Mathematical Morphology as a Tool for Shape Description

Abstract In many domains of information processing, such as knowledge representation, preference modeling, argumentation, multi-criteria decision analysis, spatial reasoning, both vagueness, or imprecision, and bipolarity, encompassing positive and negative parts of information, are core features of the information to be modeled and processed. This led to the development of the concept of bipolar fuzzy sets, and of associated models and tools, such as fusion and aggregation, similarity and distances, mathematical morphology. Here we propose to extend these tools by defining algebraic and topological relations between bipolar fuzzy sets, including intersection, inclusion, adjacency and RCC relations widely used in mereotopology, based on bipolar connectives (in a logical sense) and on mathematical morphology operators. These definitions are shown to have the desired properties and to be consistent with existing definitions on sets and fuzzy sets, while providing an additional bipolar feature. The proposed relations can be used for instance for preference modeling or spatial reasoning. They apply more generally to any type of functions taking values in a poset or a complete lattice, such as L-fuzzy sets.

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Compensatory fuzzy mathematical morphology

Signal Image and Video Processing ◽

10.1007/s11760-017-1058-y ◽

2017 ◽

Vol 11 (6) ◽

pp. 1065-1072 ◽

Cited By ~ 2

Author(s):

Agustina Bouchet ◽

Juan I. Pastore ◽

Marcel Brun ◽

Virginia L. Ballarin

Keyword(s):

Mathematical Morphology ◽

Fuzzy Mathematical Morphology

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Boundary Morphology for Hierarchical Simplification of Archaeological Fragments

Mathematical Morphology - Theory and Applications ◽

10.1515/mathm-2020-0101 ◽

2020 ◽

Vol 4 (1) ◽

pp. 46-63

Author(s):

Hanan ElNaghy ◽

Leo Dorst

Keyword(s):

Mathematical Morphology ◽

Masking Effect ◽

Morphological Operations ◽

Fracture Surfaces ◽

Morphological Approach ◽

Archaeological Artifacts ◽

Scale Spaces ◽

Extrusion Method

AbstractWhen fitting archaeological artifacts, one would like to have a representation that simplifies fragments while preserving their complementarity. In this paper, we propose to employ the scale-spaces of mathematical morphology to hierarchically simplify potentially fitting fracture surfaces. We study the masking effect when morphological operations are applied to selected subsets of objects. Since fitting locally depends on the complementarity of fractures only, we introduce ‘Boundary Morphology’ on surfaces rather than volumes. Moreover, demonstrating the Lipschitz nature of the terracotta fractures informs our novel extrusion method to compute both closing and opening operations simultaneously. We also show that in this proposed representation the effects of abrasion and uncertainty are naturally bounded, justifying the morphological approach. This work is an extension of our contribution earlier published in the proceedings of ISMM2019 [10].

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