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
An overview of morphological filtering
Circuits, Systems, and Signal Processing - Special issue: median and morphological filters
Morphological connected filters and intra-region smoothing for image segmentation
Morphological connected filters and intra-region smoothing for image segmentation
Theoretical aspects of morphological filters by reconstruction
Signal Processing
Attribute openings, thinnings, and granulometries
Computer Vision and Image Understanding
Locality and Adjacency Stability Constraints for MorphologicalConnected Operators
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
Auto-dual connected operators based on iterative merging algorithms
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 filtering and segmentation using component trees
Computer Vision and Image Understanding
Mathematical morphology on complete semilattices and its applications to image processing
Fundamenta Informaticae - Special issue on mathematical morphology
Inf-Semilattice Approach to Self-Dual Morphology
Journal of Mathematical Imaging and Vision
Connectivity on complete lattices: new results
Computer Vision and Image Understanding
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Spatio-Temporal Segmentation Using 3D Morphological Tools
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Morphology on Label Images: Flat-Type Operators and Connections
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Flat Morphology on Power Lattices
Journal of Mathematical Imaging and Vision
Geodesy and connectivity in lattices
Fundamenta Informaticae
Reconstructing masks from markers in non-distributive lattices
Applicable Algebra in Engineering, Communication and Computing
Beyond self-duality in morphological image analysis
Image and Vision Computing
Journal of Visual Communication and Image Representation
Convergence, continuity, and iteration in mathematical morphology
Journal of Visual Communication and Image Representation
Flat morphological operators on arbitrary power lattices
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Antiextensive connected operators for image and sequence processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
Flat morphological operators on arbitrary power lattices
Proceedings of the 11th international conference on Theoretical foundations of computer vision
CTIC'12 Proceedings of the 4th international conference on Computational Topology in Image Context
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Morphological operators based on the numerical ordering of grey-levels are used to filter regional minima and maxima in images. It is argued that label images constitute an appropriate framework for morphological filtering of regions which are neither minima nor maxima. Following a previous paper where we introduced morphological operations on label images [C. Ronse, V. Agnus, Morphology on label images: flat-type operators and connections, Journal of Mathematical Imaging and Vision 22 (2/3) (2005) 283-307], we study geodesic dilation (or erosion) and reconstruction. Since the lattice of label images is not distributive, some strange results may happen, so the standard definition of geodesic dilation and reconstruction must be modified in order to be effective; standard properties of geodesic operations are preserved only if we make some restrictions on the labels present in the mask or marker image. We give the relation between geodesic reconstruction and the flat zone connection on label images. We illustrate the theory with an application of morphology and geodesy on label images, to the segmentation of moving objects in video sequences.