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On the Continuity of Granulometry

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Abstract

One of the most fundamental operators of mathematical morphology, the granulometry operator Ψ t assigning to a compact set (or to a grayscale function) its granulometric opening by a convex set, is generally considered to be upper semicontinuous but not continuous. We consider this a deficiency and intend to rectify it, mainly by an adjustment of convergence assumptions.

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  1. DB Systel GmbH, Jürgen-Ponto-Platz 1, 60329, Frankfurt am Main, Germany

    Bernd Günther

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  1. Bernd Günther
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Correspondence to Bernd Günther.

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Günther, B. On the Continuity of Granulometry. J Math Imaging Vis 46, 29–43 (2013). https://doi.org/10.1007/s10851-012-0364-9

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