Morphological methods in image and signal processing
Morphological methods in image and signal processing
A Representation Theory for Morphological Image and Signal Processing
IEEE Transactions on Pattern Analysis and Machine Intelligence
The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
Theoretical Aspects of Gray-Level Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Methods and Criteria for Detecting Significant Regions in Medical Image Analysis
ISMDA '01 Proceedings of the Second International Symposium on Medical Data Analysis
Set Connections and Discrete Filtering (Invited Paper)
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
On the Strong Property of Connected Open-Close and Close-Open Filters
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
Multiscale Connected Operators
Journal of Mathematical Imaging and Vision
A Lattice Approach to Image Segmentation
Journal of Mathematical Imaging and Vision
Flat Morphology on Power Lattices
Journal of Mathematical Imaging and Vision
Geodesy on label images, and applications to video sequence processing
Journal of Visual Communication and Image Representation
The Strong Property of Morphological Connected Alternated Filters
Journal of Mathematical Imaging and Vision
Levelings and Geodesic Reconstructions
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Adjacency stable connected operators and set levelings
Image and Vision Computing
Fundamenta Morphologicae Mathematicae
Fundamenta Informaticae
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This paper investigates two constraints for the connected operator class. For binary images, connected operators are those that treat grains and pores of the input in an all or nothing way, and therefore they do not introduce discontinuities. The first constraint, called connected-component (c.c.) locality, constrains the part of the input that can be used for computing the output of each grain and pore. The second, called adjacency stability, establishes an adjacency constraint between connected components of the input set and those of the output set. Among increasing operators, usual morphological filters can satisfy both requirements. On the other hand, some (non-idempotent) morphological operators such as the median cannot have the adjacency stability property. When these two requirements are applied to connected and idempotent morphological operators, we are lead to a new approach to the class of filters by reconstruction. The important case of translation invariant operators and the relationships between translation invariance and connectivity are studied in detail. Concepts are developed within the binary (or set) framework; however, conclusions apply as well to flat non-binary (gray-level) operators.