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The algebraic basis of mathematical morphology
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Set-Theoretical Algebraic Approaches to Connectivityin Continuous or Digital Spaces
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Hausdorff distances and interpolations
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Connectivity on Complete Lattices
Journal of Mathematical Imaging and Vision
The Viscous Watershed Transform
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Geodesy and connectivity in lattices
Fundamenta Informaticae
Constructing multiscale connectivities
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A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Partial Partitions, Partial Connections and Connective Segmentation
Journal of Mathematical Imaging and Vision
An Axiomatic Approach to Hyperconnectivity
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Hyperconnectivity, Attribute-Space Connectivity and Path Openings: Theoretical Relationships
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Constructing multiscale connectivities
Computer Vision and Image Understanding
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Morphological Connected Filtering on Viscous Lattices
Journal of Mathematical Imaging and Vision
Connective segmentation generalized to arbitrary complete lattices
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Hyperconnections and openings on complete lattices
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Hypercomplex Mathematical Morphology
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Adaptive morphology using tensor-based elliptical structuring elements
Pattern Recognition Letters
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Let E be an arbitrary space, and 驴 an extensive dilation of P(E) into itself, with an adjoint erosion 驴. Then, the image 驴[P(E)] of P(E) by 驴 is a complete lattice P where the sup is the union and the inf the opening of the intersection according to 驴 驴. The lattice L, named viscous, is not distributive, nor complemented. Any dilation 驴 on P(E) admits the same expression in L. However, the erosion in L is the opening according to 驴 驴 of the erosion in P(E). Given a connection C on P(E) the image of C under 驴 turns out to be a connection C 驴 on L as soon as 驴 驴 (C)驴eq C. Moreover, the elementary connected openings 驴x of C and 驴驴驴(x) are linked by the relation 驴驴驴(x) = 驴驴x驴. A comprehensive class of connection preverving closings 驴 驴 is constructed. Two examples, binary and numerical (the latter comes from the heart imaging), prove the relevance of viscous lattices in interpolation and in segmentation problems.