Linear Quadtree Research Articles

Social space keyword query based on semantic trajectory

With the booming development of smart phones and location-based services, spatial keyword queries of semantic trajectories can take location information and multiple keywords as parameters and return semantic trajectories related to these parameters in space and text. With the development of the Location Based Social Network (LBSN) in recent years, social data can be used to improve query results. Generally, the semantic trajectory of having more supporters (users with positive comments about the location) who are more closely related to the query user is more likely to be the recommended result. Considering social information in the query can recommend more satisfactory results for users, this paper studies a new problem of semantic trajectory space keyword query: Social space Keyword Query based on semantic Trajectory (SKQT). This paper proposes a hybrid index structure that introduces social factors called Social Inverted Linear Quadtree (SIL-Quadtree) to improve the efficiency of SKQT query. The experiments use two datasets, Gowalla and Brightkite. The results show that the algorithm and index structure proposed in this paper perform better on running time and I/O.

ESPM: Efficient Spatial Pattern Matching

With recent advances in information technologies such as global position system and mobile internet, a huge volume of spatio-textual objects have been generated from location-based services, which enable a wide range of spatial keyword queries. Recently, researchers have proposed a novel query, called Spatial Pattern Matching (SPM), which uses a pattern to capture the user's intention. It has been demonstrated to be fundamental and useful for many real applications. Despite its usefulness, the SPM problem is computationally intractable. Existing algorithms suffer from the low efficiency issue, especially on large scale datasets. To enhance the performance of SPM, in this paper we propose a novel Efficient Spatial Pattern Matching (ESPM) algorithm, which exploits the inverted linear quadtree index and computes matched node pairs and object pairs level by level in a top-down manner. In particular, it focuses on pruning unpromising nodes and node pairs at the high levels, resulting in a large number of unpromising objects and object pairs to be pruned before accessing them from disk. We experimentally evaluate the performance of ESPM on real large datasets. Our results show that ESPM is over one order of magnitude faster than the state-of-the-art algorithm, and also uses much less I/O cost.

Utilizing extended geocodes for handling massive three-dimensional point cloud data

Point clouds have become a primitive and fundamental material for manifold spatial representations. It can precisely render real-world environments as high-density points which include three-dimensional (3D) coordinates (x, y & z) and other features (color, intensity, and so on). Accordingly, various applications, including robot navigation and self-driving, make use of point clouds not only to detect near objects but to comprehend overall geospatial surroundings. However, it is challenging to exploit the point clouds in terms of spatial query processing in traditional database systems because of its enormous volume and nonstructural formats. In this paper, we propose an efficient method for the manipulation of 3D point cloud based on a Discrete Global Grid System (DGGS). As DGGS represents the Earth as hierarchical sequences of equal area/volume tessellations, it provides an accurate partitioning to integrate and analyze big geospatial data, unlike a base64 geohash representation. This study extends our previous DGGS-based encoding/decoding work to process 3D range queries with more than 64 bits for precise 3D coordinates of point clouds. In particular, we apply PH-tree as a multi-resolution tessellation storage and indexing structure for 3D bounding box queries. The experimental results show that our query processing significantly outperforms the baseline with a linear quadtree. Also, we present the encoding/decoding efficiency of converting large Morton codes from geographic coordinates by using the combination of bit interleaving and lookup tables.

Extending general compact querieable representations to GIS applications

The raster model is commonly used for the representation of images in many domains, and is especially useful in Geographic Information Systems (GIS) to store information about continuous variables of the space (elevation, temperature, etc.). Current representations of raster data are usually designed for external memory or, when stored in main memory, lack efficient query capabilities. In this paper we propose compact representations to efficiently store and query raster datasets in main memory. We present different representations for binary raster data, general raster data and time-evolving raster data. We experimentally compare our proposals with traditional storage mechanisms such as linear quadtrees or compressed GeoTIFF files. Results show that our structures are up to 10 times smaller than classical linear quadtrees, and even comparable in space to non-querieable representations of raster data, while efficiently answering a number of typical queries.

Inverted Linear Quadtree: Efficient Top K Spatial Keyword Search

With advances in geo-positioning technologies and geo-location services, there are a rapidly growing amount of spatio-textual objects collected in many applications such as location based services and social networks, in which an object is described by its spatial location and a set of keywords (terms). Consequently, the study of spatial keyword search which explores both location and textual description of the objects has attracted great attention from the commercial organizations and research communities. In the paper, we study two fundamental problems in the spatial keyword queries: top $k$ spatial keyword search (TOPK-SK), and batch top $k$ spatial keyword search (BTOPK-SK). Given a set of spatio-textual objects, a query location and a set of query keywords, the TOPK-SK retrieves the closest $k$ objects each of which contains all keywords in the query. BTOPK-SK is the batch processing of sets of TOPK-SK queries. Based on the inverted index and the linear quadtree, we propose a novel index structure, called inverted linear quadtree (IL-Quadtree), which is carefully designed to exploit both spatial and keyword based pruning techniques to effectively reduce the search space. An efficient algorithm is then developed to tackle top $k$ spatial keyword search. To further enhance the filtering capability of the signature of linear quadtree, we propose a partition based method. In addition, to deal with BTOPK-SK, we design a new computing paradigm which partition the queries into groups based on both spatial proximity and the textual relevance between queries. We show that the IL-Quadtree technique can also efficiently support BTOPK-SK. Comprehensive experiments on real and synthetic data clearly demonstrate the efficiency of our methods.

A Neighbor-finding Algorithm Involving the Application of SNAM in Binary-image Representation

In view of the low execution efficiency and poor practicability of the existing neighbor-finding method, a fast neighbor-finding algorithm is put forward on the basis of Square Non-symmetry and Anti-packing Model (SNAM) for binary-image. First of all, the improved minor-diagonal scanning way is applied to strengthen SNAM’s adaptability to various textures, thus reducing the total number of nodes after coding; then the storage structures for its sub-patterns are standardized and a grid array is used to recover the spatial-position relationships among sub-patterns, so as to further reduce the complexity of the neighbor-finding algorithm. Experimental result shows that this method’s execution efficiency is significantly higher than that of the classic Linear Quad Tree (LQT)-based neighbor-finding method.

A novel binary image representation algorithm by using NAM and coordinate encoding procedure and its application to area calculation

We propose a novel binary image representation algorithm using the non-symmetry and anti-packing model and the coordinate encoding procedure (NAMCEP). By taking some idiomatic standard binary images in the field of image processing as typical test objects, and by comparing our proposed NAMCEP representation with linear quadtree (LQT), binary tree (Bintree), non-symmetry and anti-packing model (NAM) with K-lines (NAMK), and NAM representations, we show that NAMCEP can not only reduce the average node, but also simultaneously improve the average compression. We also present a novel NAMCEP-based algorithm for area calculation and show experimentally that our algorithm offers significant improvements.

Research on Point Cloud Data Management Based on Spatial Index and Database

Laser point set has a massive quantity of data, which not only increases system load, but greatly reduces the follow-up processing efficiency as well. Considering the difficulty of mass point cloud data organization and management, grid index of point cloud data based on the decimal linear quadtree is proposed in this paper, point cloud data is segmented and encoded by means of linear quadtree based on decimal system, which will be stored in SQL Server, then, we can block and index point cloud in terms of Morton code or rectangular region, combine with the advantages of both spatial index and database to manage point cloud efficiently and safely. The results show that the proposed method ideally solves the problem of point cloud data organization and management.

Calculation of profile error for complex surface

Evaluation of profile error is important in manufacturing and detection of complex surface. In this paper, an algorithm is presented to calculate surface profile error accurately based on linear quadtree after rough localization and accurate registration. In rough localization, the best transformation is selected from four transformations. Then two algorithms are adopted to realize accurate registration and comparison is performed. One algorithm is the combination of LM algorithm and ICP algorithm. The other algorithm is BFGS algorithm. Experiment result shows that complex surface profile error is evaluated effectively through the proposed algorithm.

Efficient encoding and spatial operation scheme for aperture 4 hexagonal discrete global grid system

Discrete global grid systems (DGGSs) are considered to be promising structures for global geospatial information representation. Square and triangular DGGSs have had the advantage over hexagonal ones in geospatial data processing over the past few decades. Despite a significant body of research supporting hexagonal grids as the superior alternative, the application thereof has been hindered partly owing to the lack of a hierarchy. This study presents an original perspective to combine two types of aperture 4 hexagonal discrete grid systems into a hierarchy. Each cell of the hierarchy is assigned a unique code using a linear quadtree that constructs the hexagonal quaternary balanced structure (HQBS). The mathematical system described by HQBS addressing and the vector operations, including addition, subtraction, multiplication, and division, are defined. Essential spatial operations for HQBS cell retrieval, transformation between HQBS codes and other coordinate systems, and arrangement of HQBS cells on spherical surfaces were studied and implemented. The accuracy and efficiency of algorithms were validated through experiments. The results indicate that the average efficiency of cell retrieval using the HQBS is higher than that using other schemes, thus proving it to be more efficient.

Sorting of Section Contour Data Based on Linear Quadtree

A method based on the linear quadtree is proposed to sort the discrete data of the section contour. Firstly the contour data are distributed to different nodes of the linear quadtree and the data in the same node are sorted. Then neighbor node search regulations are established to help sort data in different nodes counter-clockwise. Experiment shows that the presented method can sort the data effectively.

Low-Altitude Airship Remote Sensing Images Matching Based on Improved Hybrid Ant Colony Algorithm

Low-altitude unmanned airship remote sensing is attractive to various applications. However, at present, since the airship is bulky, weak to resist wind, unstable to flight attitude, and can not be equipped with specialized remote sensing sensors, image data processing is confronted with new challenges when traditional data processing methods are used. In this paper, improved hybrid ant colony algorithm (HACA), a new image matching method, is proposed. Firstly we perform a pre-registration process that roughly aligns the image pairs by GPS/electronic compass geolocation. Once the pre-registration is completed, a fine-scale registration process is executed by applying a hybrid algorithm of genetic algorithm (GA) and ant colony algorithm (ACA) based on neighborhood search strategy that is detected by the linear quadtree Morton coding. The image pairs are then matched by using optimal solution obtained from the automatic updates of ant colony pheromone. By compared with traditional genetic algorithm and ant colony algorithm, the improved HACA results show that search calculation time is increased by the maximum 406℅, standard root mean square error of image matching by the best 235℅. The experiment result proves that improved HACA exactly provides an effective method for image matching. The local maxima of the function can be avoided efficiently and search speed of the global optimum is increased greatly.

A Novel Gray Image Representation Method Based on NAM Using Nonoverlapping Square Subpatterns

In this paper, we propose a novel gray image representation method based on the non-symmetry and anti-packing model (NAM) by using the nonoverlapping square subpatterns, which is called the square NAM for gray images (SNAMG) representation method. Also, a SNAMG representation algorithm is put forward and the storage structures, the total data amount, and the time complexity of the proposed algorithm are analyzed in detail. By taking some standard gray images, such as ‘F16’ and ‘Peppers’, as the typical test objects, and comparing the proposed algorithm with those of the triangle NAM for gray images (TNAMG) and the classic linear quadtree (LQT), the theoretical and experimental results show that the former is obviously superior to the latter with respect to the numbers of subpatterns (nodes) and the data storage, and therefore it is a better method to represent the gray image pattern.

Image-pyramid-oriented linear quadtree coding and features

Based on the linear quadtree,an image-element coding method oriented to image pyramid was introduced.According to the coding rules and Bounding BOX(BBOX) recurrence formula,the corresponding feature,location feature,existence feature and neighborhood feature were analyzed.Furthermore,a global multi-resolution virtual terrain environment and zoom-in operation algorithm were constructed to test the coding method.The results show that the method can distinguish boundary image-element and neighborhood image-element rapidly,and has a higher rate than other similar algorithms.

Single Core Hardware Module to Implement Partial Encryption of Compressed Image

Problem statement: Real-time secure image and video communication is challenging due to the processing time and computational requirement for encryption and decryption. In order to cope with these concerns, innovative image compression and encryption techniques are required. Approach: In this research, we have introduced partial encryption technique on compressed images and implemented the algorithm on Altera FLEX10K FPGA device that allows for efficient hardware implementation. The compression algorithm decomposes images into several different parts. We have used a secured encryption algorithm to encrypt only the crucial parts, which are considerably smaller than the original image, which result in significant reduction in processing time and computational requirement for encryption and decryption. The breadth-first traversal linear lossless quadtree decomposition method is used for the partial compression and RSA is used for the encryption. Results: Functional simulations were commenced to verify the functionality of the individual modules and the system on four different images. We have validated the advantage of the proposed approach through comparison, verification and analysis. The design has utilized 2928 units of LC with a system frequency of 13.42MHz. Conclusion: In this research, the FPGA prototyping of a partial encryption of compressed images using lossless quadtree compression and RSA encryption has been successfully implemented with minimum logic cells. It is found that the compression process is faster than the decompression process in linear quadtree approach. Moreover, the RSA simulations show that the encryption process is faster than the decryption process for all four images tested.

Star-quadtrees and guard-quadtrees: I/O-efficient indexes for fat triangulations and low-density planar subdivisions

We present a new I/O-efficient index structure for storing planar subdivisions. This so-called guard-quadtree is a compressed linear quadtree, which is provably efficient for map overlay, point location, and range queries in low-density subdivisions. In particular, we can preprocess a low-density subdivision with n edges, in O ( sort ( n ) ) I/Os, to build a guard-quadtree that allows us to: (i) compute the intersections between the edges of two such preprocessed subdivisions in O ( scan ( n ) ) I/Os, where n is the total number of edges in the two subdivisions; (ii) answer a single point location query in O ( log B n ) I/Os, and k batched point location queries in O ( scan ( n ) + sort ( k ) ) I/Os; and (iii) answer range queries for any constant-complexity query range Q in O ( 1 ε ( log B n ) + scan ( k ε ) ) I/Os for every ε > 0 , where k ε is the number of edges of the subdivision within distance ε ⋅ diam ( Q ) from Q. For the special case where the subdivision is a fat triangulation, we show how to obtain the same results with an ordinary (uncompressed) linear quadtree, which we call the star-quadtree. The star-quadtree is fully dynamic and needs only O ( log B n ) I/Os per update. Our algorithms and data structures improve on the previous best known bounds for overlaying general subdivisions, both in the number of I/Os and space usage. The constants in the asymptotic bounds are small, which makes our results applicable in practice. Moreover, our algorithms are simpler than previous approaches and almost all of them are cache-oblivious.

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.

A NAM Representation Method for Data Compression of Binary Images

A representation method using the non-symmetry and anti-packing model (NAM) for data compression of binary images is presented. The NAM representation algorithm is compared with the popular linear quadtree and run length encoding algorithms. Theoretical and experimental results show that the algorithm has a higher compression ratio for both lossy and lossless cases of binary images and better reconstructed quality for the lossy case.

A novel algorithm for image perimeter computation based on non-symmetry anti-packing representation

The non-symmetry anti-packing image representation (NAIR) uses a sequence of the instances of some predefined prototypes to represent an image. While significantly reducing the instances required to represent an image in contrary to the quadtree and the linear quadtree, however, NAIR has lost the explicit space relationship among these instances and hence made some geometric operations such as perimeter computation hard to be implemented. In this paper, longitude and latitude grid (L2G), a data structure which can restore lost space relationship from the NAIR is first presented, and then a novel algorithm to compute the perimeters of the images represented by the NAIR is presented. The experimental results show that the new algorithm has saved at least 90% of the running time comparing with that based on the quadtree.

An improved algorithm for gray image representation using non-symmetry and anti-packing model with triangles and rectangles

Although the triangle non-symmetry and anti-packing model (TNAM) representation for gray images is an effective image representation method, there is still much space left for optimization. In this paper, inspired by the optimization idea of the packing problem, we proposed an improved algorithm for gray image representation using the non-symmetry and anti-packing model with triangles and rectangles (NAMTR). By comparing the representation algorithm of the NAMTR with those of the TNAM and the popular linear quadtree, theoretical and experimental results presented in this paper show that the former can greatly reduce the number of sub-patterns or nodes and simultaneously save the data storage much more effectively than the latter, and therefore it is a better method to represent gray images. Representation method of the NAMTR, as envisaged in this paper, shows a very strong promise, and it is valuable for further theoretical research and potential business foreground, such as reducing storage space, increasing transmission speed and improving pattern match efficiency.