Towards a Dynamic Data Structure for Efficient Bounded Line Range Search

Abstract We present a data structure for efficient axis-aligned orthogonal range search on a set of n lines in a bounded plane. The algorithm requires O(log n + k) time in the worst case to find all lines intersecting an axis aligned query rectangle R, where k is the number of lines in range. O(n + λ) space is required for the data structure used by the algorithm, where λ is the number of intersection points among the lines. Insertion of a new rightmost line or deletion of a leftmost line requires O(n) time in the worst case. For a sparse arrangement of lines (i.e., for λ = O(n)), insertion of a rightmost line or deletion of a leftmost line requires O( √ n) time, and O(log n + µ) expected time for µ the number of intersection points between and existing lines

Derivation of continuous zoomable road network maps through utilization of Space-Scale-Cube

The process of performing cartographic generalization in an automatic way applied on geographic information is of highly interest in the field of cartography, both in academia and industry. Many research e↵orts have been done to implement di↵erent automatic generalization approaches. Being able to answer the research question on automatic generalization, another interesting question opens up: ”Is it possible to retrieve and visualize geographic information in any arbitrary scale?” This is the question in the field of vario-scale geoinformation. Potential research works should answer this question with solutions which provide valid and efficient representation of geoinformation in any on-demand scale. More brilliant solutions will also provide smooth transitions between these on-demand arbitrary scales. Space-Scale-Cube (Meijers and Van Oosterom 2011) is a reactive tree (Van Oosterom 1991) data structure which shows positive potential for achieving smooth automatic vario-scale generalization of area features. The topic of this research work is investigation of adaptation of this approach on an interesting class of geographic information: road networks datasets. Firstly theoretical background will be introduced and discussed and afterwards, implementing the adaptation would be described. This research work includes development of a hierarchical data structure based on road network datasets and the potential use of this data structure in vario-scale geoinformation retrieval and visualization.:Declaration of Authorship i Abstract iii Acknowledgements iv List of Figures vii Abbreviations viii 1 Introduction 1 1.1 Problem Definition 2 1.1.1 Research Questions 2 1.1.2 Objectives 3 1.2 Proposed Solution 3 1.3 Structure of the Thesis 4 1.4 Notes on Terminology 4 2 Cartographic Generalization 6 2.1 Cartographic Generalization: Definitions and Classifications 6 2.2 Generalization Operators 9 2.3 Efforts on Vario-Scale Visualization of Geoinformation 10 2.4 Efforts on Generalization of Road Networks and Similar Other Networks 16 2.4.1 Geometric Generalization of Networks 17 2.4.2 Model Generalization of Networks 18 2.5 Clarification of Interest 20 3 Theory of Road Network SSC 21 3.1 Background of an SSC 21 3.1.1 tGAP 21 3.1.2 Smoothing tGAP 23 3.2 Road Network as a ’Network’ 24 3.2.1 Short Background on Graph Theory 5 3.3 Formation of Road Network SSC 26 3.3.1 Geometry 26 3.3.2 Network Topology 27 3.3.3 Building up tGAP on The Road Network 28 3.3.4 Smoothing of Road Network SSC 31 3.3.4.1 Smoothing Elimination 32 3.3.4.2 Smoothing Simplification 32 3.4 Reading from a road network SSC 34 3.4.1 Discussion on Scale 34 3.4.2 Iterating Over The Forest 35 3.4.3 Planar Slices 35 3.4.4 Non-Planar Slices 36 4 Implementation of Road Network SSC 37 4.1 General Information Regarding The Implementation 37 4.1.1 Programming Language 37 4.1.2 RDBMS 38 4.1.3 Geometry Library 39 4.1.4 Graph Library 39 4.2 Data Structure 40 4.2.1 Node 40 4.2.2 Edge 41 4.2.3 Edge-Node-Relation 41 4.3 Software Architecture 42 4.3.1 More Detail on Building The SSC 42 4.3.1.1 Initial Data Processing 42 4.3.1.2 Network Processing 43 4.3.2 More Detail on Querying The SSC 46 4.3.2.1 Database Query 46 4.3.2.2 Building Geometry 46 4.3.2.3 Interface and Visualization 47 4.4 Results 48 5 Conclusions and Outlook 49 Bibliography 5

Dynamic-parinet (D-parinet) : indexing present and future trajectories in networks

While indexing historical trajectories is a hot topic in the field of moving objects (MO) databases for many years, only a few of them consider that the objects movements are constrained. DYNAMIC-PARINET (D-PATINET) is designed for capturing of trajectory data flow in multiple discrete small time interval efficiently and to predict a MO’s movement or the underlying network state at a future time. The cornerstone of D-PARINET is PARINET, an efficient index for historical trajectory data. The structure of PARINET is based on a combination of graph partitioning and a set of composite B+-tree local indexes tuned for a given query load and a given data distribution in the network space. D-PARINET studies continuous update of trajectory data and use interpolation to predict future MO movement in the network. PARINET and D-PARINET can easily be integrated into any RDBMS, which is an essential asset particularly for industrial or commercial applications. The experimental evaluation under an off-the-shelf DBMS using simulated traffic data shows that DPARINET is robust and significantly outperforms the R-tree based access methods

Study and implementation of some tree drawing algorithms

Graph drawing deals with the geometric representation of graphs [1]. Data representation problems that require graph models can be better understood when visualized with appropriate graph drawings. The typical data structure for modeling hierarchical information is a tree whose vertices represent entities and whose edges correspond to relationships between entities. Algorithms for drawing trees are typically based on some graph-theoretic insight into the structure of the tree. It is characterized by the fact that in the drawings produced, the nodes at the same distance from the root are horizontally aligned [1]. This level-based approach can be used for both binary and general trees. Algorithms based on this approach involve some issues that lead to aesthetically wider than necessary drawings. I implemented “A Naïve Tree Drawing Algorithm” [2] as part of an independent study. This will serve as a basis and an introduction to this proposed thesis. In this thesis, we develop some tree drawing algorithms and a planarity drawing algorithm in terms of constructing a new pseudocode for each algorithm. Also, we focus on the theoretical graphic insight to the structure of the tree by building a drawing application for each algorithm. These applications provide an important view of the properties of drawing trees. In addition, these algorithms are implemented in a GUI (JEdit) that reflects an efficient aesthetic drawing. The input graph is checked to verify that it is a tree. The user sees an error message otherwise. These algorithms allow the user to select the root in an input tree. This leads to a better understanding of the algorithms. Most of these algorithms calculate the levels of the tree and the number of the nodes in each level. These algorithms are : the “Recursive Algorithm for Binary Trees” from [3], which has many steps, the “A Node-Positioning Algorithm for General Trees” from [4], the “Area-Efficient Order-Preserving Planar Straight-Line Drawings of Ordered Trees” from Section 3 of [5], and “Planarity Drawing Algorithm” from Section 2 of [6].Thesis (M.S.)Department of Computer ScienceGraph drawing basics and (GUI) for graph theory -- A naive tree drawing algorithm -- Recursive algorithm for binary trees -- A node positioning algorithm for general trees -- Area-efficient order-preserving planar straight-line drawings of ordered trees -- Planarity drawing algorithm

Automatic Retrieval of Skeletal Structures of Trees from Terrestrial Laser Scanner Data

Research on forest ecosystems receives high attention, especially nowadays with regard to sustainable management of renewable resources and the climate change. In particular, accurate information on the 3D structure of a tree is important for forest science and bioclimatology, but also in the scope of commercial applications. Conventional methods to measure geometric plant features are labor- and time-intensive. For detailed analysis, trees have to be cut down, which is often undesirable. Here, Terrestrial Laser Scanning (TLS) provides a particularly attractive tool because of its contactless measurement technique. The object geometry is reproduced as a 3D point cloud. The objective of this thesis is the automatic retrieval of the spatial structure of trees from TLS data. We focus on forest scenes with comparably high stand density and with many occlusions resulting from it. The varying level of detail of TLS data poses a big challenge. We present two fully automatic methods to obtain skeletal structures from scanned trees that have complementary properties. First, we explain a method that retrieves the entire tree skeleton from 3D data of co-registered scans. The branching structure is obtained from a voxel space representation by searching paths from branch tips to the trunk. The trunk is determined in advance from the 3D points. The skeleton of a tree is generated as a 3D line graph. Besides 3D coordinates and range, a scan provides 2D indices from the intensity image for each measurement. This is exploited in the second method that processes individual scans. Furthermore, we introduce a novel concept to manage TLS data that facilitated the researchwork. Initially, the range image is segmented into connected components. We describe a procedure to retrieve the boundary of a component that is capable of tracing inner depth discontinuities. A 2D skeleton is generated from the boundary information and used to decompose the component into sub components. A Principal Curve is computed from the 3D point set that is associated with a sub component. The skeletal structure of a connected component is summarized as a set of polylines. Objective evaluation of the results remains an open problem because the task itself is ill-defined: There exists no clear definition of what the true skeleton should be w.r.t. a given point set. Consequently, we are not able to assess the correctness of the methods quantitatively, but have to rely on visual assessment of results and provide a thorough discussion of the particularities of both methods. We present experiment results of both methods. The first method efficiently retrieves full skeletons of trees, which approximate the branching structure. The level of detail is mainly governed by the voxel space and therefore, smaller branches are reproduced inadequately. The second method retrieves partial skeletons of a tree with high reproduction accuracy. The method is sensitive to noise in the boundary, but the results are very promising. There are plenty of possibilities to enhance the method’s robustness. The combination of the strengths of both presented methods needs to be investigated further and may lead to a robust way to obtain complete tree skeletons from TLS data automatically.Die Erforschung des ÖkosystemsWald spielt gerade heutzutage im Hinblick auf den nachhaltigen Umgang mit nachwachsenden Rohstoffen und den Klimawandel eine große Rolle. Insbesondere die exakte Beschreibung der dreidimensionalen Struktur eines Baumes ist wichtig für die Forstwissenschaften und Bioklimatologie, aber auch im Rahmen kommerzieller Anwendungen. Die konventionellen Methoden um geometrische Pflanzenmerkmale zu messen sind arbeitsintensiv und zeitaufwändig. Für eine genaue Analyse müssen Bäume gefällt werden, was oft unerwünscht ist. Hierbei bietet sich das Terrestrische Laserscanning (TLS) als besonders attraktives Werkzeug aufgrund seines kontaktlosen Messprinzips an. Die Objektgeometrie wird als 3D-Punktwolke wiedergegeben. Basierend darauf ist das Ziel der Arbeit die automatische Bestimmung der räumlichen Baumstruktur aus TLS-Daten. Der Fokus liegt dabei auf Waldszenen mit vergleichsweise hoher Bestandesdichte und mit zahlreichen daraus resultierenden Verdeckungen. Die Auswertung dieser TLS-Daten, die einen unterschiedlichen Grad an Detailreichtum aufweisen, stellt eine große Herausforderung dar. Zwei vollautomatische Methoden zur Generierung von Skelettstrukturen von gescannten Bäumen, welche komplementäre Eigenschaften besitzen, werden vorgestellt. Bei der ersten Methode wird das Gesamtskelett eines Baumes aus 3D-Daten von registrierten Scans bestimmt. Die Aststruktur wird von einer Voxelraum-Repräsentation abgeleitet indem Pfade von Astspitzen zum Stamm gesucht werden. Der Stamm wird im Voraus aus den 3D-Punkten rekonstruiert. Das Baumskelett wird als 3D-Liniengraph erzeugt. Für jeden gemessenen Punkt stellt ein Scan neben 3D-Koordinaten und Distanzwerten auch 2D-Indizes zur Verfügung, die sich aus dem Intensitätsbild ergeben. Bei der zweiten Methode, die auf Einzelscans arbeitet, wird dies ausgenutzt. Außerdem wird ein neuartiges Konzept zum Management von TLS-Daten beschrieben, welches die Forschungsarbeit erleichtert hat. Zunächst wird das Tiefenbild in Komponenten aufgeteilt. Es wird eine Prozedur zur Bestimmung von Komponentenkonturen vorgestellt, die in der Lage ist innere Tiefendiskontinuitäten zu verfolgen. Von der Konturinformation wird ein 2D-Skelett generiert, welches benutzt wird um die Komponente in Teilkomponenten zu zerlegen. Von der 3D-Punktmenge, die mit einer Teilkomponente assoziiert ist, wird eine Principal Curve berechnet. Die Skelettstruktur einer Komponente im Tiefenbild wird als Menge von Polylinien zusammengefasst. Die objektive Evaluation der Resultate stellt weiterhin ein ungelöstes Problem dar, weil die Aufgabe selbst nicht klar erfassbar ist: Es existiert keine eindeutige Definition davon was das wahre Skelett in Bezug auf eine gegebene Punktmenge sein sollte. Die Korrektheit der Methoden kann daher nicht quantitativ beschrieben werden. Aus diesem Grund, können die Ergebnisse nur visuell beurteiltwerden. Weiterhinwerden die Charakteristiken beider Methoden eingehend diskutiert. Es werden Experimentresultate beider Methoden vorgestellt. Die erste Methode bestimmt effizient das Skelett eines Baumes, welches die Aststruktur approximiert. Der Detaillierungsgrad wird hauptsächlich durch den Voxelraum bestimmt, weshalb kleinere Äste nicht angemessen reproduziert werden. Die zweite Methode rekonstruiert Teilskelette eines Baums mit hoher Detailtreue. Die Methode reagiert sensibel auf Rauschen in der Kontur, dennoch sind die Ergebnisse vielversprechend. Es gibt eine Vielzahl von Möglichkeiten die Robustheit der Methode zu verbessern. Die Kombination der Stärken von beiden präsentierten Methoden sollte weiter untersucht werden und kann zu einem robusteren Ansatz führen um vollständige Baumskelette automatisch aus TLS-Daten zu generieren

Concepts for the Representation, Storage, and Retrieval of Spatio-Temporal Objects in 3D/4D Geo-Informations-Systems

The quickly increasing number of spatio-temporal applications in fields like environmental management or geology is a new challenge to the development of database systems. This thesis addresses three areas of the problem of integrating spatio-temporal objects into databases. First, a new representational model for continuously changing, spatial 3D objects is introduced and transferred into a small system of classes within an object-oriented database framework. The model extends simplicial cell complexes to the spatio-temporal setting. The problem of closure under certain operations is investigated. Second, internal data structures are introduced that represent instances of the (user-level) spatio-temporal classes. A new technique provides a compromise between compact storage and efficient retrieval of spatio-temporal objects. These structures correspond to temporal graphs and support updates as well as the maintainance of connected components over time. Third, it is shown how to realise further operations on the new type of objects. Among these operations are range queries, intersection tests, and the Euclidean distance function

Spatiotemporal Indexing With the M-Tree

Modern GIS applications for transportation and defense often require the ability to store the evolving positions of a large number of objects as they are observed in motion, and to support queries on this spatiotemporal data in real time. Because the M-Tree has been proven as an index for spatial network databases, we have selected it to be enhanced as a spatiotemporal index. We present modifications to the tree which allow trajectory reconstruction with fast insert performance and modifications which allow the tree to be built with awareness of the spatial locality of reference in spatiotemporal data

Cover contact graphs

We study problems that arise in the context of covering certain geometric objects called seeds (e.g., points or disks) by a set of other geometric objects called cover (e.g., a set of disks or homothetic triangles). We insist that the interiors of the seeds and the cover elements are pairwise disjoint, respectively, but they can touch. We call the contact graph of a cover a cover contact graph (CCG). We are interested in three types of tasks, both in the general case and in the special case of seeds on a line: (a) deciding whether a given seed set has a connected CCG, (b) deciding whether a given graph has a realization as a CCG on a given seed set, and (c) bounding the sizes of certain classes of CCG’s. Concerning (a) we give efficient algorithms for the case that seeds are points and show that the problem becomes hard if seeds and covers are disks. Concerning (b) we show that this problem is hard even for point seeds and disk covers (given a fixed correspondence between graph vertices and seeds). Concerning (c) we obtain upper and lower bounds on the number of CCG’s for point seeds

COMPRESS: A comprehensive framework of trajectory compression in road networks

National Research Foundation (NRF) Singapore under International Research Centre @ Singapore Funding Initiativ