Abstract
In this paper a notion of lighting function is introduced as an axiomatized formalization of the “face membership rules” suggested by Kovalevsky. These functions are defined in the context of the framework for digital topology previously developed by the authors. This enlarged framework provides the (α, β)-connectedness (α, β ε {6,18, 26}) defined on ℤ3 within the graph-based approach to digital topology. Furthermore, the Kong-Roscoe (α, β)-surfaces, with (α, β) ≠ (6, 6), (18, 6), are also found as particular cases of a more general notion of digital surface.
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References
R. Ayala, E. Dominguez, A.R. Francés, A.Quintero, J. Rubio. On surfaces in digital topology. Proc. of the 5th Workshop on Discrete Geometry for Computer Imagery DGCI'95. (1995) 271–276.
R. Ayala, E. Domínguez, A.R. Francés, A.Quintero. Determining the components of the complement of a digital (n-1)-manifold in ℤn. Proc. of the 6th Int. Workshop on Discrete Geometry for Computer Imagery DGCI'96. Lectures Notes in Computer Science. 1176 (1996) 163–176.
E. Domínguez, A.R. Francés, A. Márquez. A Framework for Digital Topology. Proc. of the IEEE Int. Conf. on Systems, Man, and Cybernetics. 2 (1993) 65–70.
J. Françon. On recent trends in discrete geometry in computer science. Proc. of the 6th Int. Workshop on Discrete Geometry for Computer Imagery DGCI'96. Lectures Notes in Computer Science. 1176 (1996) 163–176.
E. Khalimsky, R. Kopperman, P.R. Meyer. Computer Graphics and connected topologies on finite ordered sets. Topology and its Applications. 36 (1990) 1–17.
T.Y. Kong, A.W. Roscoe. Continuous Analogs of Axiomatized Digital Surfaces. Computer Vision, Graphics, and Image Processing. 29 (1985) 60–86.
T.Y. Kong, A. Rosenfeld. Digital Topology: Introduction and Survey. Computer Vision, Graphics, and Image Processing. 48 (1989) 357–393.
V.A. Kovalevsky. Finite topology as applied to image analysis. Computer Vision, Graphics, and Image Processing. 46 (1989) 141–161.
R. Malgouyres. A definition of surfaces of ℤ3. Proc. of the 3th Workshop on Discrete Geometry for Computer Imagery DGCI'93. (1993) 23–34.
G. Bertrand, R. Malgouyres. Some topological properties of Discrete Surfaces. Proc. of the 6th Int. Workshop on Discrete Geometry for Computer Imagery DGCI'96. Lectures Notes in Computer Science. 1176 (1996) 325–336.
D.G. Morgenthaler, A. Rosenfeld. Surfaces in Three-Dimensional Digital Images. Information and Control. 51 (1981) 227–247.
C.P. Rourke, B.J. Sanderson. Introduction to Piecewise linear topology. Ergebnisse der Math., 69. Springer, 1972.
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Ayala, R., Domínguez, E., Francés, A.R., Quintero, A. (1997). Digital lighting functions. In: Ahronovitz, E., Fiorio, C. (eds) Discrete Geometry for Computer Imagery. DGCI 1997. Lecture Notes in Computer Science, vol 1347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0024836
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DOI: https://doi.org/10.1007/BFb0024836
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