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Anamorphoses and Flat Morphological Operators on Power Lattices

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Abstract

Flat morphological operators are operators on grey-level images derived from increasing set operators by a combination of thresholding and stacking. For analog grey-levels, they commute with anamorphoses or contrast mappings, that is, continuous increasing grey-level transformations; when the underlying set operator is upper semi-continuous, they also commute with thresholding. For bounded discrete grey-levels, commutation with increasing grey-level transformations and with thresholding is guaranteed, without any continuity conditions.

In this paper we consider flat operators for images defined on an arbitrary space of points and taking their values in an arbitrary complete lattice. We study their commutation with increasing transformations of values. This requires some continuity requirements on the transformations of values or on the underlying set operator, which are expressed in terms of the lattice of values. We obtain as particular cases the known conditions for analog and discrete grey-levels, and also new conditions for other examples of values: multivalued vectors or any finite set of values.

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  1. LSIIT UMR 7005 CNRS-ULP, Parc d’Innovation, Boulevard Sébastien Brant, BP 10413, 67412, Illkirch Cedex, France

    Christian Ronse

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  1. Christian Ronse
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Correspondence to Christian Ronse.

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Ronse, C. Anamorphoses and Flat Morphological Operators on Power Lattices. Acta Appl Math 103, 59–85 (2008). https://doi.org/10.1007/s10440-008-9219-1

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  • DOI: https://doi.org/10.1007/s10440-008-9219-1

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