Computer Vision, Graphics, and Image Processing
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A taxonomy for texture description and identification
A taxonomy for texture description and identification
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
An overview of morphological filtering
Circuits, Systems, and Signal Processing - Special issue: median and morphological filters
Variational methods in image segmentation
Variational methods in image segmentation
Simple points, topological numbers and geodesic neighborhoods in cubic grids
Pattern Recognition Letters
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Theoretical aspects of morphological filters by reconstruction
Signal Processing
International Journal of Computer Vision
Locality and Adjacency Stability Constraints for MorphologicalConnected Operators
Journal of Mathematical Imaging and Vision
Extensive operators in partition lattices for image sequence analysis
Signal Processing - Video segmentation for content-based processing manipulation
Set-Theoretical Algebraic Approaches to Connectivityin Continuous or Digital Spaces
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
Connectivity on Complete Lattices
Journal of Mathematical Imaging and Vision
Connected morphological operators for binary images
Computer Vision and Image Understanding
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
Picture Segmentation by a Tree Traversal Algorithm
Journal of the ACM (JACM)
Connections for sets and functions
Fundamenta Informaticae - Special issue on mathematical morphology
Hierarchical Decomposition of Multiscale Skeletons
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Picture Processing
Geometry and Color in Natural Images
Journal of Mathematical Imaging and Vision
Random texture models for material structures
Statistics and Computing
Shape Connectivity: Multiscale Analysis and Application to Generalized Granulometries
Journal of Mathematical Imaging and Vision
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hierarchies of Partitions and Morphological Segmentation
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Connectivity on complete lattices: new results
Computer Vision and Image Understanding
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
A multiscale approach to connectivity
Computer Vision and Image Understanding
Journal of Mathematical Imaging and Vision
Multiscale Connected Operators
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Differential morphology and image processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Morphological operators on the unit circle
IEEE Transactions on Image Processing
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
Region-based representations of image and video: segmentation tools for multimedia services
IEEE Transactions on Circuits and Systems for Video Technology
Geodesy and connectivity in lattices
Fundamenta Informaticae
Morphology on Label Images: Flat-Type Operators and Connections
Journal of Mathematical Imaging and Vision
Modelling and segmentation of colour images in polar representations
Image and Vision Computing
Partial Partitions, Partial Connections and Connective Segmentation
Journal of Mathematical Imaging and Vision
Discrete Pulse Transform of Images
ICISP '08 Proceedings of the 3rd international conference on Image and Signal Processing
A New Fuzzy Connectivity Measure for Fuzzy Sets
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
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
Segmentation of 4D cardiac MRI: Automated method based on spatio-temporal watershed cuts
Image and Vision Computing
Adaptive lattices on the unit sphere: application to remote sensing
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Partition-induced connections and operators for pattern analysis
Pattern Recognition
Inverses and quotients of mappings between ordered sets
Image and Vision Computing
LULU operators and discrete pulse transform for multidimensional arrays
IEEE Transactions on Image Processing
On the Equivalence Between Hierarchical Segmentations and Ultrametric Watersheds
Journal of Mathematical Imaging and Vision
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
Preventing chaining through transitions while favouring it within homogeneous regions
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
Frequent and dependent connectivities
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
Pattern Recognition and Image Analysis
Local Mutual Information for Dissimilarity-Based Image Segmentation
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
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After a formal definition of segmentation as the largest partition of the space according to a criterion 驴 and a function f, the notion of a morphological connection is reminded. It is used as an input to a central theorem of the paper (Theorem 8), that identifies segmentation with the connections that are based on connective criteria. Just as connections, the segmentations can then be regrouped by suprema and infima. The generality of the theorem makes it valid for functions from any space to any other one. Two propositions make precise the AND and OR combinations of connective criteria.The soundness of the approach is demonstrated by listing a series of segmentation techniques. One considers first the cases when the segmentation under study does not involve initial seeds. Various modes of regularity are discussed, which all derive from Lipschitz functions. A second category of examples involves the presence of seeds around which the partition of the space is organized. An overall proposition shows that these examples are a matter for the central theorem. Watershed and jump connection based segmentations illustrate this type of situation. The third and last category of examples deals with cases when the segmentation occurs in an indirect space, such as an histogram, and is then projected back on the actual space under study.The relationships between filtering and segmentation are then investigated. A theoretical chapter introduces and studies the two notions of a pulse opening and of a connected operator. The conditions under which a family of pulse openings can yield a connected filter are clarified. The ability of segmentations to generate pyramids, or hierarchies, is analyzed. A distinction is made between weak hierarchies where the partitions increase when going up in the pyramid, and the strong hierarchies where the various levels are structured as semi-groups, and particularly as granulometric semi-groups.The last section is based on one example, and goes back over the controversy about "lattice" versus "functional" optimization. The problem is now tackled via a case of colour segmentation, where the saturation serves as a cursor between luminance and hue. The emphasis is put on the difficulty of grouping the various necessary optimizations into a single one.