Efficient Quadtree based Fractal Image Coding Scheme in Wavelet Transform Domain *

This paper presents an efficient quadtree based fractal image coding scheme in wavelet transform domain based on the wavelet based theory of fractal image compression introduced by Davis. In the scheme, zerotrees of wavelet coefficients are used to reduce the number of domain blocks, which leads to lower bit cost required to represent the location information of fractal coding, and overall entropy constrained optimization is performed for the decision trees as well as for the sets of scalar quantizers and self quantizers of wavelet subtrees. Experiment results show that at the low bit rates, the proposed scheme gives about 1 dB improvement in PSNR over the reported results.

Numerical simulation of wind-driven circulation and pollutant transport in Taihu Lake based on a quadtree grid

In this study,a two-dimensional flow-pollutant coupled model was developed based on a quadtree grid.This model was established to allow the accurate simulation of wind-driven flow in a large-scale shallow lake with irregular natural boundaries when focusing on important smallscale localized flow features.The quadtree grid was created by domain decomposition.The governing equations were solved using the finite volume method,and the normal fluxes of mass,momentum,and pollutants across the interface between cells were computed by means of a Godunov-type Osher scheme.The model was employed to simulate wind-driven flow in a circular basin with non-uniform depth.The computed values were in agreement with analytical data.The results indicate that the quadtree grid has fine local resolution and high efficiency,and is convenient for local refinement.It is clear that the quadtree grid model is effective when applied to complex flow domains.Finally,the model was used to calculate the flow field and concentration field of Taihu Lake,demonstrating its ability to predict the flow and concentration fields in an actual water area with complex geometry.

Terrain Rendering LOD Algorithm Based on Improved Restrictive Quadtree Segmentation and Variation Coefficient of Elevation

Aiming to deal with the difficult issues of terrain data model simplification and crack disposal,the paper proposed an improved level of detail(LOD)terrain rendering algorithm,in which a variation coefficient of elevation is introduced to express the undulation of topography.Then the coefficient is used to construct a node evaluation function in the terrain data model simplification step.Furthermore,an edge reduction strategy is combined with the improved restrictive quadtree segmentation to handle the crack problem.The experiment results demonstrated that the proposed method can reduce the amount of rendering triangles and enhance the rendering speed on the premise of ensuring the rendering effect compared with a traditional LOD algorithm.

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.

Spatial Topology Rule Checking Algorithm of Linear Entity Based on Quadtree

Spatial topology rule is the primary method to insure the consistency and validity of spatial topology relation in GIS software. Topology rule can be divided into three categories according to geographic entity’s geometric shape: point topology rule, line topology rule and polygon topology rule. At first, this paper summarizes the various linear geographic entities’ topological relations which have practical application, then designs a series of linear entity topology rules detailedly. Based on these rules, this paper proposes a topology rule checking algorithm using quadtree, which is designed on the basis of MAPGIS7.4 spatial data model. The algorithm has already been applied to MAPGIS platform and gained good effects.

Image Coding Using Wavelet Transform and EntropyConstrained Vector Quantization with Quadtree Structure Vectors

This paper presents a new wavelet transform image coding method. On the basis of a hierarchical wavelet decomposition of images, entropy constrained vector quantization is employed to encode the wavelet coefficients at all the high frequency bands with

Personalized trajectory data perturbation algorithm based on quadtree indexing

To solve the privacy leakage problem of truck trajectories in intelligent logistics,this paper proposes a quadtreebased personalized joint location perturbation(QPJLP)algorithm using location generalization and local differential privacy(LDP)techniques.Firstly,a flexible position encoding mechanism based on the spatial quadtree indexing is designed,and the length of the encoding can be adjusted freely according to data availability.Secondly,to meet the privacy needs of different locations of users,location categories are introduced to classify locations as sensitive and ordinary locations.Finally,the truck invokes the corresponding mechanism in the QPJLP algorithm to locally perturb the code according to the location category,allowing the protection of non-sensitive locations to be reduced without weakening the protection of sensitive locations,thereby improving data availability.Simulation experiments demonstrate that the proposed algorithm effectively meets the personalized trajectory privacy requirements while also exhibiting good performance in trajectory proportion estimation and top-k classification.

Hybrid Finite Element Method Based on Polygon-Quadtree Meshes for Heat Transfer and Thermal Elastic Analysis

A steady-state thermal hybrid element model is proposed to calculate particle-reinforced composites divided by an improved quadtree mesh.The functional of hybrid flux finite element method(HF-FEM)is constructed using the weighted residual method.This functional independently assumes a heat flux field in the cell domain and a temperature field along cell boundaries.The construction of a universal heat flux function is put forward,which is approximated by a complete polynomial,and the temperature at the cell boundary is obtained by linear interpolation.Also,the hybrid stress finite element method(HS-FEM)is constructed to solve the thermal stress.In this paper,an improved quadtree grid that can accurately describe the shape of elliptical inclusions is built.By comparing several numerical examples with the traditional FEM,it is demonstrated that the hybrid element of the thermal analysis proposed in this paper is practical.

High capacity reversible data hiding in encrypted images based on adaptive quadtree partitioning and MSB prediction

To improve the embedding capacity of reversible data hiding in encrypted images(RDH-EI),a new RDH-EI scheme is proposed based on adaptive quadtree partitioning and most significant bit(MSB)prediction.First,according to the smoothness of the image,the image is partitioned into blocks based on adaptive quadtree partitioning,and then blocks of different sizes are encrypted and scrambled at the block level to resist the analysis of the encrypted images.In the data embedding stage,the adaptive MSB prediction method proposed by Wang and He(2022)is improved by taking the upper-left pixel in the block as the target pixel,to predict other pixels to free up more embedding space.To the best of our knowledge,quadtree partitioning is first applied to RDH-EI.Simulation results show that the proposed method is reversible and separable,and that its average embedding capacity is improved.For gray images with a size of 512×512,the average embedding capacity is increased by 25565 bits.For all smooth images with improved embedding capacity,the average embedding capacity is increased by about 35530 bits.

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.

L curve for spherical triangle region quadtrees

The sequence of facets and nodes has a direct influence on the efficiency of access to spherical triangle region quadtree. Based on the labeling schema by Lee, spatial curves both for facets and nodes are proposed and the main algorithms for coordinate translation, node Lsequence generation and visiting nodes are presented. In particular,constant time algorithms for generating node Lsequence are advanced by using bit manipulation operations,which can be easily implemented with hardware. In L curve the distance between three nodes of a facet is mostly limited in a range of small value, thus making fast access possible. Though codes of sibling facets are continuous, the difference between codes of some cousins may occasionally be very large and makes the distance of a few facets also very large, thus greatly increasing the mean node distance and the total traversing distance. Therefore an m cluster of nodes is proposed as a basic storage unit fo n cluster, which should store eery shared node in each,and the distance between three nodes of a facet is limited to a controllagle scope.

Coupling of wave and current numerical model with unstructured quadtree grid for nearshore coastal waters

This paper presents 2D wave-current interaction model for evaluating nearly horizontal wave-induced currents in the surf-zone and coastal waters.The hydrodynamic model is the two-dimensional depth-averaged nonlinear shallow water equations by using an unstructured non-staggered and multiple-level quadtree rectangular mesh,this mesh information is stored in simple data structures and it is easy to obtain a locally high resolution for important region.The intercell fluxes are computed based on the HLL(Harten-Lax-van Leer) approximate Riemann solver with shock capturing capability for computing the dry-to-wet interface of coastal line.The effects of pressure and gravity are included in source term in the model,this treatment can simplify the computation and eliminate numerical imbalance between source and flux terms.The wave model readily provides the radiation stresses that represent the shortwave-averaged forces in a water column for the hydrodynamic model and the wave model takes into account the effect of wave-induced nearshore currents and water level.The coupling model is applied to verify different experimental cases and real life case of considering the wave-current interaction.The calculated results agree with analytical solution,experimental and field data.The results show that the modeling approach presented herein should be useful in simulating the nearshore processes in complicated natural coastal domains.

Loose architecture of multi-level massive geospatial data based on virtual quadtree

This paper proposed a virtual quadtree (VQT) based loose architecture of multi-level massive geospatial data for integrating massive geospatial data dispersed in the departments of different hierarchies in the same sector into a unified GIS (Geographic Information System) platform. By virtualizing the nodes of the quad-tree,the VQT separates the structure of data organization from data storage,and screens the difference between the data storage in local computer and in the re-mote computers in network environment. And by mounting,VQT easily integrates the data from the remote computers into the local VQT so as to implement seam-less integration of distributed multi-level massive geospatial data. Based on that mode,the paper built an application system with geospatial data over 1200 GB distributed in 12 servers deployed in 12 cities. The experiment showed that all data can be seamlessly rapidly traveled and performed zooming in and zooming out smoothly.

Solution of N-S equations based on the quadtree cut cell method

With the characteristic of the quadtree data structure, a new mesh generation method, which adopts square meshes to decompose a background domain and a cut cell approach to express arbitrary boundaries, is proposed to keep the grids generated with a good orthogonality easily. The solution of N-S equations via finite volume method for this kind of unstructured meshes is derived. The mesh generator and N-S solver are implemented to study two benchmark cases, i.e. a lid driven flow within an inclined square and a natural convection heat transfer flow in a square duct with an inner hot circular face. The simulation results are in agreement with the benchmark values, verifying that the present methodology is valid and will be a strong tool for two-dimensional flow and heat transfer simulations, especially in the case of complex boundaries.

An Efficient Representation of Quadtrees and Bintrees for Multiresolution Terrain Models

A space-filling curve in 2,3,or higher dimensions can be thought as a path of a continuously moving point.As its main goal is to preserve spatial proximity,this type of curves has been widely used in the design and implementation of spatial data structures and nearest neighbor-finding techniques.This paper is essentially focused on the efficient representation of Digital Ele-vation Models(DEM) that entirely fit into the main memory.We propose a new hierarchical quadtree-like data structure to be built over domains of unrestricted size,and a representation of a quadtree and a binary triangles tree by means of the Hilbert and the Sierpinski space-filling curves,respectively,taking into account the hierarchical nature and the clustering properties of this kind of curves.Some triangulation schemes are described for the space-filling-curves-based approaches to efficiently visualize multiresolu-tion surfaces.

An optimized hexagonal quadtree encoding and operation scheme for icosahedral hexagonal discrete global grid systems

Although research on the discrete global grid systems (DGGSs) has become an essential issue in the era of big earth data,there is still a gap between the efficiency of current encoding and operation schemes for hexagonal DGGSs and the needs of practical applications. This paper proposes a novel and efficient encoding and operation scheme of an optimized hexagonal quadtree structure (OHQS) based on aperture 4 hexagonal discrete global grid systems by translation transformation. A vector model is established to describe and calculate the aperture 4 hexagonal grid system. This paper also provides two different grid code addition algorithms based on induction and ijk coordinate transformation. We implement the transformation between OHQS codes and geographic coordinates through the ij,ijk and IJK coordinate systems. Compared with existing schemes,the scheme in this paper greatly improves the efficiency of the addition operation,neighborhood retrieval and coordinate transformation,and the coding is more concise than other aperture 4 hexagonal DGGSs. The encoding operation based on the ijk coordinate system is faster than the encoding operation based on the induction and addition table. Spatial modeling based OHQS DGGSs are also provided. A case study with rainstorms demonstrated the availability of this scheme.

Differentially Private Spatial Decompositions for Geospatial Point Data

Technological advancements in data analysis and data releasing have put forward higher security requirements, such as privacy guarantee and strictly provable security, this new area of research is called differential privacy. As for geospatial point data, the exiting methods use the tree structure to split the data space to enhance the data utility and usually adopt uniform budgeting method. Different from this, we propose a novel non-uniform allocation scheme for privacy budget which is a parameter to specify the degree of privacy guarantee. Firstly, the spatial data is indexed by quadtree, then, different privacy budget is allocated to each layer of quadtree using Fibonacci series features, and we designate this budgeting method as Fibonacci allocation. Experimental results show that Fibonacci allocation is significantly more accurate in data queries than the state-of-the-art methods under the same privacy guarantee level and fits for arbitrary range queries. Furthermore, data utility can be improved by post-processing and threshold determination.

A two-dimensional numerical wave flume based on SA-MPLS method

A spatially adaptive (SA) two-dimensional (2-D) numerical wave flume is presented based on the quadtree mesh system,in which a new multiple particle level set (MPLS) method is proposed to solve the problem of interface tracking,in which common intersection may be traversed by multiple interfaces.By using the adaptive mesh technique and the MPLS method,mesh resolution is updated automatically with time according to flow characteristics in the modeling process with higher resolution around the free surface and the solid boundary and lower resolution in less important area.The model has good performance in saving computer memory and CPU time and is validated by computational examples of small amplitude wave,second-order Stokes wave and cnoidal wave.Computational results also indicate that standing wave and wave overtopping are also reasonably simulated by the model.

HQ-Tree： A Distributed Spatial Index Based on Hadoop

In this paper,we propose a novel spatial data index based on Hadoop:HQ-Tree.In HQ-Tree,we use PR QuadTrec to solve the problem of poor efficiency in parallel processing,which is caused by data insertion order and space overlapping.For the problem that HDFS cannot support random write,we propose an updating mechanism,called "Copy Write",to support the index update.Additionally,HQ-Tree employs a two-level index caching mechanism to reduce the cost of network transferring and I/O operations.Finally,we develop MapReduce-based algorithms,which are able to significantly enhance the efficiency of index creation and query.Experimental results demonstrate the effectiveness of our methods.

Finite cell method compared to h-version finite element method for elasto-plastic problems

The finite cell method （FCM） combines the high-order finite element method （FEM） with the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is used to the Prandtl-Reuss flow theory of plasticity, and the results are compared with the h-version finite element method （h-FEM）. The numerical results show that the FCM is more efficient compared to the h-FEM for elasto-plastic problems, although the mesh does not conform to the boundary. It is also demonstrated that the FCM performs well for elasto-plastic loading and unloading.