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E-book: Computing in Geographic Information Systems

(Center for Artificial Intelligence and Robotics (CAIR), Bangalore, India)
  • Format: 303 pages
  • Pub. Date: 10-Jul-2014
  • Publisher: CRC Press Inc
  • Language: eng
  • ISBN-13: 9781482223163
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Computing in Geographic Information SystemsLarger Image
  • Format: 303 pages
  • Pub. Date: 10-Jul-2014
  • Publisher: CRC Press Inc
  • Language: eng
  • ISBN-13: 9781482223163
Other books in subject:

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Capable of acquiring large volumes of data through sensors deployed in air, land, and sea, and making this information readily available in a continuous time frame, the science of geographical information system (GIS) is rapidly evolving. This popular information system is emerging as a platform for scientific visualization, simulation, and computation of spatio-temporal data. New computing techniques are being researched and implemented to match the increasing capability of modern-day computing platforms and easy availability of spatio-temporal data. This has led to the need for the design, analysis, development, and optimization of new algorithms for extracting spatio-temporal patterns from a large volume of spatial data.Computing in Geographic Information Systems considers the computational aspects, and helps students understand the mathematical principles of GIS. It provides a deeper understanding of the algorithms and mathematical methods inherent in the process of designing and developing GIS functions. It examines the associated scientific computations along with the applications of computational geometry, differential geometry, and affine geometry in processing spatial data. It also covers the mathematical aspects of geodesy, cartography, map projection, spatial interpolation, spatial statistics, and coordinate transformation. The book discusses the principles of bathymetry and generation of electronic navigation charts.The book consists of 12 chapters. Chapters one through four delve into the modeling and preprocessing of spatial data and prepares the spatial data as input to the GIS system. Chapters five through eight describe the various techniques of computing the spatial data using different geometric and statically techniques. Chapters nine through eleven define the technique for image registration computation and measurements of spatial objects and phenomenon.Examines cartographic modeling and map projectionCovers the mathematical aspects of different map projectionsExplores some of the spatial analysis techniques and applications of GISIntroduces the bathymetric principles and systems generated using bathymetric chartsExplains concepts of differential geometry, affine geometry, and computational geometry Discusses popular analysis and measurement methods used in GISThis text outlines the key concepts encompassing GIS and spatio-temporal information, and is intended for students, researchers, and professionals engaged in analysis, visualization, and estimation of spatio-temporal events.

Reviews

"This book addresses mathematics and computational methods that are not usually covered by common GIS books. Unlike other books that only teach people how to apply GIS and use GIS software, this book describes the underlying principles and mathematical equations. Engineers who develop innovative tools for GIS users would find this book useful." --Shipeng Sun, University of Minnesota, Minneapolis, USA "There are only few books that deal with mathematical aspects of GIS. This book will help to fill this gap. The most valuable contribution of this book is the fact that it effectively pervades mathematical equations and formulas to discuss geospatial concepts and principles. GIS topics are amply covered, and are approached in a way that will help students of GIS to gain greater knowledge of the computational aspects of spatial data collection, transformation, manipulation, analysis and application." --Shrinidhi Ambinakudige, Mississippi State University

List of Figures xv
List of Tables xix
Introduction xxi
Preface xxiii
Acknowledgments xxv
Author Bio xxvii
1 Introduction 1(18)
1.1 Definitions and Different Perspectives of GIS
2(11)
1.1.1 Input Domain of GIS
2(1)
1.1.2 Functional Profiling of GIS
3(4)
1.1.3 Output Profiling of GIS
7(1)
1.1.4 Information Architecture of GIS
7(4)
1.1.4.1 Different Architectural Views of GIS
8(3)
1.1.5 GIS as a Platform for Multi-Sensor Data Fusion
11(1)
1.1.6 GIS as a Platform for Scientific Visualization
12(1)
1.2 Computational Aspects of GIS
13(1)
1.3 Computing Algorithms in GIS
14(1)
1.4 Purpose of the Book
14(3)
1.5 Organization of the Book
17(1)
1.6 Summary
18(1)
2 Computational Geodesy 19(16)
2.1 Definition of Geodesy
19(1)
2.2 Mathematical Models of Earth
20(2)
2.2.1 Physical Surface of Earth
21(1)
2.2.2 The Reference Geoid
21(1)
2.2.3 The Reference Ellipsoid
22(1)
2.3 Geometry of Ellipse and Ellipsoid
22(3)
2.3.1 Relation between 'e' and 'f'
25(1)
2.4 Computing Radius of Curvature
25(3)
2.4.1 Radius of Curvature at Prime Vertical Section
27(1)
2.5 Concept of Latitude
28(5)
2.5.1 Modified Definition of Latitude
28(1)
2.5.2 Geodetic Latitude
28(1)
2.5.3 Geocentric Latitude
29(1)
2.5.4 Spherical Latitude
29(1)
2.5.5 Reduced Latitude
29(1)
2.5.6 Rectifying Latitude
30(1)
2.5.7 Authalic Latitude
31(1)
2.5.8 Conformal Latitude
31(1)
2.5.9 Isometric Latitude
32(1)
2.5.10 Astronomical Latitude
32(1)
2.6 Applications of Geodesy
33(1)
2.7 The Indian Geodetic Reference System (IGRS)
33(1)
2.8 Summary
34(1)
3 Reference Systems and Coordinate Transformations 35(26)
3.1 Definition of Reference System
35(1)
3.2 Classification of Reference Systems
36(1)
3.3 Datum and Coordinate System
37(1)
3.4 Attachment of Datum to the Real World
37(1)
3.5 Different Coordinate Systems Used in GIS
38(12)
3.5.1 The Rectangular Coordinate System
39(1)
3.5.2 The Spherical Coordinate System
39(1)
3.5.3 The Cylindrical Coordinate System
40(2)
3.5.4 The Polar and Log-Polar Coordinate System
42(1)
3.5.5 Earth-Centered Earth-Fixed (ECEF) Coordinate System
43(2)
3.5.6 Inertial Terrestrial Reference Frame (ITRF)
45(1)
3.5.7 Celestial Coordinate System
46(2)
3.5.8 Concept of GRID, UTM, Mercator's GRID and Military GRID
48(2)
3.6 Shape of Earth
50(2)
3.6.1 Latitude and Longitude
50(1)
3.6.2 Latitude
51(1)
3.6.3 Longitude
51(1)
3.7 Coordinate Transformations
52(3)
3.7.1 2D Coordinate Transformations
53(1)
3.7.2 3D Coordinate Transformations
54(1)
3.8 Datum Transformation
55(3)
3.8.1 Helmert Transformation
57(1)
3.8.2 Molodenskey Transformation
58(1)
3.9 Usage of Coordinate Systems
58(1)
3.10 Summary
59(2)
4 Basics of Map Projection 61(26)
4.1 What Is Map Projection? Why Is It Necessary?
61(1)
4.2 Mathematical Definition of Map Projection
62(1)
4.3 Process Flow of Map Projection
63(1)
4.4 Azimuthal Map Projection
64(4)
4.4.1 Special Cases of Azimuthal Projection
66(1)
4.4.2 Inverse Azimuthal Projection
67(1)
4.5 Cylindrical Map Projection
68(3)
4.5.1 Special Cases of Cylindrical Projection
69(1)
4.5.1.1 Gnomonic Projection
70(1)
4.5.1.2 Stereographic Projection
70(1)
4.5.1.3 Orthographic Projection
70(1)
4.5.2 Inverse Transformation
70(1)
4.6 Conical Map Projection
71(3)
4.7 Classification of Map Projections
74(6)
4.7.1 Classification Based on the Cartographic Quantity Preserved
75(1)
4.7.2 Classification Based on the Position of the Viewer
76(1)
4.7.3 Classification Based on Method of Construction
77(1)
4.7.4 Classification Based on Developable Map Surface
78(1)
4.7.5 Classification Based on the Point of Contact
79(1)
4.8 Application of Map Projections
80(3)
4.8.1 Cylindrical Projections
80(2)
4.8.1.1 Universal Transverse Mercator (UTM)
80(1)
4.8.1.2 Transverse Mercator projection
81(1)
4.8.1.3 Equidistant Cylindrical Projection
81(1)
4.8.1.4 Pseudo-Cylindrical Projection
81(1)
4.8.2 Conic Map Projection
82(1)
4.8.2.1 Lambert's Conformal Conic
82(1)
4.8.2.2 Simple Conic Projection
82(1)
4.8.2.3 Albers Equal Area Projection
82(1)
4.8.2.4 Polyconic Projection
82(1)
4.8.3 Azimuthal Projections
83(1)
4.9 Summary
83(4)
5 Algorithms for Rectification of Geometric Distortions 87(20)
5.1 Sources of Geometric Distortion
88(3)
5.1.1 Definition and Terminologies
89(1)
5.1.2 Steps in Image Registration
89(2)
5.2 Algorithms for Satellite Image Registration
91(2)
5.2.1 Polynomial Affine Transformation (PAT)
91(1)
5.2.2 Similarity Transformation
92(1)
5.3 Scale Invariant Feature Transform (SIFT)
93(7)
5.3.1 Detection of Scale-Space Extrema
94(1)
5.3.2 Local Extrema Detection
94(1)
5.3.3 Accurate Key Point Localization
95(3)
5.3.4 Eliminating Edge Responses
98(2)
5.4 Fourier Mellin Transform
100(2)
5.4.1 The Log-Polar Transformation Algorithm
101(1)
5.5 Multiresolution Image Analysis
102(1)
5.6 Applications of Image Registration
103(2)
5.7 Summary
105(2)
6 Differential Geometric Principles and Operators 107(12)
6.1 Gradient (First Derivative)
107(1)
6.2 Concept of Curvature
108(2)
6.3 Hessian: The Second Order Derivative
110(1)
6.4 Gaussian Curvature
111(1)
6.5 Mean Curvature
112(2)
6.6 The Laplacian
114(1)
6.7 Properties of Gaussian, Hessian and Difference of Gaussian
114(3)
6.7.1 Gaussian Function
115(1)
6.7.2 Hessian Function
115(1)
6.7.3 Difference of Gaussian
116(1)
6.8 Summary
117(2)
7 Computational Geometry and Its Application to GIS 119(36)
7.1 Introduction
119(1)
7.2 Definitions
120(2)
7.2.1 Triangulation and Partitioning
120(1)
7.2.2 Convex Hull
121(1)
7.2.3 Voronoi Diagram and Delaunay Triangulation
121(1)
7.3 Geometric Computational Techniques
122(1)
7.4 Triangulation of Simple Polygons
123(10)
7.4.1 Theory of Polygon Triangulation
124(2)
7.4.2 Dual Tree
126(1)
7.4.3 Polygon Triangulation
127(2)
7.4.3.1 Order Type
127(2)
7.4.4 Line Segment Intersection
129(2)
7.4.5 Finding Diagonals in a Polygon
131(1)
7.4.6 Naive Triangulation Algorithm
132(1)
7.5 Convex Hulls in Two Dimensions
133(2)
7.5.1 Graham's Scan:
133(2)
7.5.1.1 Steps of Graham's Scan
134(1)
7.6 Divide and Conquer Algorithm
135(4)
7.6.1 Divide and Conquer Convex Hull
136(1)
7.6.1.1 Lower Tangent
136(1)
7.6.2 Quick Hull
137(2)
7.7 Voronoi Diagrams
139(2)
7.7.1 Properties of Voronoi Diagrams
140(1)
7.8 Delaunay Triangulation
141(2)
7.8.1 Properties of Delaunay Triangulation
141(2)
7.9 Delaunay Triangulation: Randomized Incremental Algorithm
143(4)
7.9.1 Incremental Update
143(4)
7.10 Delaunay Triangulations and Convex Hulls
147(4)
7.11 Applications of Voronoi Diagram and Delaunay Triangulation
151(1)
7.11.1 Applications of Voronoi Diagrams
152(1)
7.12 Summary
152(3)
8 Spatial Interpolation Techniques 155(14)
8.1 Non-Geostatistical Interpolators
156(5)
8.1.1 Nearest Neighbours
156(1)
8.1.2 Triangular Irregular Network
156(1)
8.1.3 Natural Neighbours
156(2)
8.1.4 Inverse Distance Weighting
158(1)
8.1.5 Regression Models
159(1)
8.1.6 Trend Surface Analysis
159(1)
8.1.7 Splines and Local Trend Surfaces
159(1)
8.1.8 Thin Plate Splines
159(1)
8.1.9 Classification Methods
160(1)
8.1.10 Regression Tree
160(1)
8.1.11 Fourier series
160(1)
8.1.12 Lapse Rate
161(1)
8.2 Geostatistics
161(6)
8.2.1 Introduction of Geostatistics
161(1)
8.2.2 Semivariance and Variogram
162(1)
8.2.3 Kriging Estimator
163(1)
8.2.4 Simple Kriging
164(1)
8.2.5 Ordinary Kriging
165(1)
8.2.6 Kriging with a Trend
165(1)
8.2.7 Block Kriging
165(1)
8.2.8 Factorial Kriging
165(1)
8.2.9 Dual Kriging
166(1)
8.2.10 Simple Kriging with Varying Local Means
166(1)
8.2.11 Kriging with an External Drift
166(1)
8.2.12 Cokriging
166(1)
8.3 Summary
167(2)
9 Spatial Statistical Methods 169(16)
9.1 Definition of Statistics
169(1)
9.2 Spatial Statistics
170(1)
9.3 Classification of Statistical Methods
171(2)
9.3.1 Descriptive Statistics
171(2)
9.4 Role of Statistics in GIS
173(1)
9.5 Descriptive Statistical Methods
174(4)
9.5.1 Mean
174(1)
9.5.2 Median
175(1)
9.5.3 Mode
175(1)
9.5.4 Variance
175(1)
9.5.5 Standard Deviation
175(1)
9.5.5.1 Best Estimation of Standard Deviation
176(1)
9.5.5.2 Mean Deviation
176(1)
9.5.6 Standard Error
176(1)
9.5.7 Range
176(1)
9.5.8 Skewness
177(1)
9.5.9 Kurtosis
177(1)
9.6 Inferential Statistics
178(4)
9.6.1 Correlation Coefficient (R)
178(1)
9.6.2 Moran's Index, or Moran's I
179(1)
9.6.3 Geary's C
180(1)
9.6.4 General G Statistic
181(1)
9.7 Point Pattern Analysis in GIS
182(1)
9.8 Applications of Spatial Statistical Methods
183(1)
9.9 Summary
183(2)
10 An Introduction to Bathymetry 185(16)
10.1 Introduction and Definition
185(1)
10.2 Bathymetric Techniques
185(2)
10.3 Difference between Bathymetry and Topography
187(1)
10.4 Bathymetric Data Survey and Modeling
188(2)
10.4.1 Bathymetric Data Models
188(2)
10.4.1.1 S-57
189(1)
10.4.1.2 S-52
189(1)
10.4.1.3 S-63
190(1)
10.4.1.4 S-100
190(1)
10.5 Representation of Sea Depth and Sounding
190(4)
10.5.1 Nautical Chart
191(1)
10.5.2 Details on Nautical Chart
191(3)
10.6 Map Projection, Datum and Coordinate Systems Used in Bathymetry
194(1)
10.7 Application of Bathymetry Used in Preparation of bENCs
194(1)
10.8 Differences between ENC, SENC, and RENC
195(1)
10.8.1 ENC - Electronic Navigational Chart
196(1)
10.8.2 SENC - System Electronic Navigational Chart
196(1)
10.8.3 RENC - Regional ENC Coordinating Center
196(1)
10.9 Differences between a Map and a Chart
196(3)
10.10 Summary
199(2)
11 Spatial Analysis of Bathymetric Data and Sea GIS 201(8)
11.1 Difference between a Nautical Chart and an Electronic Chart
202(1)
11.1.1 Sailing Charts
202(1)
11.1.2 General Charts
203(1)
11.1.3 Coastal Charts
203(1)
11.1.4 Harbour Charts
203(1)
11.2 Projection Used in ENC
203(2)
11.2.1 Some Characteristics of a Mercator Projection
203(1)
11.2.2 Scale of ENC
204(1)
11.3 Elements in a Bathymetric Chart
205(2)
11.4 Summary
207(2)
12 Measurements and Analysis Using GIS 209(24)
12.1 Location
209(2)
12.2 Distance Measure
211(3)
12.2.1 Linear Distance
211(1)
12.2.2 Geodetic Distance
211(1)
12.2.3 Manhattan Distance
212(1)
12.2.4 Haversine Formula
212(2)
12.2.4.1 Haversine Formula for Calculating Distance
213(1)
12.2.5 Vincenty's Formula
214(1)
12.3 Shortest Distance
214(5)
12.3.1 Dijkstra's Algorithm
215(2)
12.3.1.1 Intuition behind Dijkstra's Algorithm
215(1)
12.3.1.2 Idea of Dijkstra's Algorithm
215(1)
12.3.1.3 Pseudo Code for Dijkstra's Algorithm
216(1)
12.3.1.4 Analysis of the Time Complexity
217(1)
12.3.2 Direction
217(2)
12.3.2.1 Azimuth
217(1)
12.3.2.2 Bearings
218(1)
12.3.2.3 North, Magnetic North and Grid North
218(1)
12.4 Area
219(2)
12.4.1 Planimetric Area
220(1)
12.5 Computation of Volume
221(1)
12.6 Computation of Slope and Aspect
222(2)
12.7 Curvature
224(1)
12.8 Hill Shade Analysis
224(1)
12.9 Visibility Analysis
224(4)
12.9.1 Line of Sight Analysis
224(4)
12.10 Flood Inundation Analysis
228(2)
12.11 Overlay Analysis
230(1)
12.11.1 Discrete Time Overlay Analysis
230(1)
12.11.2 Continuous Time Overlay Analysis
231(1)
12.12 Summary
231(2)
13 Appendix A 233(8)
13.1 Reference Ellipsoids
233(1)
13.2 Geodetic Datum Transformation Parameters (Local to WGS-84)
234(1)
13.3 Additional Figures, Charts and Maps
235(4)
13.4 Line of Sight
239(2)
14 Appendix B 241(6)
14.1 Definitions
241(6)
14.1.1 Earth Sciences
241(1)
14.1.2 Geddesy
241(1)
14.1.3 Geography
241(1)
14.1.4 Bathymetry
241(1)
14.1.5 Hypsometry
242(1)
14.1.6 Hydrography
242(1)
14.1.7 Terrain
242(1)
14.1.8 Contour, Isoline, Isopleths
242(1)
14.1.9 LIDAR
243(1)
14.1.10 RADAR
243(1)
14.1.11 Remote Sensing
243(1)
14.1.12 Global Positioning System
243(1)
14.1.13 Principal Component Analysis
244(1)
14.1.14 Affine Transformation
244(1)
14.1.15 Image Registration
244(1)
14.1.16 Photogrammetry
245(1)
14.1.17 Universal Transverse Mercator (UTM)
245(2)
15 Glossary of GIS Terms 247(8)
Bibliography 255(4)
Index 259
Dr. Narayan Panigrahi is a practicing geo-spatial scientist in the Centre for Artificial Intelligence and Robotics (CAIR), Bangalore, India. He obtained his master's degree from the J.K. Institute of Applied Physics and Technology, University of Allahabad, his M Tech from the Indian Institute of Technology (IIT), Kharagpur, and his PhD from IIT, Bombay, India. His current research interests include geographical information science, design and optimization of algorithms for computation of spatial data in vector and raster form obtained through different sensors, and application of GIS for resource mapping and operation planning.
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