The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
The algebraic basis of mathematical morphology
CVGIP: Image Understanding
Set-Theoretical Algebraic Approaches to Connectivityin Continuous or Digital Spaces
Journal of Mathematical Imaging and Vision
Connectivity on Complete Lattices
Journal of Mathematical Imaging and Vision
Connected morphological operators for binary images
Computer Vision and Image Understanding
Set Connections and Discrete Filtering (Invited Paper)
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Spatio-Temporal Segmentation Using 3D Morphological Tools
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Connections for sets and functions
Fundamenta Informaticae
A Theoretical Tour of Connectivity in Image Processing and Analysis
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Morphology on Label Images: Flat-Type Operators and Connections
Journal of Mathematical Imaging and Vision
Multiscale Connected Operators
Journal of Mathematical Imaging and Vision
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
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This paper generalizes the notion of symmetrical neighbourhoods, which have been used to define connectivity in the case of sets, to the wider framework of complete lattices having a sup-generating family. Two versions (weak and strong) of the notion of a symmetrical dilation are introduced, and they are applied to the generation of "connected components" from the so-called "geodesic dilations". It turns out that any "climbing" "weakly symmetrical" extensive dilation induces a "geodesic" connectivity. When the lattice is the one of subsets of a metric space, the connectivities which are obtained in this way may coincide with the usual ones under some conditions, which are clarified. The abstract theory can be applied to grey-level and colour images, without any assumption of translation-invariance of operators.