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First Steps in the Algorithmic Reconstruction of Digital Convex Sets

  • Paolo Dulio
  • Andrea Frosini
  • Simone Rinaldi
  • Lama TarsissiEmail author
  • Laurent Vuillon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10432)

Abstract

Digital convex (DC) sets plays a prominent role in the framework of digital geometry providing a natural generalization to the concept of Euclidean convexity when we are dealing with polyominoes, i.e., finite and connected sets of points. A result by Brlek, Lachaud, Provençal and Reutenauer (see [4]) on this topic sets a bridge between digital convexity and combinatorics on words: the boundary word of a DC polyomino can be divided in four monotone paths, each of them having a Lyndon factorization that contains only Christoffel words.

The intent of this paper is to provide some local properties that a boundary words has to fulfill in order to allow a single point modifications that preserves the convexity of the polyomino.

Keywords

Digital convexity Discrete geometry Discrete tomography Reconstruction problem 

Notes

Acknowledgment

This study has been partially supported by INDAM - GNCS Project 2017.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Paolo Dulio
    • 1
  • Andrea Frosini
    • 2
  • Simone Rinaldi
    • 3
  • Lama Tarsissi
    • 4
    Email author
  • Laurent Vuillon
    • 4
  1. 1.Dipartimento di Matematica “F. Brioschi”Politecnico di MilanoMilanoItaly
  2. 2.Dipartimento di Matematica e Informatica “U. Dini”Università di FirenzeFirenzeItaly
  3. 3.Dipartimento di Ingegneria dell’Informazione e Scienze MatematicheUniversità di SienaSienaItaly
  4. 4.Laboratoire de MathématiquesUniversité de Savoie Mont Blanc, CNRS UMR 5127Le Bourget du LacFrance

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