Abstract
In this paper, we provide an unified view of two definitions of digital lines in 3D via the use of lattice theory and specific projections of the lattice ℤ3. We use this unified vision to explain the extension of the definition of Voss [1] to an arbitrary dimension and we show how to extend the definition of Figueiredo and Reveillès [2] to an arbitrary dimension.
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Voss, K.: Discrete Images, Objects and Functions in ℤn. Springer, Heidelberg (1993)
Figueiredo, O., Reveillès, J.P.: New results about 3D digital lines. In: Melter, R.A., Wu, A.Y., Latecki, L. (eds.) Vision Geometry V., vol. 2826, pp. 98–108 (1996)
Klette, R., Rosenfeld, A.: Digital Geometry. Morgan Kaufmann, San Francisco (2004)
Kim, C.: Three-dimensional digital line segments. IEEE Trans. Pattern Analysis and Machine Intelligence 5, 231–234 (1983)
Debled-Rennesson, I.: Etude et reconnaissance des droites et plans discrets. Ph.D thesis, Université Louis Pasteur - Strasbourg (1995)
Coeurjolly, D., Debled-Rennesson, I., Teytaud, O.: Segmentation and Length Estimation of 3D Discrete Curves. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 299–317. Springer, Heidelberg (2002)
Reveillès, J.P.: Géométrie discrète, calcul en nombres entiers et algorithmique. Thèse d’etat, Université Louis Pasteur, Strasbourg (1991)
Figueiredo, O., Reveillès, J.P.: A contribution to 3D digital lines. In: Proc. Discrete Geometry for Computer Imagery, Université d’Auvergne - LLAIC, pp. 187–198 (1995)
Ibanez, L., Hamitouche, C., Roux, C.: A Vectorial Algorithm for Tracing Discrete Straight Lines in N-Dimensional Generalized Grids. IEEE Trans. Vis. Comput. Graph. 7(2), 97–108 (2001)
Klette, R.: The m-dimensional grid point space. Computer Vision, Graphics, and Image Processing 30, 1–12 (1985)
Stojmenovic, I., Tosic, R.: Digitization Schemes and the Recognition of Digital Straight Lines, Hyperplanes, and Flats in Arbitrary Dimensions. Contemporary Mathematics 119, 197–212 (1991)
Reveillès, J.P.: The Geometry of the Intersection of Voxel Spaces. In: Fourey, S., Herman, G.T., Kong, T.Y. (eds.) IWCIA 2001. Electronic Notes in Theoretical Computer Science, vol. 46, pp. 1–24. Elsevier, Amsterdam (2001)
Debled, I., Reveillès, J.P.: A linear algorithm for segmentation of digital curves. In: 3rd IWPIA (1994)
Arnold, V.: Higher dimensional Continued Fractions. Regular and Chaotics Dynamics 33, 10–17 (1998)
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Feschet, F., Reveillès, JP. (2006). A Generic Approach for n-Dimensional Digital Lines. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds) Discrete Geometry for Computer Imagery. DGCI 2006. Lecture Notes in Computer Science, vol 4245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11907350_3
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DOI: https://doi.org/10.1007/11907350_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47651-1
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