Abstract
In this paper we introduce a notion of digital implicit surface in arbitrary dimensions. The digital implicit surface is the result of a morphology inspired digitization of an implicit surface {x ∈ ℝn : f(x) = 0} which is the boundary of a given closed subset of ℝn, {x ∈ ℝn : f(x) ≤ 0}. Under some constraints, the digital implicit surface has some interesting properties, such as k-tunnel freeness. Furthermore, for a large class of the digital implicit surfaces, there exists a very simple analytical characterization.
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Toutant, JL., Andres, E., Largeteau-Skapin, G., Zrour, R. (2014). Implicit Digital Surfaces in Arbitrary Dimensions. In: Barcucci, E., Frosini, A., Rinaldi, S. (eds) Discrete Geometry for Computer Imagery. DGCI 2014. Lecture Notes in Computer Science, vol 8668. Springer, Cham. https://doi.org/10.1007/978-3-319-09955-2_28
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DOI: https://doi.org/10.1007/978-3-319-09955-2_28
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09954-5
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