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Grain Filters

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Abstract

Motivated by operators simplifying the topographic map of a function, we study the theoretical properties of two kinds of “grain” filters. The first category, discovered by L. Vincent, defines grains as connected components of level sets and removes those of small area. This category is composed of two filters, the maxima filter and the minima filter. However, they do not commute. The second kind of filter, introduced by Masnou, works on “shapes”, which are based on connected components of level sets. This filter has the additional property that it acts in the same manner on upper and lower level sets, that is, it commutes with an inversion of contrast. We discuss the relations of Masnou's filter with other classes of connected operators introduced in the literature. We display some experiments to show the main properties of the filters discussed above and compare them.

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Authors and Affiliations

  1. Department de Tecnologia, Universitat Pompeu-Fabra, Passeig de Circumvalació 8, 08003, Barcelona, Spain

    Vicent Caselles

  2. CMLA, ENS Cachan, 61 Av. du President Wilson, 94235, Cachan Cedex, France

    Pascal Monasse

Authors
  1. Vicent Caselles
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  2. Pascal Monasse
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Caselles, V., Monasse, P. Grain Filters. Journal of Mathematical Imaging and Vision 17, 249–270 (2002). https://doi.org/10.1023/A:1020715626538

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