Generation and recognition of digital planes using multi-dimensional continued fractions

DOI10.1016/j.patcog.2008.11.003zbMath1176.68180OpenAlexW2061610309MaRDI QIDQ834258

Thomas Fernique

Publication date: 19 August 2009

Published in: Pattern Recognition (Search for Journal in Brave)

Full work available at URL: https://hal-lirmm.ccsd.cnrs.fr/lirmm-00379208

zbMATH Keywords

continued fractionsdiscrete geometryBrun algorithmsubstitutiondual mapdigital plane generationdigital plane recognition

Mathematics Subject Classification ID

Pattern recognition, speech recognition (68T10)

Related Items (14)

An output-sensitive algorithm to compute the normal vector of a digital plane ⋮ Two plane-probing algorithms for the computation of the normal vector to a digital plane ⋮ A study of Jacobi-Perron boundary words for the generation of discrete planes ⋮ Combinatorial generation of planar sets ⋮ Approximation of digital surfaces by a hierarchical set of planar patches ⋮ A combinatorial technique for generation of digital plane using GCD ⋮ Brun expansions of stepped surfaces ⋮ An optimized framework for plane-probing algorithms ⋮ About thin arithmetic discrete planes ⋮ Discrete segments of \(\mathbb{Z}^3\) constructed by synchronization of words ⋮ An alternative definition for digital convexity ⋮ A combinatorial approach to products of Pisot substitutions ⋮ Arithmetic Discrete Planes Are Quasicrystals ⋮ Digital Plane Recognition with Fewer Probes

Cites Work

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• Digital planarity -- a review
• Geometric interpretation of the Euclidean algorithm and recognition of segments
• Combinatorics on patterns of a bidimensional Sturmian sequence
• On the topology of an arithmetic plane
• Some properties of invertible substitutions of rank \(d\), and higher dimensional substitutions.
• Plane digitization and related combinatorial problems
• Digital straightness -- a review
• Functional stepped surfaces, flips, and generalized substitutions
• Generation and Recognition of Digital Planes Using Multi-dimensional Continued Fractions
• Higher dimensional extensions of substitutions and their dual maps
• Pisot substitutions and Rauzy fractals

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