Algorithms and methodology for inflection line identification within information and mathematical model of relief

The relevance of this research topic lies in the fact that a universal technology for automated recognition and identification of structural relief elements is currently not available. This task is one of the main analytical directions of geomorphological mapping, and its solution will reduce the time for its development, unify the results, and expand the field of application of the homomorphic and genetically homogeneous elementary surface model in interdisciplinary research. To solve this problem, an information and mathematical relief model is developed, the purpose of which is to present surface relief in the form of a consistent set of all structural elements, simulate the obtained surface in 3D space, provide a complete automated cycle of highlighting and classifying structural relief elements, and present various algorithms for its analysis. The described work stage includes the development of original algorithms and methods for automatic identification of slope inflection lines as part of an information and mathematical model. Slope inflection lines are structuring in material-energy flow redistribution between and within genetically homogeneous surfaces. Automation of the selection of inflection lines is the penultimate stage of constructing the target terrain models. In the study, we discuss the main stages of the automated technology supplying the initial data for the developed algorithms, give an overview of the existing methods and software products used to determine the slope inflection lines, describe the mathematical and algorithmic techniques used in the developed algorithms, and discuss the peculiarities of using these techniques in relation to the developed general technology. The result of the work is an original automatic methodology for determining slope inflection lines, which allows us to proceed to automatic identification and classification of elementary surfaces.