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JonLeonard-TheQuadtreeAndRelatedHierarchialDataStructures

JonLeonard-TheQuadtreeAndRelatedHierarchialDataStructures -...

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The Quadtree and Related Hierarchical Data Structures HANAN $AMET Computer Science Department, University of Maryland, College Park, Maryland 20742 A tutorial survey is presented of the quadtree and related hierarchical data structures. They are based on the principle of recursive decomposition. The emphasis is on the representation of data used in applications in image processing, computer graphics, geographic information systems, and robotics. There is a greater emphasis on region data {i.e., two-dimensional shapes) and to a lesser extent on point, curvilinear, and three- dimensional data. A number of operations in which such data structures find use are examined in greater detail. Categories and Subject Descriptors: E.1 [Data]: Data Structures--trees; H.3.2 [Information Storage and Retrieval]: Information Storage--file organization; 1.2.1 [Artificial Intelligence]: Applications and Expert Systems--cartography; 1.2.10 [Artificial Intelligence]: Vision and Scene Understanding--representations, data structures, and transforms; 1.3.3 [Computer Graphics]: Picture/Image Generation-- display algorithms; viewing algorithms; 1.3.5 [Computer Graphics]: Computational Geometry and Object Modeling--curve, surface, solid, and object representations; geometric algorithms, languages, and systems; 1.4.2 [Image Processing]: Compression ( Coding)--approximate methods; exact coding; 1.4.7 [Image Processing]: Feature Measurement--moments; projections; size and shape; J.6 [Computer-Aided Engineering]: Computer-Aided Design {CAD) General Terms: Algorithms Additional Key Words and Phrases: Geographic information systems, hierarchical data structures, image databases, multiattribute data, multidimensional data structures, octrees, pattern recognition, point data, quadtrees, robotics INTRODUCTION Hierarchical data structures are becoming increasingly important representation tech- niques in the domains of computer graph- ics, image processing, computational geom- etry, geographic information systems, and robotics. They are based on the principle of recursive decomposition (similar to divide and conquer methods [Aho et al. 1974]). One such data structure is the quadtree. As we shall see, the term quadtree has taken on a generic meaning. In this survey it is our goal to show how a number of data structures used in different domains are related to each other and to quadtrees. This presentation concentrates on these differ- ent representations and illustrates how a number of basic operations that use them are performed. Hierarchical data structures are useful because of their ability to focus on the interesting subsets of the data. This focus- ing results in an efficient representation and improved execution times and is thus particularly useful for performing set op- erations. Many of the operations that we describe can often be performed equally as Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To
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