Fuzzy and Bipolar Mathematical Morphology, Applications in Spatial Reasoning [chapter]

Isabelle Bloch
2009 Lecture Notes in Computer Science  
Mathematical morphology is based on the algebraic framework of complete lattices and adjunctions, which endows it with strong properties and allows for multiple extensions. In particular, extensions to fuzzy sets of the main morphological operators, such as dilation and erosion, can be done while preserving all properties of these operators. Another, more recent, extension, concerns bipolar fuzzy sets. These extensions have numerous applications, two of each being presented here. The first one
more » ... oncerns the definition of spatial relations, for applications in spatial reasoning and model-based recognition of structures in images. The second one concerns the handling of the bipolarity feature of spatial information. Keywords: Fuzzy mathematical morphology, bipolar mathematical morphology, spatial relations, bipolar spatial information, spatial reasoning. ∀X ⊆ S, δ B (X) = {x ∈ S |B x ∩ X = ∅}, ε B (X) = {x ∈ S | B x ⊆ X}, C. Sossai and G.
doi:10.1007/978-3-642-02906-6_1 fatcat:gbyqydvw2ncvvbtr3vuulupn4e