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
Connectivity on complete lattices: new results
Computer Vision and Image Understanding
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
A Theoretical Tour of Connectivity in Image Processing and Analysis
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Geodesy and connectivity in lattices
Fundamenta Informaticae
Attribute-space connectivity and connected filters
Image and Vision Computing
Reconstructing masks from markers in non-distributive lattices
Applicable Algebra in Engineering, Communication and Computing
A New Fuzzy Connectivity Measure for Fuzzy Sets
Journal of Mathematical Imaging and Vision
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
Constrained Connectivity and Transition Regions
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Morphological Connected Filtering on Viscous Lattices
Journal of Mathematical Imaging and Vision
On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds
Journal of Mathematical Imaging and Vision
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Orders on partial partitions and maximal partitioning of sets
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
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
Ultimate opening and gradual transitions
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Mathematical morphology in computer graphics, scientific visualization and visual exploration
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Climbing: a unified approach for global constraints on hierarchical segmentation
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part III
Global-local optimizations by hierarchical cuts and climbing energies
Pattern Recognition
Local Mutual Information for Dissimilarity-Based Image Segmentation
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
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In connective segmentation (Serra in J. Math. Imaging Vis. 24(1):83---130, [2006]), each image determines subsets of the space on which it is "homogeneous", in such a way that this family of subsets always constitutes a connection (connectivity class); then the segmentation of the image is the partition of space into its connected components according to that connection.Several concrete examples of connective segmentations or of connections on sets, indicate that the space covering requirement of the partition should be relaxed. Furthermore, morphological operations on partitions require the consideration of wider framework.We study thus partial partitions (families of mutually disjoint non-void subsets of the space) and partial connections (where connected components of a set are mutually disjoint but do not necessarily cover the set). We describe some methods for generating partial connections. We investigate the links between the two lattices of partial connections and of partial partitions. We generalize Serra's characterization of connective segmentation and discuss its relevance. Finally we give some ideas on how the theory of partial connections could lead to improved segmentation algorithms.