Abstract
In this paper we define and study the notion of digital flatness. We extend to dimension two various definitions and classical results about digital lines and rays. In particular, we resolve a conjecture of Maurice Nivat restricted to the case of digital planes, and define and characterize 2D Sturmian rays.
Chapter PDF
Similar content being viewed by others
Keywords
References
Amir, A., Benson, G.: Two-dimensional periodicity and its applications. In: Proc. 3rd ACM-SIAM Symp. on Discrete Algorithms, pp. 440–452 (1992)
Brimkov, V.E.: Digital flatness and related combinatorial problems, CITR-TR-120, University of Auckland, New Zealand, p. 44 (2002), http://www.citr.auckland.ac.nz/techreports/?year=2002
Brimkov, V.E.: Notes on digital flatness, TR 2002-01, Laboratory on Signal, Image and Communication, CNRS, University of Poitiers, France, p. 52 (July 2002)
Brons, R.: Linguistic methods for description of a straight line on a grid. Computer Graphics Image Processing 2, 48–62 (1974)
Bruckstein, A.M.: Self-similarity properties of digitized straight lines. Contemp. Math. 119, 1–20 (1991)
Coven, E., Hedlund, G.: Sequences with minimal block growth. Math. Systems Theory 7, 138–153 (1973)
Epifanio, C., Koskas, M., Mignosi, F.: On a conjecture on bidimensional words, http://dipinfo.math.unipa.it/mignosi/periodicity.html
Galil, Z., Park, K.: Truly alphabet-independent two-dimensional pattern matching. In: Proc. 33rd IEEE Symp. Found, pp. 247–256 (1992)
Grünbaum, B., Shephard, G.C.: Tilings and patterns. Freeman & Co, New York (1987)
Kong, T.Y., Rosenfeld, A.: Digital topology: introduction and survey. Comput. Vision Graphics Image Processing 48, 357–393 (1989)
Lunnon, W.F., Pleasants, P.A.B.: Characterization of two-distance sequences. J. Austral. Math. Soc (Ser. A) 53, 198–218 (1992)
Mignosi, F., Perillo, G.: Repetitions in the Fibonacci infinite words. RAIRO Theor. Inform. Appl. 26, 199–204 (1992)
Morse, M., Hedlund, G.A.: Symbolic dynamics II: Sturmian sequences. Amer. J. Math. 61, 1–42 (1940)
Nivat, M.: Invited talk at ICALP 1997. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds.) ICALP 1997. LNCS, vol. 1256. Springer, Heidelberg (1997)
Rosenfeld, A., Klette, R.: Digital straightness. Electronic Notes in Theoretical Computer Science 46 (2001), http://www.elsevier.nl/locate/entcs/volume46.html
Rosenfeld, A.: Digital straight line segments. IEEE Trans. Computers 23, 1264–1269 (1974)
Smeulders, A.W.M., Dorst, L.: Decomposition of discrete curves into piecewise segments in linear time. Contemporary Mathematics 119, 169–195 (1991)
Wu, A.Y.: On the chain code of a line. IEEE Trans. Pattern Analysis Machine Intelligence 4, 347–353 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Brimkov, V.E., Barneva, R.P. (2003). Digital Flatness. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds) Discrete Geometry for Computer Imagery. DGCI 2003. Lecture Notes in Computer Science, vol 2886. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-39966-7_6
Download citation
DOI: https://doi.org/10.1007/978-3-540-39966-7_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20499-2
Online ISBN: 978-3-540-39966-7
eBook Packages: Springer Book Archive
