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2. Algorithms for Pixelwise Shape Deformations Preserving Digital Convexity

Author

Tarsissi, Lama, Kenmochi, Yukiko, Djerroumi, Hadjer, Coeurjolly, David, Romon, Pascal, Borel, Jean-Pierre, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Baudrier, Étienne, editor, Naegel, Benoît, editor, Krähenbühl, Adrien, editor, and Tajine, Mohamed, editor

Published
2022
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5. Some New Results on Palindromic Factors of Billiard Words

Author

Borel, Jean-Pierre, Reutenauer, Christophe, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Dough, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, De Felice, Clelia, editor, and Restivo, Antonio, editor

Published
2005
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6. Convexity preserving deformations of digital sets: Characterization of removable and insertable pixels

Author

Tarsissi, Lama, Kenmochi, Yukiko, Romon, Pascal, Cœurjolly, David, Borel, Jean-Pierre, Tarsissi, Lama, Sorbonne university Abu Dhabi, Laboratoire d'Informatique Gaspard-Monge (LIGM), École des Ponts ParisTech (ENPC)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Equipe Image - Laboratoire GREYC - UMR6072, Groupe de Recherche en Informatique, Image et Instrumentation de Caen (GREYC), Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU)-École Nationale Supérieure d'Ingénieurs de Caen (ENSICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Origami (Origami), Laboratoire d'InfoRmatique en Image et Systèmes d'information (LIRIS), Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), and LIGM - Laboratoire d'Informatique Gaspard-Monge

Subjects
[MATH] Mathematics [math], [MATH]Mathematics [math]
Abstract

In this paper, we are interested in digital convexity. This notion is applied in several domains like image processing and discrete tomography. We choose to study the inflation and deflation of digital convex sets while maintaining the convexity property. Knowing that any digital convex set can be read and identified by its boundary word, we use the combinatorics on words perspective instead of a purely geometric approach. In this context, we characterize the points that can be added or removed over the digital convex sets without loosing its convexity. Some algorithms are given at the end of each section with examples on each process.

Published
2022

18. Digital Straight Lines and Billiard Words

Author

Borel, Jean-Pierre, DMI, XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), and Vieceli, Yolande

Subjects
ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2009

19. Complexity and palindromic complexity of billiard words

Author

Borel, Jean-Pierre, Laboratoire d'Arithmétique, de Calcul formel et d'Optimisation (LACO), Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM), Brlek & Reutenauer, Arithmétique, Cryptographie, Codage, and Vieceli, Yolande

Subjects
ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2005

20. Some new results on palindromic factors of billard words. Developments in language theory

Author

Borel, Jean-Pierre, Reutenauer, Christophe, Vieceli, Yolande, Laboratoire d'Arithmétique, de Calcul formel et d'Optimisation (LACO), Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM), Arithmétique, Cryptographie, and Codage

Subjects
ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2005

21. Palindromic factors of billard words

Author

Borel, Jean-Pierre, Reutenauer, Christophe, Vieceli, Yolande, Laboratoire d'Arithmétique, de Calcul formel et d'Optimisation (LACO), Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM), Arithmétique, Cryptographie, and Codage

Subjects
ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2005

23. On Christoffel classes

Author

Borel, Jean-Pierre, Reutenauer, Christophe, Borel, Jean-Pierre, and Reutenauer, Christophe

Abstract

We characterize conjugation classes of Christoffel words (equivalently of standard words) by the number of factors. We give several geometric proofs of classical results on these words and sturmian words.

Published
2006

27. Some New Results on Palindromic Factors of Billiard Words.

Author

Felice, Clelia, Restivo, Antonio, Borel, Jean-Pierre, and Reutenauer, Christophe

Abstract

For heuristic reasons billiard words may have more palindromic factors than any other words. Many results are already known, concerning the palindromic factors and the palindromic prefixes of Sturmian words and billiard words on two letters. We give general results concerning multidimensional billiard words, which describe very different situations. In some cases, these words have arbitrary long palindromic prefix factors. In other cases, at the opposite, they have finitely many distinct palindromic factors. Keywords: Words, languages, Sturmian, Billiard, palindromes. AMS classification: 68R15. [ABSTRACT FROM AUTHOR]

Published
2005
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33. A geometrical approach to Palindromic Factors of Standard Billiard Words.

Author

Borel, Jean-Pierre

Subjects
*FORMAL languages, *LANGUAGE & languages, *MACHINE theory, *PALINDROMES, *ALGORITHMS
Abstract

Many results are already known, concerning the palindromic factors and the palindomic prefixes of Standard billiard words, i.e., Sturmian words and billiard words in any dimension, starting at the origin. We give new geometrical proofs of these results, especially for the existence in any dimension of Standard billiard words with arbitrary long palindromic prefixes. [ABSTRACT FROM AUTHOR]

Published
2007

38. On Christoffel classes

Author

Borel, Jean-Pierre, Reutenauer, Christophe, Borel, Jean-Pierre, and Reutenauer, Christophe

Abstract

We characterize conjugation classes of Christoffel words (equivalently of standard words) by the number of factors. We give several geometric proofs of classical results on these words and sturmian words.

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