Mathematical Morphology in Geomorphology and GISci 1st Edition by Behara Seshadri Daya Sagar 1138374598 9781138374591

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ISBN 10: 1138374598

ISBN 13: 9781138374591

Author: Behara Seshadri Daya Sagar

Mathematical Morphology in Geomorphology and GISci presents a multitude of mathematical morphological approaches for processing and analyzing digital images in quantitative geomorphology and geographic information science (GISci). Covering many interdisciplinary applications, the book explains how to use mathematical morphology not only to perform

Mathematical Morphology in Geomorphology and GISci 1st Table of contents:

1 Introduction
Surficial Features
Spatial Data
General Organization of the Book
Pattern Retrieval (Chapter 4)
Pattern Analysis (Chapters 5 through 8)
Modeling (Chapter 9)
Mathematical Morphology in GISci (Chapters 10 through 14)
References

2 Mathematical Morphology: An Introduction
Birth of Mathematical Morphology
Elements of Set Theory and Logical Operations
Grid Utilized for Morphological Transformations
Theory of Structuring Elements
Characteristic Information of Structuring Element
Decomposition of Structuring Element
Property of Iteration
Four Basic Principles of the Theory of Mathematical Morphology
Invariance Under Translation
Erosion and Dilation
Parallel Composition
Serial Composition
Local Knowledge
Binary Mathematical Morphological Operations
Minkowski Operations and Morphological Operations
Dilation
Erosion
Opening and Closing
Multiscale Morphological Operations
Homotopic Operations Based on Basic Binary Morphological Transformations
Morphological Skeleton
Hit or Miss Transformation
Grassfire Transformation
Convex Hull of Sets
Grayscale Morphological Operations
Grayscale Dilation and Erosion
Grayscale Opening and Closing
Multiscale Grayscale Morphological Operations
Threshold Decomposition of a Function
References

3 Simulated, Realistic Digital Elevation Models, Digital Bathymetric Maps, Remotely Sensed Data, and Thematic Maps
Numerical Array as a Spatial Function
Generation of Planar Fractal Basins (Sets)
Fractal Basin Generation
Generation of Fractal Landscapes and Fractal Dems (Functions)
Fractal Landscape from Quadric Fractal Basin
Fractal Landscape from Triadic Fractal Basin
Realistic Dems and Dbms
Synthetic Basins and DBMs
Remotely Sensed Satellite Data
References

4 Feature Extraction
Unique Feature Retrieval via Binary Skeletonization
Some Background Studies of Unique Feature Extraction
What Do Angular Points in DEM Represent?
Valley Connectivity Network Extraction from DEM Using Binary Morphological Operations
Morphological Skeleton of Xt
Ridge and Valley Connectivity Networks via Grayscale Skeletonization
Retrieval of Physiographic Features from Dems via Morphological Segmentation
Mountain Extraction
Conditional Dilation of the Peaks of the DEM
Removal of Small Islands of Mountain Pixels Observed in Flat Areas
Basin Extraction
Conditional Dilation of Pits of the DEM
Removal of Small Islands of Non-Basin Pixels Enclosed within Basin Regions
Removal of Small Islands of Basin Pixels Observed in Non-Basin Areas
Extraction of Piedmont Slopes
Extraction of Morphologically Significant Zones
Decomposition of Morphologically Significant Zones from a Binary Fractal
Binary Convex Hull Construction
Cloud Field Segmentation via Multiscale Convexity Analysis
Generation of Cloud Field at Multiple Coarser Spatial Scales
Construction of Grayscale Convex Hull
Areas of Multiscale Clouds and Their Convex Hulls
Computation of Convexity Measure for Spatial Fields
References

5 Terrestrial Surface Characterization: A Quantitative Perspective
Network Morphometry: A Valuable Tool to Characterize Surficial Phenomena: A Review
Horton-Strahler Order Designation
Order versus Number/Mean Length of Network
Mean Length versus Number
Fractal Relationship of Medial Axis Length to the Water Body Area
Fractal Relation of Perimeter to the Water Body Area
Allometric Scaling Relationships in Hortonian Fractal Digital Elevation Model
Scaling Laws in F-DEM
Allometric Relationships between Travel Time Channel Networks, Convex Hulls, and Convexity Measures
Universal Scaling Laws in Water Bodies and Their Zones of Influence
Zones of Influence (ZI(Xi))
Generation of Zones of Influence of Water Bodies
Allometry-Based Scaling Laws
References

6 Size Distributions, Spatial Heterogeneity, and Scaling Laws
Size Distributions of Water Bodies and Zones of Influence
Estimation of Number-Area-Frequency Dimension of Surface Water Bodies
Self-Similar Size Distributions of Water Bodies by Iterated Bisecting
Is the Spatial Distribution of Smaller Water Bodies More Homogeneous?
Size Distribution–Based Scaling Laws
References

7 Morphological Shape Decomposition: Scale-Invariant but Shape-Dependent Measures
Introduction on MSD and Its Application in Various Fields
Morphological Shape Decomposition
MSD and Various Power-Laws (Scale Invariant but Shape Dependent)
Estimation of Fractal Dimension
Modeling, Description, and Characterization of Fractal Pore
Decomposition of the Pore Space into Pore Bodies and Pore–Body Network
3-D Fractal Binary Pore
MSD on Each Slice
Visualization of PBN in 3-D Space: A Fractal Binary Pore
Pore-Body and Its Fragmentation
Ordering Scheme of Morphological Quantities
Estimation of Order-Wise Pore Bodies in 3-D
Relationships between Pore Morphological Quantities: Results and Discussion
Use of Scale-Invariant but Shape-Dependent Dimensions for Process Characterization
Morphometry of Nonnetwork Space
Why Morphometry of Nonnetwork Space in Place of Morphometry of Networks?
Nonnetwork Space of Basins
Morphometry of Network and Nonnetwork Space of Eight Basins of Gunung Ledang Region
Morphometry of Networks
Morphological Decomposition of Nonnetwork Space
Morphometry of Nonnetwork Spaces
Additional Case on Durian Tunggal Basin
Morphometry of Networks versus Morphometry of Nonnetwork Spaces
References

8 Granulometries, Convexity Measures, and Geodesic Spectrum for DEM Analyses
Grayscale Granulometric Analysis
Granulometries via Multiscale Opening
Granulometries via Multiscale Closing
Morphological Convexity Measures for Terrestrial Basins Derived from Digital Elevation Models
Channel Density, Convexity Measure, and Importance of Elevation Values
Data Used and Their Specifications
Methodology
Derivation of a Channel Network from a Basin Function
Derivation of a Convex Hull of a Basin Function
Area Estimations for Functions and Convexity Measure Computation
Demonstrations and Comparisons
Conclusion
Derivation of Geodesic Flow Fields and Spectrum in Digital Topographic Basin
Decomposition of Basin into TERs
Geodesic Propagation: Methods
Simulations of Geodesic Flow Fields
Geodesic Flow Function Analysis
Properties of Geodesic Flow Fields in Geophysical Basin
Geodesic Flow Spectrum
Results and Discussion on Geodesic Spectrum
Why Geodesic Spectrum?
References

9 Synthetic Examples to Understand Spatiotemporal Dynamics of Certain Geo(morpho)logical Processes
Logistic Map: A Toy Model
Logistic Map as a Viable Model to Simulate Dynamical Behaviors of Certain Geomorphological Processes
First-Order Nonlinear Difference Equation: Logistic Map
Logistic Equation in Modeling the Geomorphological Phenomena (Lakes)
Ranking of Lakes: Logistic Models
Sample Study
Morphological Description: A Scope to Geomorphic Evolution Process Modeling
Introduction of Morphological Behavior
Laws of Structures
Geomorphic Evolution Modeling: A Scope
Evolution of Lake Morphology
Modeling of Morphological Dynamics of a Lake: A Qualitative Study
Discrete Simulations of Spatiotemporal Dynamics of Small Water Bodies Under Varied Stream Flow Discharges
Introduction of Spatiotemporal Dynamics
Expansion–Contraction due to Flood–Drought
Unique Connectivity Networks
Impact of Stream Flow Discharge on Spatial Organization of SWBs: Numeric versus Graphic
Geomorphological Attractors
Numerical Simulations Through First-Order Nonlinear Difference Equation to Study Highly Ductile Symmetric Fold Dynamics: A Conceptual Study
Symmetric Folds with Three (Fold Type I) and Two (Fold Type II) Limbs
Logistic Equations to Study Fold Dynamics
First-Order Difference Equation as a Dynamical Rule
Computation of SSM
Symmetric Fold Dynamics Under the Influence of Constant Stress
Fold Morphological Dynamics Under the Influence of Time-Dependent Stress
Computation of IA(θ) of Corresponding NFD(α) of a Symmetrical Fold Under Dynamics
Relation between α and θ
Iteration by Considering θs at Discrete Time Intervals
Computation of Metric Universality by Considering the AIAs of Symmetric Folds Under Dynamics
Results of Simulations
Fold Dynamical System Under the Influence of Constant Stress
Fold Dynamical System Under the Influence of Time-Dependent Stress
Period Locking
Bifurcation Diagrams
Fold Dynamics Under the Influence of Constant Stress
Dynamical System Under the Influence of TDSD
Results and Discussion
Logistic Equation in Sand Dunes
Morphological Evolution of a Pyramidal Sand Dune through Bifurcation Theory: A Qualitative Model
Definition of a Profile of a Sand Dune
Rule to Perform Numerical Simulation of Dune Morphological Dynamics by Incorporating Normalized Fractal Dimensions
Relationship between Normalized Fractal Dimension and Inter-Slipface Angle
Computation of Inter-Slipface Angle of a Sand Dune Under Dynamics
Attracting Inter-Slipface Angles
Bifurcation Phenomenon
Computation of Metric Universality Considering θ*s
Avalanches in a Numerically Simulated Sand Dune Dynamics
Is There Any Sand Dune That Possesses the Angle of Repose of More than 45°?
Avalanches in a Simulated Sand Dune
Sample Study and Results
Strength of Nonlinearity versus the Avalanche Size Distribution
Classification of Dunes Based on Occurrence of Avalanches
Avalanche Distribution in Different Sizes of Dunes
References

10 Quantitative Spatial Relationships and Spatial Reasoning
Spatial Reasoning and Mathematical Morphology
Background on Strategic Set Identification
Modeling Concepts
Recognition and Visualization of Strategically Significant Spatial Sets via Morphological Analysis
Distance between the Sets
Strategic Sets
Length of Boundary Being Shared between Origin Set and Destination Sets
Dilation Distance between Origin Set and Destination Set(s)
Shape-Size Similarities between Sets
Contextuality between Origin and Destination Sets
Spatial Complexity between Origin Set and Destination Sets
Strategically Significant Set
Experimental Results on Clusters of Sets
Ideal Spatial System
Nonideal Spatial System: Planar Forms of States of India
Discussion and Open Problems
References

11 Derivation of Spatially Significant Zones from a Cluster
Background on Derivation of Spatially Significant Zones from a Cluster
Spatial System and Its Subsystems
Dilation Distances between Origin and Destination Zones
Spatial Significance Index of a Zone
Synthetic Example
Experimental Results
Cluster of Zones of Water Body Influence
States of India
Conclusions
References

12 Directional Spatial Relationship
Background on Directional Spatial Relationship
Directional Spatial Relationship via Origin-Specific Dilation Distances
Methods to Derive the Directional Spatial Relationship
Directional Dilation and Dilation Distance
Dilation Distance
Directional Spatial Relationship
Experimental Results and Discussion
States of India as Planar Sets
Surface Water Bodies
Conclusion
References

13 “Between” Space
Background on “Between” Space
Spatial Analysis and Reasoning via Hausdorff Distance–Based Morphological Closing
Hausdorff Dilation Distance between Disjointed Compact Sets
Methods to Derive the “Between” Space
Sets without Concavities
Sets with Concavities within “Between” Space
Sets with Concavities in All the Sides
Derivation of Contextual Type of “Between” Space between Sets of Category 3
Extension to Grayscale Features
Experimental Results and Discussion
States of India as Planar Sets
Elevation Structures as Grayscale Functions
Potential Applications
Visibility Region (Line of Sight) within “Between” Space
Path between Two Points (Cities) of Nonadjacent Sets (States) via “Between” Space
Shape–Size Similarities between Sets
Degree of Contextuality between Nonadjacent Disjoint Sets
Conclusion
References

14 Spatial Interpolations
Introduction
Generation of Zonal Map from Point Data via Weighted Skeletonization by Influence Zone
Conversion of Point-Specific Values into Zonal Map via WSKIZ
Location-Specific Data over Geographic Space
Model to Generate Zonal Map from Point Data
Computation of Point-Dependent Recursive Geodesic Dilations
Model Demonstration
Experimental Results
Conclusion on Conversion of Point Data into Zonal Map
Visualization of Spatiotemporal Behavior of Discrete Maps via Generation of Recursive Median Elements
Hausdorff Erosion Distance and Hausdorff Dilation Distance
Computation of the Median Set
Layered Information as Sets: Spatial Interpolation
Limited Layered Sets
Spatial Relationships between Sets and Their Categorization
Description of Categories via Logical Relations
Description of Categories Using Hausdorff Distances
Morphologic Interpolation via Median Element Computation
Sequence of Interpolated Sets
Experimental Results
Case Study on Small Water Bodies
Case Study on Spatial Maps of Epidemic
Validation of the Middle Elements as Interpolators
Potential Applications: A Brief Discussion
Conclusions
References

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