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ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
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Journal of Mathematical Imaging and Vision
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Computer Vision and Image Understanding
Connectivity in Digital Pictures
Journal of the ACM (JACM)
Connected filtering and segmentation using component trees
Computer Vision and Image Understanding
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Fundamenta Informaticae - Special issue on mathematical morphology
Digital Image Processing Methods
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SIBGRAPI '99 Proceedings of the XII Brazilian Symposium on Computer Graphics and Image Processing
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Morphological Image Analysis: Principles and Applications
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A multiscale approach to connectivity
Computer Vision and Image Understanding
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Journal of Mathematical Imaging and Vision
Levelings, Image Simplification Filters for Segmentation
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Multiscale Connected Operators
Journal of Mathematical Imaging and Vision
Geodesy and connectivity in lattices
Fundamenta Informaticae
IEEE Transactions on Image Processing
Flat zones filtering, connected operators, and filters by reconstruction
IEEE Transactions on Image Processing
Levelings and Geodesic Reconstructions
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Morphological Connected Filtering on Viscous Lattices
Journal of Mathematical Imaging and Vision
Adjacency stable connected operators and set levelings
Image and Vision Computing
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This paper studies connectivity aspects that arise in image operators that process connected components. The focus is on morphological image analysis (i.e., on increasing image operators) and, in particular, on a robustness property satisfied by certain morphological filters that is denominated the strong property. The behavior of alternated compositions of openings and closings is investigated under certain assumptions, particularly connectedness and a connected component preserving condition. It is shown that these conditions cannot in general guarantee the strong property of certain connected alternated filters because of issues related to the locality of the filters. As treated in the paper, there have been a series of misunderstandings in the literature concerning this topic, and it is important to clarify them. The root cause of those problems is discussed, and a solution is indicated. The class of connected openings and closings used to build connected alternated filters should therefore be defined to avoid such situations, since the strong property of alternated filters should be a distinctive characteristic of this class.