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Algorithmic Foundation of Multi-Scale Spatial Representation




ISBN 9780849390722
Published October 4, 2006 by CRC Press
281 Pages - 8 Color & 256 B/W Illustrations

 
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Book Description

With the widespread use of GIS, multi-scale representation has become an important issue in the realm of spatial data handling. However, no book to date has systematically tackled the different aspects of this discipline. Emphasizing map generalization, Algorithmic Foundation of Multi-Scale Spatial Representation addresses the mathematical basis of multi-scale representation, specifically, the algorithmic foundation.

Using easy-to-understand language, the author focuses on geometric transformations, with each chapter surveying a particular spatial feature. After an introduction to the essential operations required for geometric transformations as well as some mathematical and theoretical background, the book describes algorithms for a class of point features/clusters. It then examines algorithms for individual line features, such as the reduction of data points, smoothing (filtering), and scale-driven generalization, followed by a discussion of algorithms for a class of line features including contours, hydrographic (river) networks, and transportation networks. The author also addresses algorithms for individual area features, a class of area features, and various displacement operations. The final chapter briefly covers algorithms for 3-D surfaces and 3-D features.

Providing a thorough treatment of low-level algorithms, Algorithmic Foundation of Multi-Scale Spatial Representation supplies the mathematical groundwork for multi-scale representations of spatial data.

Table of Contents

INTRODUCTION
Spatial Representation: Representation of Spatial Data
Multi-Scale Spatial Representation
Transformations in Multi-Scale Spatial Representation
Operations for Geometric Transformations in Multi-Scale Spatial Representation
Scope of This Book
References

MATHEMATICAL BACKGROUND
Geometric Elements and Parameters for Spatial Representation
Mathematical Morphology
Delaunay Triangulation and the Voronoi Diagram
Skeletonization and Medial Axis Transformation
References

THEORETICAL BACKGROUND
Scale in Geographical Space
Relativity in Scale: The Natural Principle
The Radical Laws: Principles of Selection
Strategies for Transformations of Spatial Representations in Scale
References

ALGORITHMS FOR TRANSFORMATIONS OF POINT FEATURES
Algorithms for Point Features: An Overview
Algorithms for Aggregation of a Set of Point Features
Algorithms for Selective Omission of a Set of Point Features
Algorithms for Structural Simplification of a Set of Point Features
Algorithms for Outlining a Set of Point Features: Regionization
References

ALGORITHMS FOR POINT-REDUCTION OF INDIVIDUAL LINE FEATURES
Algorithms for Line Point-Reduction: An Overview
Sequential Algorithms with Geometric Parameters as Criteria
Iterative Algorithms with Geometric Parameters as Criteria
Algorithms with Functions of Geometric Parameters as Criteria
Evaluation of Point-Reduction Algorithms.
Attempts to Improve Point-Reduction Algorithms
References

ALGORITHMS FOR SMOOTHING OF INDIVIDUAL LINE FEATURES
Smoothing of a Line: An Overview
Smoothing by Moving Averaging in the Space Domain
Smoothing by Curve Fitting in the Space Domain
Smoothing by Frequency Cutting in the Frequency Domain
Smoothing by Component Exclusion in the Space Domain
Evaluation of Line Smoothing Algorithms
References

ALGORITHMS FOR SCALE-DRIVEN GENERALIZATION OF INDIVIDUAL LINE FEATURES
Scale-Driven Generalization: An Overview
Algorithms Based on Gaussian Spatial-Scale
Algorithms Based on e-Circle Rolling
Algorithms Based on the Natural Principle
Evaluation of Scale-Driven Line Generalization Algorithms
References

ALGORITHMS FOR TRANSFORMATIONS OF A SET OF LINE FEATURES
A Set of Line Features: An Overview
Algorithms for Transformation of a Set of Contour Lines
Algorithms for Transformation of River Networks
Algorithms for Transformation of Transportation Networks
References

ALGORITHMS FOR TRANSFORMATIONS OF INDIVIDUAL AREA FEATURES
Transformation of Individual Area Features: An Overview
Algorithms for Boundary-Based Shape Simplification of an Area Feature
Algorithms for Region-Based Shape Simplification of an Area Feature
Algorithms for Collapse of Area Features
Algorithms for Area Elimination
Algorithms for Splitting an Area Feature
Algorithms for Exaggeration
References

ALGORITHMS FOR TRANSFORMATIONS OF A SET OF AREA FEATURES
Transformation of a Class of Area Features: An Overview
Algorithms for Simplification of the Shape of a Polygonal Network
Algorithms for Combining Area Features: Aggregation and Amalgamation
Algorithms for Merging and Dissolving Area Features
Algorithms for Agglomeration of Area Features
Algorithms for Structural Simplification of Area Patches
Algorithms for Typification of Area Features
References

ALGORITHMS FOR DISPLACEMENT OF FEATURES
Displacement of Features: An Overview
Algorithms for Translations of Features
Displacement by Partial Modification of a Curved Line
Algorithms and Models for Relocation of Features
References

ALGORITHMS FOR TRANSFORMATIONS OF THREE-DIMENSIONAL SURFACES AND FEATURES
Algorithms for Transformations of Three-Dimensional Features: An Overview
Algorithms for Transformations of DTM Surfaces
Algorithms for Transformation of 3-D Features
References

EPILOGUE
INDEX

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Author(s)

Biography

Zhilin Li