Finite topology as applied to image analysis
Computer Vision, Graphics, and Image Processing
Digital topology: introduction and survey
Computer Vision, Graphics, and Image Processing
Morphological operators for image sequences
Computer Vision and Image Understanding
Attribute openings, thinnings, and granulometries
Computer Vision and Image Understanding
Set-Theoretical Algebraic Approaches to Connectivityin Continuous or Digital Spaces
Journal of Mathematical Imaging and Vision
Complete ordering and multivariate mathematical morphology
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
Connectivity in Digital Pictures
Journal of the ACM (JACM)
Connected filtering and segmentation using component trees
Computer Vision and Image Understanding
Tree Representation for Image Matching and Object Recognition
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Efficient Algorithms to Implement the Confinement Tree
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Connectivity on complete lattices: new results
Computer Vision and Image Understanding
Morphology on Label Images: Flat-Type Operators and Connections
Journal of Mathematical Imaging and Vision
A main stem concept for image matching
Pattern Recognition Letters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mask-Based Second-Generation Connectivity and Attribute Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
A comparative study on multivariate mathematical morphology
Pattern Recognition
On lexicographical ordering in multivariate mathematical morphology
Pattern Recognition Letters
An evaluation of area morphology scale-spaces for colour images
Computer Vision and Image Understanding
Constrained Connectivity for Hierarchical Image Decomposition and Simplification
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometry-Based Image Retrieval in Binary Image Databases
IEEE Transactions on Pattern Analysis and Machine Intelligence
Concurrent Computation of Attribute Filters on Shared Memory Parallel Machines
IEEE Transactions on Pattern Analysis and Machine Intelligence
Component-Trees and Multi-value Images: A Comparative Study
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Journal of Visual Communication and Image Representation
A document binarization method based on connected operators
Pattern Recognition Letters
An extension of component-trees to partial orders
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Geometric Description of Images as Topographic Maps
Geometric Description of Images as Topographic Maps
Paths, Homotopy and Reduction in Digital Images
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Interactive segmentation based on component-trees
Pattern Recognition
Antiextensive connected operators for image and sequence processing
IEEE Transactions on Image Processing
Building the Component Tree in Quasi-Linear Time
IEEE Transactions on Image Processing
Volumetric Attribute Filtering and Interactive Visualization Using the Max-Tree Representation
IEEE Transactions on Image Processing
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Component-trees model the structure of grey-level images by considering their binary level-sets obtained from successive thresholdings. They also enable to define anti-extensive filtering procedures for such images. In order to extend this image processing approach to any (grey-level or multivalued) images, both the notion of component-tree, and its associated filtering framework, have to be generalised. In this article we deal with the generalisation of the component-tree structure. We define a聽new data structure, the component-graph, which extends the notion of component-tree to images taking their values in any (partially or totally) ordered set. The component-graphs are declined in three variants, of increasing richness and size, whose structural properties are studied.