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Morphological Image Analysis. Mathematical Foundations and Applicationsстатья Глава в книге
- Авторы: Pyt'ev Yu P., Chulichkov A.I., Falomkina O.V., Balakin D.A., Zubyuk A.V.
- Сборник: Image Analysis and Pattern Recognition. State of the Art in the Russian Federation
- Глава в коллективной монографии
- Год издания: 2019
- Место издания: World Scientific Publishing Co. Pte. Ltd Singapore
- DOI: 10.1142/9789811267215_0002
- Аннотация: A short review of mathematical methods of image analysis is provided. Mathematical models of shapes of signals and images are formulated, and mathematical methods and numerical algorithms for calculating characteristics of closeness (connectedness and dependence) of two signal or image shapes using oblique projection technique are considered. Examples of using morphological image analysis to solve applied problems are given. In addition, elements of mathematical formalism of subjective modeling of categories of fuzziness and uncertainty that reflect incompleteness and unreliability of information used in construction of a subjective morphological model to take into account researcher’s subjective notions. As their applications, the mathematical foundations of morphological image analysis, oblique projection approach and analysis of dependency of relative image shapes and connectedness of their absolute shapes are shown to have an interpretation in terms of subjective modeling, with examples of subjective morphological models and optimization of decisions based on them using oblique projection and subjective optimization. It is shown that optimal solutions of morphological problems of image analysis and image interpretation can be formulated in terms of oblique image projection and subjective optimization.
- Добавил в систему: Балакин Дмитрий Александрович