Self-dual morphological operators and filters
Journal of Mathematical Imaging and Vision
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Mathematical morphology on complete semilattices and its applications to image processing
Fundamenta Informaticae - Special issue on mathematical morphology
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Journal of Mathematical Imaging and Vision
Morphology on Label Images: Flat-Type Operators and Connections
Journal of Mathematical Imaging and Vision
Flat Morphology on Power Lattices
Journal of Mathematical Imaging and Vision
Ambiguity and fuzziness measures defined on the set of closed intervals in [0,1]
Information Sciences: an International Journal
Adjacency lattices and shape-tree semilattices
Image and Vision Computing
Modelling and segmentation of colour images in polar representations
Image and Vision Computing
Computer Vision and Image Understanding
A comparative study on multivariate mathematical morphology
Pattern Recognition
Geodesy on label images, and applications to video sequence processing
Journal of Visual Communication and Image Representation
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Beyond self-duality in morphological image analysis
Image and Vision Computing
Flat morphological operators on arbitrary power lattices
Proceedings of the 11th international conference on Theoretical foundations of computer vision
A general framework for tree-based morphology and its applications to self-dual filtering
Image and Vision Computing
Permutation-based finite implicative fuzzy associative memories
Information Sciences: an International Journal
Hypercomplex Mathematical Morphology
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
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Today, the theoretical framework of mathematical morphology is phrased in terms of complete lattices and operators defined on them. The characterization of a particular class of operators, such as erosions or openings, depends almost entirely upon the choice of the underlying partial ordering. This is not so strange if one realizes that the partial ordering formalizes the notions of foreground and background of an image. The duality principle for partially ordered sets, which says that the opposite of a partial ordering is also a partial ordering, gives rise to the fact that all morphological operators occur in pairs, e.g., dilation and erosion, opening and closing, etc. This phenomenon often prohibits the construction of tools that treat foreground and background of signals in exactly the same way. In this paper we discuss an alternative framework for morphological image processing that gives rise to image operators which are intrinsically self-dual. As one might expect, this alternative framework is entirely based upon the definition of a new self-dual partial ordering.