Abstract
In this paper we study the relationship between the Euclidean and the discrete world thru two operations based on the Euclidean scaling function: the discrete smooth scaling and the discrete based geometrical simplification.
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Andres, E., Menon, R., Sibata, C., Acharya, R.: Rational bitmap scaling. Pattern Recognition Letters 17(14), 1471–1475 (1996)
Cohen-Or, D., Kaufman, A.: Fundamentals of surface voxelization. Graphical models and image processing 57(6), 453–461 (1995)
Andres, E., Menon, R., Acharya, R., Sibata, C.: Discrete linear objects in dimension n: The standard model. Graphical Models 65, 92–111 (2003)
Andres, E., Acharya, R., Sibata, C.: The supercover 3d polygon. In: Discrete Geometry for Computer Imagery, Lyon, France. LNCS, pp. 237–242. Springer, Heidelberg (1996)
Andres, E., Nehlig, P., Françon, J.: Supercover of straight lines, planes and triangles. In: Ahronovitz, E. (ed.) DGCI 1997. LNCS, vol. 1347, pp. 243–257. Springer, Heidelberg (1997)
Lincke, C., Wuthrich, W.: Towards a unified approach between digitization of linear objects and discrete analytical objects. In: Skala, V. (ed.) WSCG 2000 Workshop, pp. 124–131 (2000)
Breton, R., Sivignon, I., Dupont, F., Andrès, É.: Towards an invertible euclidean reconstruction of a discrete object. In: Nyström, I., Sanniti di Baja, G., Svensson, S. (eds.) DGCI 2003. LNCS, vol. 2886, pp. 246–256. Springer, Heidelberg (2003)
Dexet, M., Andrès, É.: Linear discrete line recognition and reconstruction based on a generalized preimage. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds.) IWCIA 2006. LNCS, vol. 4040, pp. 174–188. Springer, Heidelberg (2006)
Françon, J., Schramm, J.M., Tajine, M.: Recognizing arithmetic straight lines and planes. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 141–150. Springer, Heidelberg (1996)
Rosenfeld, A., Klette, R.: Digital straightness. In: UMD (2001)
Reveillès, J.P.: Géométrie discrète, Calcul en nombres entiers et algorithmique. Ph.D thesis, Université Louis Pasteur, Strasbourg, France (1991)
Dorst, L., Smeulders, A.: Discrete representation of straight lines. IEEE Transactions on Pattern Analysis and Machine Intelligence 6(4), 450–463 (1984)
Tajine, M., Ronse, M.: Preservation of topolgy by hausdorff discretization and comparison to other discretization schemes. Theoretical Computer Science 283(1), 243–268 (2002)
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Largeteau-Skapin, G., Andres, E. (2006). Two Discrete-Euclidean Operations Based on the Scaling Transform. 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_4
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DOI: https://doi.org/10.1007/11907350_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47651-1
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