Mathematical Morphology in Geomorphology and GISci
Mathematical Morphology in Geomorphology and GISci
Opis: Mathematical Morphology in Geomorphology and GISci - 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 quantitative morphologic and scaling analyses of terrestrial phenomena and processes, but also to deal with challenges encountered in quantitative spatial reasoning studies. For understanding the spatiotemporal characteristics of terrestrial phenomena and processes, the author provides morphological approaches and algorithms to: Retrieve unique geomorphologic networks and certain terrestrial features Analyze various geomorphological phenomena and processes via a host of scaling laws and the scale-invariant but shape-dependent indices Simulate the fractal-skeletal-based channel network model and the behavioral phases of geomorphologic systems based on the interplay between numeric and graphic analyses Detect strategically significant sets and directional relationships via quantitative spatial reasoning Visualize spatiotemporal behavior and generate contiguous maps via spatial interpolation Incorporating peer-reviewed content, this book offers simple explanations that enable readers-even those with no background in mathematical morphology-to understand the material. It also includes easy-to-follow equations and many helpful illustrations that encourage readers to implement the ideas. "The new book addressing the application of mathematical morphology to problems in geomorphology by Dr. B.S. Daya Sagar is timely and fills a needed gap. Dr. Sagar is one of the world's leading experts on mathematical morphology. This book is large but well organized and clearly written. It is accessible to those with no knowledge of mathematical morphology, as early chapters introduce the basic structuring elements and provide numerous examples. There are practical examples throughout the book and the theoretical underpinnings are tied to examples. As a statistician, I found the quantitative spatial relationships and reasoning especially interesting. Many of us educated in North America perhaps may have had limited exposure to this subject but it merits serious consideration, given the importance of spatial-temporal relationships and clustering." -John H. (Jack) Schuenemeyer, President, Southwest Statistical Consulting, LLC "Professor Daya Sagar's book is a triumph in the literature on morphology. It provides rich, comprehensive insight into the mathematics of morphology, using problems and examples from the geographic sciences. In addition, scholars of image processing, computer vision, and medical imagery will also find useful material in shape analysis and recognition." -Kentaro Toyama, University of California, Berkeley "Professor Daya Sagar's book is a tour de force. He approaches mathematical morphology in depth from a variety of perspectives and practitioners and researchers from many fields will find much to learn. His linking of pattern retrieval, pattern analysis and modelling is innovative and powerful." -Sir Alan Wilson, University College London "A wide-ranging treatise by an erudite scholar." -Jayanth Banavar, University of Maryland "This book attacks the deep problem of analyzing mathematically the form of landscapes by mathematical tools, in particular by involving the discipline founded by geoscientists Matheron and Serra: mathematical morphology. The approach is original and pedagogic. It systematically combines experiments on numerical synthetic landscape models with experiments on real digital elevation models. Some chapters are very original, as they aim at the explanation of complex geomorphological phenomena. For example, the formation of dunes is explored by its underlying bifurcation theory." -Jean-Michel Morel, Ecole Normale Superieure de Cachan, CMLA, France "... describes several techniques of mathematical morphology to address problems of image processing and data analysis with applications in geophysical information retrieval, analysis, reasoning, and modeling. ... provides not only details of various techniques of mathematical morphology, but also several illustrations of application. ... One of several novel aspects of the book is the integration of mathematical morphology and fractal analysis. ... contains extensive discussion and illustration of many more applications of image and data analysis in geomorphology and geographic information science. Coming from a different background in biomedical signal and image analysis, I find the illustrations and examples provided in the book to be not only interesting but also attractive and intriguing. The detailed procedures described in the book along with the large number of illustrations of application should assist researchers and practitioners in geographic information science and other areas of application of image processing and data analysis." -Rangaraj M. Rangayyan, University of Calgary "This book represents an interesting application of approaches of mathematical morphology to digital terrain modelling." -Igor Florinsky, Russian Academy of Sciences "... a welcome addition to the literature. It fills a gap that has existed for some time in the field of image analysis by providing a comprehensive mathematically based overview of methods to systematically analyze the great variety of features observed at the surface of the Earth. ... The author has included numerous instructive examples of application with a substantial number of them related to the analysis of fractal patterns. Overall, the treatment of the subjects is thorough and the book can be regarded as a follow-up to the original approach to mathematical morphology commenced by Georges Matheron in the 1970s and 1980s. ... The author offers excellent explanations and examples of application of non-linear process modelling ... I also highly recommend this new book to all teachers engaged in presenting courses on geomorphology and GISci to university students." -Frits Agterberg, Geological Survey of Canada "This enticing book introduces mathematical morphology to GI scientists in a way that is persuasive and accessible using ideas that the author himself has pioneered in the last 20 years. It should be read by all those with an interest in how we represent surfaces in the environmental and urban domain. What is so appealing about this book is that the author introduces geomorphology using models of mathematical structure that are rooted in new approaches to geometry, particularly fractals and chaos. He adopts a basic model of a fractal river basin from which he extracts skeletal structures, thereby introducing ideas about networks in the landscape in an entirely natural way. He uses this as a basis for developing many other aspects of mathematical morphology-the use of sets to generate partitions of areas, the use of interpolation to produce surface representations, and the identification of spatial clusters. Towards the end of the book, he generalises many of these ideas to more human spatial systems using the regionalisation of India as his exemplar and in so doing, he has produced as comprehensive a treatment of morphology in geographic information science as you will find anywhere. This is an important book that should be explored by all those who profess to be interested in spatial morphologies." -Michael Batty, University College London "Since the initial birthing of computational geography and GIS over fifty years ago, the field of geography has been evolving with many contributions from both the academic and research side as well as the application world. I am happy to see the emergence of Mathematical Morphology in Geomorphology and GISci. This text further extends our understanding of GIScience-how fundamental quantitative approaches can extend how we understand geography and our wIntroduction Surficial Features Spatial Data General Organization of the Book Mathematical Morphology: An Introduction Birth of Mathematical Morphology Elements of Set Theory and Logical Operations Grid Utilized for Morphological Transformations Theory of Structuring Elements Four Basic Principles of the Theory of Mathematical Morphology Binary Mathematical Morphological Operations Multiscale Morphological Operations Homotopic Operations Based on Basic Binary Morphological Transformations Grayscale Morphological Operations Multiscale Grayscale Morphological Operations Threshold Decomposition of a Function 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) Generation of Fractal Landscapes and Fractal DEMs (Functions) Realistic DEMs and DBMs Remotely Sensed Satellite Data Feature Extraction Unique Feature Retrieval via Binary Skeletonization Retrieval of Physiographic Features from DEMs via Morphological Segmentation Extraction of Morphologically Significant Zones Terrestrial Surface Characterization: A Quantitative Perspective Network Morphometry: A Valuable Tool to Characterize Surficial Phenomena: A Review 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 Allometric Relationships between Travel Time Channel Networks, Convex Hulls, and Convexity Measures Universal Scaling Laws in Water Bodies and Their Zones of Influence 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 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) Morphometry of Nonnetwork Space Granulometries, Convexity Measures, and Geodesic Spectrum for DEM Analyses Grayscale Granulometric Analysis Morphological Convexity Measures for Terrestrial Basins Derived from Digital Elevation Models Derivation of Geodesic Flow Fields and Spectrum in Digital Topographic Basin Synthetic Examples to Understand Spatiotemporal Dynamics of Certain Geo(morpho)logical Processes Logistic Map: A Toy Model Logistic Equation in Modeling the Geomorphological Phenomena (Lakes) Numerical Simulations through First-Order Nonlinear Difference Equation to Study Highly Ductile Symmetric Fold Dynamics: A Conceptual Study Logistic Equation in Sand Dunes Quantitative Spatial Relationships and Spatial Reasoning Spatial Reasoning and Mathematical Morphology Recognition and Visualization of Strategically Significant Spatial Sets via Morphological Analysis Strategically Significant Set Experimental Results on Clusters of Sets Discussion and Open Problems Derivation of Spatially Significant Zones from a Cluster Background on Derivation of Spatially Significant Zones from a Cluster Spatial System and Its Subsystems Experimental Results Conclusions Directional Spatial Relationship Background on Directional Spatial Relationship Directional Spatial Relationship via Origin-Specific Dilation Distances Methods to Derive the Directional Spatial Relationship Experimental Results and Discussion Conclusion "Between" Space Background on "Between" Space Spatial Analysis and Reasoning via Hausdorff Distance-Based Morphological Closing Methods to Derive the "Between" Space Extension to Grayscale Features Experimental Results and Discussion Potential Applications Conclusion Spatial Interpolations Introduction Generation of Zonal Map from Point Data via Weighted Skeletonization by Influence Zone Visualization of Spatiotemporal Behavior of Discrete Maps via Generation of Recursive Median Elements Conclusions Index References appear at the end of each chapter.