Theoretical Foundations of Spatially-Variant Mathematical Morphology Part II: Gray-Level Images
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 sig...
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Published in | IEEE transactions on pattern analysis and machine intelligence Vol. 30; no. 5; pp. 837 - 850 |
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Main Authors | , |
Format | Journal Article |
Language | English |
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Los Alamitos, CA
IEEE
01.05.2008
IEEE Computer Society The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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Abstract | 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 (that is, 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 gray-level 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 semicontinuous V-systems. This representation unifies a large class of spatially-variant-linear and nonlinear systems under the same mathematical framework. The theory is used for analyzing special cases of signal and image processing systems such as SV order rank filters and ' linear-time-varying systems. Finally, simulation results show the potential power of the general theory of gray-level SV mathematical morphology in several image analysis and computer vision applications. |
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AbstractList | 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 [abstract truncated by publisher]. 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 (that is, 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 gray-level 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 semicontinuous V-systems. This representation unifies a large class of spatially-variant-linear and nonlinear systems under the same mathematical framework. The theory is used for analyzing special cases of signal and image processing systems such as SV order rank filters and ' linear-time-varying systems. Finally, simulation results show the potential power of the general theory of gray-level SV mathematical morphology in several image analysis and computer vision applications. 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. [...] simulation results show the potential power of the general theory of gray-level SV mathematical morphology in several image analysis and computer vision applications. |
Author | Schonfeld, D. Bouaynaya, N. |
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Keywords | Morphological Filtering Invariant Grey level image Image processing upper semicontinuous functions Linear time Time varying system adaptive order- statistic filters Behavioral analysis Systems engineering Operating system kernels Euclidean space Pattern analysis Geometrical theory gray-level morphology Computer vision Statistical analysis Probabilistic approach Adaptive filter Mathematical morphology Image analysis Spatially variant mathematical morphology Automatic translation Linear filter Signal processing System representation linear-time-varying systems Artificial intelligence |
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References | serra (bibttp200805083725) 1988 beucher (bibttp200805083731) 1993 bibttp200805083732 bibttp200805083730 bibttp200805083714 bibttp200805083713 bibttp200805083712 bibttp200805083711 bibttp200805083733 bibttp200805083718 bibttp200805083717 bibttp200805083716 bibttp200805083715 maragos (bibttp20080508374) 1985 heijmans (bibttp200805083710) 1994 bibttp200805083721 bibttp200805083720 matheron (bibttp20080508371) 1975 debayle (bibttp200805083719) 2006; 25 bibttp200805083724 bibttp200805083722 bibttp200805083729 bibttp200805083728 bibttp200805083727 bibttp200805083726 bibttp20080508373 bibttp20080508372 bibttp20080508375 choquet (bibttp200805083723) 1966 bibttp20080508377 bibttp20080508376 bibttp20080508379 serra (bibttp20080508378) 1982 |
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Snippet | 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... [...] simulation results show the potential power of the general theory of gray-level SV mathematical morphology in several image analysis and computer vision... |
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SubjectTerms | Algorithms Applied sciences Artificial Intelligence Color Colorimetry - methods Computational modeling Computer science; control theory; systems Computer Simulation Euclidean space Exact sciences and technology Filtering Filtering theory Filters Image analysis Image Enhancement - methods Image Interpretation, Computer-Assisted - methods Image processing Kernel Kernels Mathematical models Mathematical morphology Models, Theoretical Morphological Morphology Nonlinear systems Operators Pattern Recognition, Automated - methods Pattern recognition. Digital image processing. Computational geometry Representations Reproducibility of Results Sensitivity and Specificity Signal analysis Signal processing Signal Processing, Computer-Assisted Studies Vanadium |
Title | Theoretical Foundations of Spatially-Variant Mathematical Morphology Part II: Gray-Level Images |
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