Weak lighting functions and strong 26-surfaces

Domı́nguez, Elena; Francés, Angel R.; Quintero, A.

doi:10.1016/s0304-3975(01)00051-2

Cited by 15 publications

(70 citation statements)

References 18 publications

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“…They are established within the framework for Digital Topology introduced in [1], where we refer to for the precise definitions in a general setting. The reader should be aware that some of the material referred to [5] and [1] has been restated here in terms of the notation introduced in Section 2.…”

Section: Universal (K K)-spaces and Digital Surfacesmentioning

confidence: 99%

“…According to [1] a digital space based on R 3 is a pair (R 3 , f) where f is a lighting function: a certain map of the form f : P(cell 3 (R 3 )) × R 3 → {0, 1} satisfying five axioms, where P(cell 3 (R 3 )) stands for the family of all subsets of cell 3 (R 3 ). Here we simply recall that lighting functions are devised as procedures for associating a continuous analogue to a digital object.…”

Section: Universal (K K)-spaces and Digital Surfacesmentioning

confidence: 99%

“…From each approach distinct facets of the family S kk are revealed. Namely, the original definition, based on continuous analogues, allows to show that, among others, S 26,6 strictly contains the classes of strong 26-surfaces and simplicity 26-surfaces [1,4]. The equivalent plate-based definition of a (k, k)-surface introduced in [3] provides a geometrical interpretation of the elements of S kk as well as a tool to compute the number of different configurations that they may contain in the 26-neighbourhood of a voxel: up to 10,580 for S 26,6 .…”

Section: Main Theoremmentioning

confidence: 99%

“…This will be achieved as an application of the framework for This work has been partially supported by the project MTM2010-20445 MICINN Spain. digital topology in [1]. More precisely, we will use crucially the fact that the (k, k)-surfaces in [3] are exactly the strong separating surfaces of certain universal digital space in the sense of [1]; see [5].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Generalized Simple Surface Points

Ciria

Domı́nguez

Francés

et al. 2013

Discrete Geometry for Computer Imagery

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Abstract. By using exclusively the customary adjacency relations on Z 3 , we generalize the notion of a simple surface point given by Morgenthaler in the 80s. A new definition of simple surface arises, and we show that simple surfaces coincide with the strong separating family of a certain class of digital surfaces defined by means of continuous analogues that, in turn, contains several families of discrete surfaces in the literature.

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Section: Universal (K K)-spaces and Digital Surfacesmentioning

confidence: 99%

Section: Universal (K K)-spaces and Digital Surfacesmentioning

confidence: 99%

Section: Main Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Generalized Simple Surface Points

Ciria

Domı́nguez

Francés

et al. 2013

Discrete Geometry for Computer Imagery

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“…In addition, we establish a further condition that detects the digital surfaces in S U which are strongly separating objects. The family S U consists of all objects which are a digital surface in some homogeneous (26, 6)-connected digital space in the sense of [3]. Moreover, the subset of strongly separating surfaces of S U contains the family of simplicity 26-surfaces and other surfaces in literature as well.…”

mentioning

confidence: 99%

Local Characterization of a Maximum Set of Digital (26,6)-Surfaces

Ciria

Miguel

Domı́nguez

et al. 2005

Discrete Geometry for Computer Imagery

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Abstract. This paper provides a local characterization for a set of digital surfaces S U defined in [6] by mean of continuous analogues. For this, we firstly identify the set of admisible plates for any surface S ∈ S U (i.e., the intersection S ∩ C of S with a unit cube C of Z 3 ). Then, the characterization is given in terms of a graph representing the intersection of plates. In addition, we establish a further condition that detects the digital surfaces in S U which are strongly separating objects. The family S U consists of all objects which are a digital surface in some homogeneous (26, 6)-connected digital space in the sense of [3]. Moreover, the subset of strongly separating surfaces of S U contains the family of simplicity 26-surfaces and other surfaces in literature as well.

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