ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
Spatially-Variant Anisotropic Morphological Filters Driven by Gradient Fields
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Spatially-Variant Morpho-Hessian Filter: Efficient Implementation and Application
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Binary morphology with spatially variant structuring elements: algorithm and architecture
IEEE Transactions on Image Processing
Simplification of color images using semi-flat morphological operators and statistical metrics
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Edge detection using morphological amoebas in noisy images
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Overview of adaptive morphology: trends and perspectives
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
General adaptive neighborhood mathematical morphology
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Adaptivity and group invariance in mathematical morphology
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Adaptive mathematical morphology: a unified representation theory
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Study on nonlocal morphological operators
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Morphological bilateral filtering and spatially-variant adaptive structuring functions
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
General adaptive neighborhood viscous mathematical morphology
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
An attribute weighted distance transform
Pattern Recognition Letters
Adaptive structuring elements based on salience information
ICCVG'12 Proceedings of the 2012 international conference on Computer Vision and Graphics
Adaptive morphology using tensor-based elliptical structuring elements
Pattern Recognition Letters
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In this paper, we develop a spatially-variant (SV) mathematical morphology theory for gray-level signals and images in the Euclidean space. The proposed theory preserves the geometrical concept of the structuring function, which provides the foundation of classical morphology and is essential in signal and image processing applications. We define the basic SV gray-level morphological operators (i.e., SV gray-level erosion, dilation, opening, and closing) and investigate their properties. We demonstrate the ubiquity of SV gray-level morphological systems by deriving a kernel representation for a large class of systems, called V-systems, in terms of the basic SV graylevel morphological operators. A V-system is defined to be a gray-level operator, which is invariant under gray-level (vertical) translations. Particular attention is focused on the class of SV flat gray-level operators. The kernel representation for increasing V-systems is a generalization of Maragos' kernel representation for increasing and translation-invariant function-processing systems. A representation of V-systems in terms of their kernel elements is established for increasing and upper-semi-continuous V-systems. This representation unifies a large class of spatially-variant linear and non-linear systems under the same mathematical framework. Finally, simulation results show the potential power of the general theory of gray-level spatially-variant mathematical morphology in several image analysis and computer vision applications.