Algorithmic Foundation of Multi-scale Spatial Representation,9780849390722

Algorithmic Foundation of Multi-scale Spatial Representation

by ;
ISBN13: 9780849390722
ISBN10: 0849390729
Format: Hardcover
Pub. Date: 2006-10-04
Publisher(s): CRC Press
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Summary

With the widespread use of GIS, multi-scale representation has become an important issue in the realm of spatial data handling. Focusing on geometric transformations, this resource presents comprehensive coverage of the low-level algorithms available for the multi-scale representations of different types of spatial features, including point clusters, individual lines, a class of lines, individual areas, and a class of areas. It also discusses algorithms for multi-scale representation of 3-D surfaces and 3-D features. Containing over 250 illustrations to supplement the discussion, the book provides the most recent research results, such as raster-based work, algorithm improvements, snakes, wavelets, and empirical mode decomposition.

Table of Contents

Chapter 1 Introduction 1(28)
1.1 Spatial Representation: Representation of Spatial Data
1(6)
1.1.1 Forms of Spatial Representation
1(3)
1.1.2 Dynamics of Spatial Representation
4(3)
1.2 Multi-Scale Spatial Representation
7(3)
1.2.1 Spatial Representation as a Record in the Scale–Time System
7(1)
1.2.2 Transformations of Spatial Representations in Time: Updating
7(1)
1.2.3 Transformations of Spatial Representations in Scale: Generalization
8(2)
1.3 Transformations in Multi-Scale Spatial Representation
10(7)
1.3.1 Geometric Transformations
10(2)
1.3.2 Relational Transformations
12(5)
1.3.3 Thematic Transformations
17(1)
1.4 Operations for Geometric Transformations in Multi-Scale Spatial Representation
17(7)
1.4.1 A Strategy for Classification of Operations for Geometric Transformations
17(1)
1.4.2 Operations for Transformations of Point Features
18(1)
1.4.3 Operations for Transformations of Line Features
19(2)
1.4.4 Operations for Transformations of Area Features
21(2)
1.4.5 Operations for Transformations of 3-D Surfaces and Features
23(1)
1.5 Scope of This Book
24(1)
References
25(4)
Chapter 2 Mathematical Background 29(28)
2.1 Geometric Elements and Parameters for Spatial Representation
29(9)
2.1.1 Coordinate Systems
29(1)
2.1.2 Representation of Geometric Elements in Vector and Raster Spaces
30(1)
2.1.3 Some Commonly Used Geometric Parameters
31(3)
2.1.4 Dimensionality of Spatial Features
34(4)
2.2 Mathematical Morphology
38(7)
2.2.1 Basic Morphological Operators
38(3)
2.2.2 Advanced Morphological Operators
41(4)
2.3 Delaunay Triangulation and the Voronoi Diagram
45(5)
2.3.1 Delaunay Triangulation
45(1)
2.3.2 Constrained Delaunay Triangulation
46(2)
2.3.3 Voronoi Diagram
48(2)
2.4 Skeletonization and Medial Axis Transformation
50(3)
2.4.1 Skeletonization by Means of MAT and Distance Transform
50(1)
2.4.2 Skeletonization by Means of Voronoi Diagram and Triangulation
51(1)
2.4.3 Skeletonization by Means of Thinning
52(1)
References
53(4)
Chapter 3 Theoretical Background 57(18)
3.1 Scale in Geographical Space
57(5)
3.1.1 Geo-Scale in the Scale Spectrum
57(1)
3.1.2 Measures (Indicators) of Scale
58(1)
3.1.3 Transformations of Spatial Representation in Scale in Geographical Space
59(3)
3.2 Relativity in Scale: The Natural Principle
62(4)
3.2.1 The Idea of a Natural Principle
62(2)
3.2.2 Estimation of Parameters for the Natural Principle
64(2)
3.3 The Radical Laws: Principles of Selection
66(3)
3.3.1 Number of Symbols at Different Scales: A Theoretical Analysis
66(1)
3.3.2 Principle of Selection: Empirical Formula or Radical Law
67(1)
3.3.3 Fractal Extension of the Principle of Selection
68(1)
3.4 Strategies for Transformations of Spatial Representations in Scale
69(3)
3.4.1 Separation of Scale-Driven from Graphics-Driven Transformations
69(1)
3.4.2 Separation of Geometric Transformation from High-Level Constraints
70(1)
3.4.3 Distinguishing Three Levels of Transformations for Spatial Representation
71(1)
3.4.4 Integration of Raster-Based Manipulation into Vector-Based Data Structure
72(1)
References
72(3)
Chapter 4 Algorithms for Transformations of Point Features 75(16)
4.1 Algorithms for Point Features: An Overview
75(1)
4.2 Algorithms for Aggregation of a Set of Point Features
76(5)
4.2.1 K-Means Clustering Algorithm
76(2)
4.2.2 Iterative Self-Organizing Data Analysis Technique Algorithm (ISODATA)
78(2)
4.2.3 Determination of a Representative Point for a Cluster of Point Features
80(1)
4.3 Algorithms for Selective Omission of a Set of Point Features
81(3)
4.3.1 Settlement-Spacing Ratio Algorithm
82(1)
4.3.2 Circle-Growth Algorithm
83(1)
4.4 Algorithms for Structural Simplification of a Set of Point Features
84(3)
4.4.1 Structural Simplification Based on Metric Information
84(2)
4.4.2 Structural Simplification Concerning Metric and Thematic Information
86(1)
4.5 Algorithms for Outlining a Set of Point Features: Regionization
87(1)
References
88(3)
Chapter 5 Algorithms for Point-Reduction of Individual Line Features 91(26)
5.1 Algorithms for Line Point-Reduction: An Overview
91(3)
5.2 Sequential Algorithms with Geometric Parameters as Criteria
94(4)
5.2.1 Algorithm Based on Number of Points
94(1)
5.2.2 Algorithm Based on Length
95(2)
5.2.3 Algorithm Based on Angle
97(1)
5.2.4 Algorithm Based on Perpendicular Distance
97(1)
5.3 Iterative Algorithms with Geometric Parameters as Criteria
98(6)
5.3.1 Algorithm Based on Minima and Maxima
99(1)
5.3.2 Progressive Splitting Based on Perpendicular Distance
100(1)
5.3.3 Split-and-Merge Based on Perpendicular Distance
101(1)
5.3.4 Algorithm Based on Area
102(2)
5.4 Algorithms with Functions of Geometric Parameters as Criteria
104(4)
5.4.1 Algorithm Based on Cosine Value
105(1)
5.4.2 Algorithm Based on Distance/Chord Ratio
106(1)
5.4.3 Algorithm Based on Local Length Ratio
107(1)
5.5 Evaluation of Point-Reduction Algorithms
108(3)
5.5.1 Measures for Evaluation of Point-Reduction Algorithms
109(1)
5.5.2 Performance of Point-Reduction Algorithms
110(1)
5.6 Attempts to Improve Point-Reduction Algorithms
111(2)
5.6.1 Attempts to Avoid Topological Conflicts
112(1)
5.6.2 Attempts to Make Algorithms Robust
112(1)
5.6.3 Attempts to Make Algorithms Self-Adaptive
113(1)
5.6.4 Attempts to Make Algorithms More Efficient
113(1)
References
113(4)
Chapter 6 Algorithms for Smoothing of Individual Line Features 117(24)
6.1 Smoothing of a Line: An Overview
117(1)
6.2 Smoothing by Moving Averaging in the Space Domain
117(3)
6.2.1 Smoothing by Simple Moving Averaging
117(2)
6.2.2 Smoothing by Weighted Moving Averaging
119(1)
6.3 Smoothing by Curve Fitting in the Space Domain
120(7)
6.3.1 Smoothing by Best Fitting: Least-Squares
120(2)
6.3.2 Smoothing by Exact Fitting: Cubic Spline
122(1)
6.3.3 Smoothing by Energy Minimization: Snakes
123(4)
6.4 Smoothing by Frequency Cutting in the Frequency Domain
127(5)
6.4.1 Smoothing by Fourier Transforms
127(1)
6.4.2 Smoothing by Wavelet Transforms
128(4)
6.5 Smoothing by Component Exclusion in the Space Domain
132(5)
6.5.1 Smoothing by EMD
132(4)
6.5.2 A Comparison between EMD and Frequency-Based Transforms
136(1)
6.6 Evaluation of Line Smoothing Algorithms
137(1)
References
138(3)
Chapter 7 Algorithms for Scale-Driven Generalization of Individual Line Features 141(20)
7.1 Scale-Driven Generalization: An Overview
141(1)
7.2 Algorithms Based on Gaussian Spatial-Scale
142(4)
7.2.1 Gaussian Line Smoothing in Scale-Space
143(2)
7.2.2 Attempts to Improve Gaussian Smoothing
145(1)
7.3 Algorithms Based on s-Circle Rolling
146(3)
7.3.1 Perkal Algorithm Based on s-Circle Rolling
146(1)
7.3.2 The WHIRLPOOL Approximation of the Perkal Algorithm
147(1)
7.3.3 Waterlining and Medial Axis Transformation for Perkal's Boundary Zone
148(1)
7.4 Algorithms Based on the Natural Principle
149(6)
7.4.1 The Basic Idea of Li–Openshaw Algorithm
149(1)
7.4.2 The Li–Openshaw Algorithm in Raster Mode
150(2)
7.4.3 The Li–Openshaw Algorithm in Raster–Vector Mode
152(2)
7.4.4 Special Treatments in the Li–Openshaw Algorithm
154(1)
7.4.5 The Li–Openshaw Algorithm for Nonnatural Lines: Some Remarks
154(1)
7.5 Evaluation of Scale-Driven Line Generalization Algorithms
155(3)
7.5.1 Benchmarks for Evaluating Scale-Driven Line Generalization
156(1)
7.5.2 Performance of Scale-Driven Line Generalization Algorithms
156(2)
References
158(3)
Chapter 8 Algorithms for Transformations of a Set of Line Features 161(22)
8.1 A Set of Line Features: An Overview
161(1)
8.2 Algorithms for Transformation of a Set of Contour Lines
162(8)
8.2.1 Approaches to the Transformation of Contour Lines
162(1)
8.2.2 Selection of a Subset from the Original Set of Contour Lines: Selective Omission
163(2)
8.2.3 Objective Generalization of a Set of Contour Lines as a Whole
165(3)
8.2.4 Transformation of a Set of Contour Lines via the Removal of Small Catchments
168(2)
8.3 Algorithms for Transformation of River Networks
170(3)
8.3.1 Overview
170(1)
8.3.2 Ordering Schemes for Selective Omission of Rivers
170(2)
8.3.3 Four Strategies for Selective Omission of Ordered River Features
172(1)
8.3.4 Other Transformations for Selected River Features
173(1)
8.4 Algorithms for Transformation of Transportation Networks
173(7)
8.4.1 An Overview
173(2)
8.4.2 The Stroke Scheme for Selective Omission of Roads
175(3)
8.4.3 Road Junction Collapse: Ring-to-Point Collapse
178(1)
8.4.4 Other Transformations for Selected Transportation Lines
179(1)
References
180(3)
Chapter 9 Algorithms for Transformations of Individual Area Features 183(30)
9.1 Transformation of Individual Area Features: An Overview
183(1)
9.2 Algorithms for Boundary-Based Shape Simplification of an Area Feature
184(5)
9.2.1 Boundary-Based Area Shape Simplification: Natural versus Extremal
184(2)
9.2.2 Natural Simplification of the Boundary of an Area Feature as a Closed Curve
186(1)
9.2.3 Formation of the Convex Hull of an Area Feature
186(2)
9.2.4 Formation of the MBR of an Area Feature
188(1)
9.3 Algorithms for Region-Based Shape Simplification of an Area Feature
189(5)
9.3.1 Shape Simplification by Morphological Closing and Opening
190(1)
9.3.2 Formation of Convex Hull and Bounding Box by Morphological Thickening
191(1)
9.3.3 Shape Refinement by Morphological Operators
192(2)
9.4 Algorithms for Collapse of Area Features
194(7)
9.4.1 Area-to-Point Collapse
194(3)
9.4.2 Area-to-Line Collapse
197(2)
9.4.3 Partial Collapse
199(2)
9.5 Algorithms for Area Elimination
201(6)
9.5.1 Elimination via Sequential Eroding Using Monmonier Operators
201(1)
9.5.2 Elimination via Erosion Followed by Restoration
202(2)
9.5.3 Elimination by Mode Filter
204(1)
9.5.4 Elimination via a Change in Pixel Size
205(1)
9.5.5 Coarsening as Elimination of an Area Feature
206(1)
9.6 Algorithms for Splitting an Area Feature
207(1)
9.6.1 Splitting via Systematic Elimination and Eroding
207(1)
9.6.2 Splitting via Morphological Opening
208(1)
9.7 Algorithms for Exaggeration
208(3)
9.7.1 Whole Exaggeration by Enlargement: Buffering and Expansion
208(1)
9.7.2 Partial Exaggeration: Directional Thickening
209(2)
References
211(2)
Chapter 10 Algorithms for Transformations of a Set of Area Features 213(26)
10.1 Transformation of A Class of Area Features: An Overview
213(2)
10.2 Algorithms for Simplification of the Shape of a Polygonal Network
215(3)
10.2.1 Decomposition-Based Simplification of a Polygonal Network
215(2)
10.2.2 Whole-Based Simplification of a Polygonal Network
217(1)
10.3 Algorithms for Combining Area Features: Aggregation and Amalgamation
218(10)
10.3.1 Boundary-Based Combination via Equal-Spanning Polygons
219(1)
10.3.2 Boundary-Based Combination via Convex Hulls
219(4)
10.3.3 Boundary-Based Combination via Constrained Hulls
223(1)
10.3.4 Region-Based Combination via Gap Bridging
224(1)
10.3.5 Region-Based Morphological Combination
225(3)
10.4 Algorithms for Merging and Dissolving Area Features
228(2)
10.4.1 Merge via a Union Operation
228(1)
10.4.2 Dissolve via Split and Merge
229(1)
10.5 Algorithms for Agglomeration of Area Features
230(1)
10.6 Algorithms for Structural Simplification of Area Patches
231(3)
10.6.1 Vector-Based Structural Simplification
231(2)
10.6.2 Raster-Based Structural Simplification
233(1)
10.7 Algorithms for Typification of Area Features
234(3)
10.7.1 Typification of Aligned Area Features
234(2)
10.7.2 Typification of Irregularly Distributed Area Features
236(1)
References
237(2)
Chapter 11 Algorithms for Displacement of Features 239(16)
11.1 Displacement of Features: An Overview
239(2)
11.2 Algorithms for Translations of Features
241(2)
11.2.1 Uniform Translation in a Single Direction in Raster Mode
241(2)
11.2.2 Translation in Normal Directions in Vector Mode
243(1)
11.3 Displacement by Partial Modification of a Curved Line
243(6)
11.3.1 Partial Modification with a Vector Backbone
243(1)
11.3.2 Partial Modification with Morphological Algorithms
243(3)
11.3.3 Partial Modification Based on Snakes Techniques
246(3)
11.4 Algorithms and Models for Relocation of Features
249(4)
11.4.1 Relocation of Features with Displacement Fields
249(2)
11.4.2 Relocation of Features with Finite Elements
251(1)
11.4.3 Relocation of Features with Least-Squares Adjustment
252(1)
11.4.4 Relocation of Features with a Ductile Truss and Finite Elements
253(1)
References
253(2)
Chapter 12 Algorithms for Transformations of Three-Dimensional Surfaces and Features 255(16)
12.1 Algorithms for Transformations of Three-Dimensional Features: An Overview
255(1)
12.2 Algorithms for Transformations of DTM Surfaces
255(11)
12.2.1 Multi-Scale Transformation of DTM Surfaces: An Overview
255(3)
12.2.2 Metric Multi-Scale Representation through Filtering and Resampling
258(2)
12.2.3 Metric Multi-Scale Representation Based on the Natural Principle
260(2)
12.2.4 Visual Multi-Scale Representation through View-Dependent LoD
262(4)
12.3 Algorithms for Transformation of 3-D Features
266(3)
12.3.1 Transformation of Individual Buildings
266(2)
12.3.2 Transformation of a Set of Buildings
268(1)
References
269(2)
Epilogue 271(2)
Index 273

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