Theoretical Aspects of Gray-Level Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
Theoretical aspects of morphological filters by reconstruction
Signal Processing
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
Connectivity on Complete Lattices
Journal of Mathematical Imaging and Vision
Connected morphological operators for binary images
Computer Vision and Image Understanding
Connectivity in Digital Pictures
Journal of the ACM (JACM)
Computer and Robot Vision
Nonlinear PDEs and Numerical Algorithms for Modeling Levelings and Reconstruction Filters
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Morphological Scale-Space Representation with Levelings
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Morphological grayscale reconstruction in image analysis: applications and efficient algorithms
IEEE Transactions on Image Processing
Geodesy and connectivity in lattices
Fundamenta Informaticae
Fundamenta Morphologicae Mathematicae
Fundamenta Informaticae
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Classically, connectivity is a topological notion for sets, often introduced by means of arcs. An algebraic definition, called connection, has been proposed by Serra to extend the notion of connectivity to complete sup-generated lattices. A connection turns out to be characterized by a family of openings parameterized by the sup-generators, which partition each element of the lattice into maximal components. Starting from a first connection, several others may be constructed; e.g., by applying dilations. The present paper applies this theory to numerical functions. Every connection leads to segmenting the support of the function under study into regions. Inside each region, the function is &rgr;-continuous, for a modulus of continuity &rgr; given a priori, and characteristic of the connection. However, the segmentation is not unique, and may be particularized by other considerations (self-duality, large or low number of point components, etc.). These variants are introduced by means of examples for three different connections: flat zone connections, jump connections, and smooth path connections. They turn out to provide remarkable segmentations, depending only on a few parameters. In the last section, some morphological filters are described, based on flat zone connections, namely openings by reconstruction, flattenings and levelings.