Sturmian words, Lyndon words and trees
Theoretical Computer Science
Detection of the discrete convexity of polyominoes
Discrete Applied Mathematics
Digital straightness: a review
Discrete Applied Mathematics - The 2001 international workshop on combinatorial image analysis (IWCIA 2001)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
Shuffle operations on discrete paths
Theoretical Computer Science
On the tiling by translation problem
Discrete Applied Mathematics
Algorithms for polyominoes based on the discrete Green theorem
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
On minimal moment of inertia polyominoes
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
A note on a result of daurat and nivat
DLT'05 Proceedings of the 9th international conference on Developments in Language Theory
An optimal algorithm for detecting pseudo-squares
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Lyndon + Christoffel = digitally convex
Pattern Recognition
A linear time and space algorithm for detecting path intersection
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
A linear time and space algorithm for detecting path intersection in Zd
Theoretical Computer Science
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The notion of convexity translates non-trivially from Euclidean geometry to discrete geometry, and detecting if a discrete region of the plane is convex requires analysis. In this paper we study digital convexity from the combinatorics on words point of view, and provide a fast optimal algorithm checking digital convexity of polyominoes coded by the contour word. The result is based on the Lyndon factorization of the contour word, and the recognition of Christoffel factors that are approximations of digital lines.