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Fuzzy-marker-based segmentation using hierarchies

Abstract : This article extends a classical marker-based image segmentation method proposed by Salembier and Garrido in 2000. In the original approach, the segmentation relies on two sets of pixels which play the role of object and background markers. In the proposed extension, the markers are not represented by crisp sets, but by fuzzy ones, i.e., functions of the image domain into the real interval [0, 1] indicating the degree of membership of each pixel to the markers. We show that when the fuzzy markers are indicator functions of crisp sets, the proposed method produces the same result as the original one. We present a linear-time algorithm for computing the result of the proposed method given two fuzzy markers and we establish the correctness of this algorithm. Additionally, we discuss possible applications of the proposed approach, such as adjusting marker strength in interactive image segmentation procedures and optimizing marker locations with gradient descent methods.
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https://hal.archives-ouvertes.fr/hal-03179706
Contributor : Benjamin Perret <>
Submitted on : Wednesday, March 24, 2021 - 1:25:50 PM
Last modification on : Thursday, May 13, 2021 - 2:03:57 PM

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  • HAL Id : hal-03179706, version 1

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Gabriel Barbosa da Fonseca, Benjamin Perret, Romain Negrel, Jean Cousty, Silvio Jamil Ferzoli Guimarães. Fuzzy-marker-based segmentation using hierarchies. International Conference on Discrete Geometry and Mathematical Morphology (DGMM), 2021, Uppsala, Sweden. ⟨hal-03179706⟩

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