Abstract
We propose a new class of hyper-connections in order to improve the consistency of hyper-connected filters and to simplify their design. Our idea relies on the principle that the decomposition of an image into h-components must be necessary and sufficient. We propose a set of three equivalent axioms to achieve this goal. We show that an existing h-connection already fulfils these properties and we propose a new h-connection based on flat functions that also fulfils these axioms. Finally we show that this new class brings several new interesting properties that simplify the use of h-connections and guarantee the consistency of h-connected filters as they ensure that: 1) every deletion of image components will effectively modify the filtered image 2) a deleted component can not re-appear in the filtered image.
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Perret, B., Lefèvre, S., Collet, C. (2011). Toward a New Axiomatic for Hyper-Connections. In: Soille, P., Pesaresi, M., Ouzounis, G.K. (eds) Mathematical Morphology and Its Applications to Image and Signal Processing. ISMM 2011. Lecture Notes in Computer Science, vol 6671. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21569-8_8
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DOI: https://doi.org/10.1007/978-3-642-21569-8_8
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