But it is hard to realize for larger size images or video frames in real time due to its iterative sequential data flow pattern. A quad-tree data structure is quite popular for software implementation of the algorithm, where a local parallelism is difficult to establish due to inherent data dependency between processes. In this paper, we have proposed a parallel algorithm of splitting and merging which depends only on local operations. The algorithm is mapped onto a hierarchical cell network, which is a parallel version of Locally Excitory Globally Inhibitory Oscillatory Network (LEGION). Simulation results show that the proposed design is faster than any of the standard split and merge algorithmic implementations, without compromising segmentation quality. The timing performance enhancement is manifested in its Finite State Machine based VLSI implementation in VIRTEX series FPGA platforms. We have also shown that, though segmentation qualitywise split-and-merge algorithm is little bit behind the state-of-the-art algorithms, computational speedwise it over performs those sophisticated and complex algorithms. Good segmentation performance with minimal computational cost enables the proposed design to tackle real time segmentation problem in live video streams. In this paper, we have demonstrated live PAL video segmentation using VIRTEX 5 series FPGA. Moreover, we have extended our design to HD resolution for which the time taken is less than 5 ms rendering a processing throughput of 200 frames per second.