Discrete Combinatorial Surfaces

Francon, J

doi:10.1006/gmip.1995.1003

Cited by 54 publications

(52 citation statements)

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“…4, we obtain 1720 instead of 1412 in Table 8. We verified that our results for m = 6 are the same as those in reference [8], which are illustrated in Fig. 2.…”

Section: Local Configurations In Discrete Combinatorial Surfacessupporting

confidence: 88%

“…16) is similar to the definition of a two-dimensional combinatorial manifold with (resp. without) boundary in reference [8]. In fact, the notion of cyclic stars in Definition 13 corresponds to that of umbrellas in [8].…”

Section: Topological Characteristics Of Stars In Two Dimensionsmentioning

confidence: 99%

“…For the 6-neighborhood system, the definition of discrete combinatorial surfaces is given by Françon in [8] and he showed that there are 6 local configurations of discrete surfaces for the 6-neighborhood system as illustrated in Fig. 2.…”

Section: Introductionmentioning

confidence: 99%

“…In [8], however, the 18-and 26-neighborhoods are not practically treated so that we do not see how to generate discrete combinatorial surfaces for the 18-and 26-neighborhood systems, even if the mathematical definition is given for any neighborhood system. Morgenthaler et al defined discrete surfaces by using the point connectivity based on the Jordan surface theorem; any Jordan surface divides the space into two [18].…”

Section: Introductionmentioning

confidence: 99%

“…2. The 6 local configurations of discrete combinatorial surfaces for the 6-neighborhood system [8,10,11] where the five left ones appears in discrete planes [9,13].…”

Section: Introductionmentioning

confidence: 99%

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Local configurations in discrete combinatorial surfaces

Kenmochi

Nomura

2007

Image and Vision Computing

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Representing discrete objects by polyhedral complexes, we can define all conceivable topological characteristics of points in discrete objects, namely those of vertices of polyhedral complexes. Such a topological characteristic is determined for each point by observing a configuration of object points in the 3 × 3 × 3 local point set of its neighbors. We study a topological characteristic such that the point is in the boundary of a 3D polyhedral complex and the boundary forms a 2D combinatorial surface. By using the topological characteristic, we present an algorithm which examines whether the central point of a local point set is in a combinatorial surface, and show how many local point configurations exist in combinatorial surfaces in a 3D discrete space.

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“…4, we obtain 1720 instead of 1412 in Table 8. We verified that our results for m = 6 are the same as those in reference [8], which are illustrated in Fig. 2.…”

Section: Local Configurations In Discrete Combinatorial Surfacessupporting

confidence: 88%

Section: Topological Characteristics Of Stars In Two Dimensionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…2. The 6 local configurations of discrete combinatorial surfaces for the 6-neighborhood system [8,10,11] where the five left ones appears in discrete planes [9,13].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations