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| Reference : Anchors of morphological operators and algebraic openings |
| Parts of books : Contribution to collective works | |||
| Engineering, computing & technology : Electrical & electronics engineering | |||
| http://hdl.handle.net/2268/17697 | |||
| Anchors of morphological operators and algebraic openings | |
| English | |
Van Droogenbroeck, Marc  [Université de Liège - ULg > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Télécommunications >] | |
| Aug-2009 | |
| Advances in Imaging and Electron Physics | |
| Hawkes, Peter | |
| Elsevier | |
| volume 158 | |
| 173-201 | |
| 9780123747693 | |
| [en] Mathematical morphology ; Anchor ; Opening ; Algorithm ; Algebra | |
| [en] Opening and closing operators play an important role in the field of mathematical morphology,
mainly because of their useful property of idempotence, which is similar to the notion of ideal filter in linear filtering. From a theoretical point of view, the study of openings has focused on the algebraic characterization of the operators themselves. Morphological filters have been studied for more than 30 years; the effects of the first filters (erosions, openings, and so on) are known in depth. In discussing the effects of a filter, it is not only the operator that is studied but also its relationship with the processed function or image and, in the particular case of mathematical morphology, the structuring element. In addition, there are several approaches to this analysis. For example, the analysis can consider the whole function or some subparts of the function, as in Van Droogenbroeck and Buckley (2005), who introduced the notion of morphological anchors. Anchors were defined in the context of morphological openings, as defined by the cascade of an erosion followed by a dilation. The extension to other kinds of openings is not straightforward. Despite the fact that all morphological openings induce the appearance of anchors, some opening operators (like the quantization opening defined in this chapter) might have no anchors. This chapter presents the theory of anchors related to morphological erosions and openings, and establishes some properties for the extended scope of algebraic openings. It is shown under which circumstances anchors exist for algebraic openings and how to locate some anchors; for example, it suffices for an opening to be spatial or shift-invariant to guarantee the existence of anchors. As for morphological openings, the existence of anchors may help clarify some algorithms or lead to new algorithms to compute algebraic openings. | |
| Intelsig | |
| Researchers ; Professionals ; Students ; General public | |
| http://hdl.handle.net/2268/17697 | |
| 10.1016/S1076-5670(09)00010-X |
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