Pattern Spectrum and Multiscale Shape Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Theoretical aspects of morphological filters by reconstruction
Signal Processing
Locality and Adjacency Stability Constraints for MorphologicalConnected Operators
Journal of Mathematical Imaging and Vision
Set-Theoretical Algebraic Approaches to Connectivityin Continuous or Digital Spaces
Journal of Mathematical Imaging and Vision
From connected operators to levelings
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Face segmentation using connected operators
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
Connected filtering and segmentation using component trees
Computer Vision and Image Understanding
Connections for sets and functions
Fundamenta Informaticae - Special issue on mathematical morphology
Digital Picture Processing
Connectivity on complete lattices: new results
Computer Vision and Image Understanding
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
Robust motion estimation using connected operators
ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 1 - Volume 1
Constructing multiscale connectivities
Computer Vision and Image Understanding
Antiextensive connected operators for image and sequence processing
IEEE Transactions on Image Processing
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
Geodesy and connectivity in lattices
Fundamenta Informaticae
Object-Based Image Analysis Using Multiscale Connectivity
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Flat Morphology on Power Lattices
Journal of Mathematical Imaging and Vision
Size-density spectra and their application to image classification
Pattern Recognition
The Strong Property of Morphological Connected Alternated Filters
Journal of Mathematical Imaging and Vision
Morphological multiscale decomposition of connected regions with emphasis on cell clusters
Computer Vision and Image Understanding
Journal of Biomedical Informatics
Morphological Connected Filtering on Viscous Lattices
Journal of Mathematical Imaging and Vision
Automatic clump splitting for cell quantification in microscopical images
CIARP'07 Proceedings of the Congress on pattern recognition 12th Iberoamerican conference on Progress in pattern recognition, image analysis and applications
Adjacency stable connected operators and set levelings
Image and Vision Computing
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
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Among the major developments in Mathematical Morphology in the last two decades are the interrelated subjects of connectivity classes and connected operators. Braga-Neto and Goutsias have proposed an extension of the theory of connectivity classes to a multiscale setting, whereby one can assign connectivity to an object observed at different scales. In this paper, we study connected operators in the context of multiscale connectivity. We propose the notion of a 驴-connected operator, that is, an operator connected at scale 驴. We devote some attention to the study of binary 驴-grain operators. In particular, we show that families of 驴-grain openings and 驴-grain closings, indexed by the connectivity scale parameter, are granulometries and anti-granulometries, respectively. We demonstrate the use of multiscale connected operators with image analysis applications. The first is the scale-space representation of grayscale images using multiscale levelings, where the role of scale is played by the connectivity scale. Then we discuss the application of multiscale connected openings in granulometric analysis, where both size and connectivity information are summarized. Finally, we describe an application of multiscale connected operators to an automatic target recognition problem.