Implicit Digital Surfaces in Arbitrary Dimensions

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 ∈ R^n : f (x) = 0 } which is the boundary of a given closed subset of R^n , { x ∈ R^n : 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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18th IAPR International Conference, DGCI 2014, Siena, Italy., Sep 2014, Siena, Italy. Springer Verlag, Lecture Notes in Computer Science, 8668, pp.332-343, Discrete Geometry for Computer Imagery. 〈10.1007/978-3-319-09955-2_28〉
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Jean-Luc Toutant, Eric Andres, Gaëlle Largeteau-Skapin, Rita Zrour. Implicit Digital Surfaces in Arbitrary Dimensions. 18th IAPR International Conference, DGCI 2014, Siena, Italy., Sep 2014, Siena, Italy. Springer Verlag, Lecture Notes in Computer Science, 8668, pp.332-343, Discrete Geometry for Computer Imagery. 〈10.1007/978-3-319-09955-2_28〉. 〈hal-01019467〉

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