Advanced mathematical morphology: from an algebraic to a stochastic point of view (Invited Paper)

Francoise J. Preteux

doi:10.1117/12.60631

1 June 1992 Advanced mathematical morphology: from an algebraic to a stochastic point of view (Invited Paper)

Francoise J. Preteux

Proceedings Volume 1769, Image Algebra and Morphological Image Processing III; (1992) https://doi.org/10.1117/12.60631
Event: San Diego '92, 1992, San Diego, CA, United States

Abstract

In this paper, Mathematical Morphology (M.M.) foundations as an algebraic, topological and geometrical theory are recalled within both a deterministic and a stochastic framework. Some new developments such as morphological filtering, Boolean model, topographical distance and fuzzy measurements, ifiustrate the relevance of these mathematical foundations. Starting from the notion of hierarchical process, we define a stochastic morphology and develop the concept of stochastic morphological operators. The example of the stochastic averaging operator is presented and its equivalence with simulated annealing stated. Moreover, we introduce stochastic operators based on specific energy functionals and show that they allow to consider statistical and soft morphologies as limiting or special cases of stochastic morphology.

Citation Download Citation

Francoise J. Preteux "Advanced mathematical morphology: from an algebraic to a stochastic point of view (Invited Paper)", Proc. SPIE 1769, Image Algebra and Morphological Image Processing III, (1 June 1992); https://doi.org/10.1117/12.60631

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