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A 2D and 3D discrete bisector function based on annulus

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Abstract

The bisector function is an important tool for analyzing and filtering Euclidean skeletons. In this paper, we are proposing a new way to compute 2D and 3D discrete bisector function based on annuli. From a continuous point of view, a point that belongs to the medial axis is the center of a maximal ball that hits the background in more than one point. The maximal angle between those points is expected to be high for most of the object points and corresponds to the bisector angle. This logic is not really applicable in the discrete space since we may miss some background points that can lead to small bisector angles. In this work we use annuli to find the background points in order to compute the bisector angle. Our approach offers the possibility to change the thickness of the annulus at a given point and is thus flexible when computing skeletons. Our work can be extended to nD and we propose the nD algorithm.

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Authors and Affiliations

  1. Laboratoire XLIM UMR CNRS 7252, ASALI, Université de Poitiers, Bld Marie et Pierre Curie, BP 30179, 86962, Futuroscope Chasseneuil Cedex, France

    Rita Zrour, Eric Andres, Sangbé Sidibe, Raphael Lenain & Gaelle Largeteau-Skapin

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  1. Rita Zrour
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  2. Eric Andres
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  3. Sangbé Sidibe
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  4. Raphael Lenain
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  5. Gaelle Largeteau-Skapin
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Correspondence to Rita Zrour.

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Zrour, R., Andres, E., Sidibe, S. et al. A 2D and 3D discrete bisector function based on annulus. Pattern Anal Applic 24, 1135–1148 (2021). https://doi.org/10.1007/s10044-021-00973-1

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