Morphological Modeling of Terrains and Volume Data

The book "Morphological Modeling of Terrains and Volume Data" offers a comprehensive examination of the mathematical foundations of discrete approaches to the morphological analysis of scalar fields. The focus is on Morse theory as well as the discrete theories of Banchoff and Forman. The algorithms and data structures presented are applied in terrain modeling, the analysis of molecular shapes, and in the analysis and visualization of 3D datasets from sensors and simulations. The work covers a wide range of application areas, including geography, geology, environmental sciences, medicine, and biology. The authors classify the various approaches to morphological analysis, all of which are based on the construction of Morse or Morse-Smale decompositions. They explain algorithms for calculating such decompositions for 2D and 3D scalar fields, including those based on the discrete watershed transformation. Additionally, current developments in research on morphological shape analysis are discussed, such as simplification operators for Morse and Morse-Smale complexes and their multiresolution representation. This book is a valuable resource for professionals and researchers involved in modeling and algorithm analysis, and it also provides useful insights for advanced students in computer science, mathematics, and geography.