Definition
Mathematical morphology is a discipline of image analysis that was introduced in the mid-1960s. From the very start it included not only theoretical results but also research on the links between geometrical textures and physical properties of the objects under study. Initially conceived as a set theory, with deterministic and random versions, it rapidly developed its concepts in the framework of complete lattices. In geosciences and in image processing, theoretical approaches may rest, or not, on the idea of reversibility. In the first case, addition is the core operation. It leads to convolution, wavelets, Fourier transformation, etc. But the visual universe can be grasped differently, by remarking that the objects are solid and not transparent. An object may cover another, or be included in it, or hit it, or be smaller than it, etc., notions which all refer to set geometry, and which all imply some loss of reversibility. Indeed, the morphological operations, whose core is...
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Serra, J. (2023). Mathematical Morphology. In: Daya Sagar, B.S., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-85040-1_22
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