Topological Properties of the First Non-Local Digitally Well-Composed Interpolation on n-D Cubical Grids

Autor: Thierry Géraud, Laurent Najman, Nicolas Boutry
Přispěvatelé: Laboratoire de Recherche et de Développement de l'EPITA (LRDE), Ecole Pour l'Informatique et les Techniques Avancées (EPITA)
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Statistics and Probability
digital topology
Computer science
Constraint (computer-aided design)
02 engineering and technology
Mathematical morphology
[INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
Mathematical proof
Image (mathematics)
[MATH.MATH-GN]Mathematics [math]/General Topology [math.GN]
[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing
0202 electrical engineering
electronic engineering
information engineering
mathematical morphology
tree of shapes
Digital topology
Applied Mathematics
Discrete space
Locality
Condensed Matter Physics
Modeling and Simulation
[MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT]
020201 artificial intelligence & image processing
Geometry and Topology
Computer Vision and Pattern Recognition
critical configurations
Algorithm
well-composed images
Interpolation
Zdroj: Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision, Springer Verlag, 2020, 62 (9), pp.1256-1284. ⟨10.1007/s10851-020-00989-y⟩
ISSN: 0924-9907
1573-7683
Popis: International audience; In discrete topology, we like digitally well-composed (shortly DWC) interpolations because they remove pinches in cubical images. Usual well-composed interpolations are local and sometimes self-dual (they treat in a same way dark and bright components in the image). In our case, we are particularly interested in n-D self-dual DWC interpolations to obtain a purely self-dual tree of shapes. However , it has been proved that we cannot have an n-D interpolation which is at the same time local, self-dual, and well-composed. By removing the locality constraint, we have obtained an n-D interpolation with many properties in practice: it is self-dual, DWC, and in-between (this last property means that it preserves the contours). Since we did not published the proofs of these results before, we propose to provide in a first time the proofs of the two last properties here (DWCness and in-betweeness) and a sketch of the proof of self-duality (the complete proof of self-duality requires more material and will come later). Some theoretical and practical results are given.
Databáze: OpenAIRE
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