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Morphological Amoebas are SelfSnakes
"... This paper is concerned with amoeba median filtering, a structureadaptive 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 segmentationlike results that are similar to those ob ..."
Abstract

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This paper is concerned with amoeba median filtering, a structureadaptive 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 segmentationlike results that are similar to those obtained by selfsnakes, an image filter based on a partial differential equation. We establish this correspondence by analysing a spacecontinuous formulation of iterated 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 selfsnakes. 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.
Mathematical Morphology in Computer Graphics, Scientific Visualization and Visual Exploration
"... Abstract. Historically, mathematical morphology has primarily focused on the processing and analysis of twodimensional image data. In this paper, we survey a number of other areas where mathematical morphology finds fruitful application, such as computer graphics and solid modeling; path planning; ..."
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Abstract. Historically, mathematical morphology has primarily focused on the processing and analysis of twodimensional image data. In this paper, we survey a number of other areas where mathematical morphology finds fruitful application, such as computer graphics and solid modeling; path planning; filtering, segmentation and visualization of volume data; or visual exploration of highdimensional data. We also mention techniques for accelerating morphological computations by using graphics hardware (GPU computing).