On-line construction of the convex hull of a simple polyline
Information Processing Letters
Quasi-Monotonic sequences: theory, algorithms and applications
SIAM Journal on Algebraic and Discrete Methods
Sturmian words, Lyndon words and trees
Theoretical Computer Science
An output sensitive algorithm for discrete convex hulls
Computational Geometry: Theory and Applications
Digital lines and digital convexity
Digital and image geometry
Detection of the discrete convexity of polyominoes
Discrete Applied Mathematics
Lyndon words, permutations and trees
Theoretical Computer Science - WORDS
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)
Algorithms on Strings
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
On the tiling by translation problem
Discrete Applied Mathematics
Combinatorial view of digital convexity
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Maximum Likelihood Estimation of Markov-Process Blob Boundaries in Noisy Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Straight Lines and Convexity of Digital Regions
IEEE Transactions on Pattern Analysis and Machine Intelligence
An optimal algorithm for detecting pseudo-squares
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Digital Convexity, Straightness, and Convex Polygons
IEEE Transactions on Pattern Analysis and Machine Intelligence
Arithmetic discrete planes are quasicrystals
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Two linear-time algorithms for computing the minimum length polygon of a digital contour
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
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Theoretical Computer Science
Equations on palindromes and circular words
Theoretical Computer Science
A linear time and space algorithm for detecting path intersection in Zd
Theoretical Computer Science
About thin arithmetic discrete planes
Theoretical Computer Science
Two linear-time algorithms for computing the minimum length polygon of a digital contour
Discrete Applied Mathematics
Asymptotic analysis and random sampling of digitally convex polyominoes
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Generic algorithms for factoring strings
Information Theory, Combinatorics, and Search Theory
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Discrete geometry redefines notions borrowed from Euclidean geometry creating a need for new algorithmical tools. The notion of convexity does not translate trivially, and detecting if a discrete region of the plane is convex requires a deeper analysis. To the many different approaches of digital convexity, we propose the combinatorics on words point of view, unnoticed until recently in the pattern recognition community. In this paper, we provide first a fast optimal algorithm checking digital convexity of polyominoes coded by their contour word. The result is based on linear time algorithms for both computing the Lyndon factorization of the contour word and the recognition of Christoffel factors that are approximations of digital lines. By avoiding arithmetical computations the algorithm is much simpler to implement and much faster in practice. We also consider the convex hull computation and relate previous work in combinatorics on words with the classical Melkman algorithm.