Morphology Computation Algorithms: Generalities

Abstract

We propose different criteria for classifying algorithms for morphology computation (Sect. 2.1). Such criteria are based on the dimension of the input scalar field (2D, 3D, or dimension-independent), on the input format (simplicial models, regular grids), on the output information (ascending or descending Morse complex, Morse-Smale complex), on the format of the output information, and on the algorithmic approach applied. This last criterion leads to a classification into boundary-based and region-growing algorithms (coming from Banchoff’s piecewise linear Morse theory), algorithms based on the watershed transform, and based on Forman’s discrete Morse theory. We will use this classification to organize the survey provided in the remainder of the book. We discuss methods to compute the critical points of the scalar field, which is a basic subcomponent of most morphology computation algorithms (Sect. 2.2), and solutions for dealing with the domain boundary (Sect. 2.3), and with plateaus (Sect. 2.4), which are common issues when applying such algorithms to real-world data.KeywordsScalar FieldSimplicial ComplexPrimal GraphRegular ModelLower LinkThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.