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
Connections for sets and functions
Fundamenta Informaticae - Special issue on mathematical morphology
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
A multiscale approach to connectivity
Computer Vision and Image Understanding
A Theoretical Tour of Connectivity in Image Processing and Analysis
Journal of Mathematical Imaging and Vision
Object-Based Image Analysis Using Multiscale Connectivity
IEEE Transactions on Pattern Analysis and Machine Intelligence
Morphology on Label Images: Flat-Type Operators and Connections
Journal of Mathematical Imaging and Vision
Multiscale Connected Operators
Journal of Mathematical Imaging and Vision
Constructing multiscale connectivities
Computer Vision and Image Understanding
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Mask-Based Second-Generation Connectivity and Attribute Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geodesy on label images, and applications to video sequence processing
Journal of Visual Communication and Image Representation
Partial Partitions, Partial Connections and Connective Segmentation
Journal of Mathematical Imaging and Vision
A New Fuzzy Connectivity Measure for Fuzzy Sets
Journal of Mathematical Imaging and Vision
Some Morphological Operators in Graph Spaces
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
An Efficient Algorithm for Computing Multi-scale Connectivity Measures
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
Partition-induced connections and operators for pattern analysis
Pattern Recognition
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
Pattern spectra from partition pyramids and hierarchies
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Filament enhancement by non-linear volumetric filtering using clustering-based connectivity
IWICPAS'06 Proceedings of the 2006 Advances in Machine Vision, Image Processing, and Pattern Analysis international conference on Intelligent Computing in Pattern Analysis/Synthesis
Morphological filtering on graphs
Computer Vision and Image Understanding
Component-Trees and Multivalued Images: Structural Properties
Journal of Mathematical Imaging and Vision
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The notion of connectivity is very important in image processing and analysis, and particularly in problems related to image segmentation. It is well understood, however, that classical notions of connectivity, including topological and graph-theoretic notions, are not compatible with each other. This motivated G. Matheron and J. Serra to develop a general framework of connectivity, which unifies most classical notions, circumvents incompatibility issues, and allows the construction of new types of connectivity for binary and grayscale images. In this paper, we enrich this theory of connectivity by providing several new theoretical results and examples that are useful in image processing and analysis. In particular, we provide new results on the semi-continuity behavior of connectivity openings, we study the reconstruction operator in a complete lattice framework, and we extend some known binary results regarding reconstruction to this framework. Moreover, we study connectivities constructed by expanding given connectivities by means of clustering operators and connectivities constructed by restricting given connectivities by means of contraction operators.