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Morphological Amoebas Are Self-snakes

Abstract

This paper is concerned with amoeba median filtering, a structure-adaptive morphological image filter. It has been introduced by Lerallut et al. in a discrete formulation. Experimental evidence shows that iterated amoeba median filtering leads to segmentation-like results that are similar to those obtained by self-snakes, an image filter based on a partial differential equation. We establish this correspondence by analysing a space-continuous formulation of iterated amoeba median filtering. We prove that in the limit of vanishing radius of the structuring elements, iterated amoeba median filtering indeed approximates the partial differential equation of self-snakes. This result holds true under very general assumptions on the metric used to construct the amoebas. We present experiments with discrete iterated amoeba median filtering that confirm qualitative and quantitative predictions of our analysis.

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Correspondence to Martin Welk.

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Welk, M., Breuß, M. & Vogel, O. Morphological Amoebas Are Self-snakes. J Math Imaging Vis 39, 87–99 (2011). https://doi.org/10.1007/s10851-010-0228-0

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Keywords

  • Morphological amoebas
  • Self-snakes
  • Median filtering
  • Mathematical morphology
  • Partial differential equations