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Convexity Preserving Contraction of Digital Sets

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Pattern Recognition (ACPR 2019)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12047))

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Abstract

Convexity is one of the useful geometric properties of digital sets in digital image processing. There are various applications which require deforming digital convex sets while preserving their convexity. In this article, we consider the contraction of such digital sets by removing digital points one by one. For this aim, we use some tools of combinatorics on words to detect a set of removable points and to define such convexity-preserving contraction of a digital set as an operation of re-writing its boundary word. In order to chose one of removable points for each contraction step, we present three geometrical strategies, which are related to vertex angle and area changes. We also show experimental results of applying the methods to repair some non-convex digital sets, which are obtained by rotations of convex digital sets.

This work was partly funded by the French National Research Agency, grant agreements ANR-10-LABX-58 (Labex Bézout) and ANR-15-CE40-0006 (CoMeDiC).

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Correspondence to Lama Tarsissi .

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Tarsissi, L., Coeurjolly, D., Kenmochi, Y., Romon, P. (2020). Convexity Preserving Contraction of Digital Sets. In: Palaiahnakote, S., Sanniti di Baja, G., Wang, L., Yan, W. (eds) Pattern Recognition. ACPR 2019. Lecture Notes in Computer Science(), vol 12047. Springer, Cham. https://doi.org/10.1007/978-3-030-41299-9_48

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  • DOI: https://doi.org/10.1007/978-3-030-41299-9_48

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-41298-2

  • Online ISBN: 978-3-030-41299-9

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