Geometric methods for on-line recognition of digital straight-line segments
Computers and Artificial Intelligence
Compression of Chain codes using digital straight line sequences
Pattern Recognition Letters
On the Number of Digital Straight Line Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detecting the straightness of digital curves in O(N) steps
Computer Vision, Graphics, and Image Processing
Geometry of continued fractions
American Mathematical Monthly
On the factors of the Sturmian sequences
Theoretical Computer Science
On the number of linear partitions of the (m,n-grid
Information Processing Letters
On the number of factors of Sturmian words
Theoretical Computer Science
Coding of digital straight lines by continued fractions
Computers and Artificial Intelligence
A New Parameterization of Digital Straight Lines
IEEE Transactions on Pattern Analysis and Machine Intelligence
A new method of analysis for discrete straight lines
Pattern Recognition Letters
Computer Vision and Image Understanding
Discrete convexity, straightness, and the 16-neighborhood
Computer Vision and Image Understanding
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Discrete analytical hyperplanes
Graphical Models and Image Processing
A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance
Journal of the ACM (JACM)
A note on minimal length polygonal approximation to a digitized contour
Communications of the ACM
On Recursive, O(N) Partitioning of a Digitized Curve into Digital Straight Segments
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recognizing arithmetic straight lines and planes
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Digital straightness and convexity (Extended Abstract)
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
A Comparative Evaluation of Length Estimators
ICPR '02 Proceedings of the 16 th International Conference on Pattern Recognition (ICPR'02) Volume 4 - Volume 4
Plane digitization and related combinatorial problems
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
A multidimensional critical factorization theorem
Theoretical Computer Science - In memoriam: Alberto Del Lungo (1965-2003)
Discrete Applied Mathematics
Functional stepped surfaces, flips, and generalized substitutions
Theoretical Computer Science
Proceedings of the twenty-fourth annual symposium on Computational geometry
Number-theoretic interpretation and construction of a digital circle
Discrete Applied Mathematics
Discrete sets with minimal moment of inertia
Theoretical Computer Science
A generalized preimage for the digital analytical hyperplane recognition
Discrete Applied Mathematics
Minimum decomposition of a digital surface into digital plane segments is NP-hard
Discrete Applied Mathematics
Offset Approach to Defining 3D Digital Lines
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
A Generic and Parallel Algorithm for 2D Image Discrete Contour Reconstruction
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
The distance geometry of music
Computational Geometry: Theory and Applications
Lyndon + Christoffel = digitally convex
Pattern Recognition
Gift-wrapping based preimage computation algorithm
Pattern Recognition
Some theoretical challenges in digital geometry: A perspective
Discrete Applied Mathematics
Optimal blurred segments decomposition of noisy shapes in linear time
Computers and Graphics
Digital Circularity and Its Applications
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Blurred Segments in Gray Level Images for Interactive Line Extraction
IWCIA '09 Proceedings of the 13th International Workshop on Combinatorial Image Analysis
Plane digitization and related combinatorial problems
Discrete Applied Mathematics - Special issue: Advances in discrete geometry and topology (DGCI 2003)
Infinite labeled trees: From rational to Sturmian trees
Theoretical Computer Science
Sturmian and episturmian words: a survey of some recent results
CAI'07 Proceedings of the 2nd international conference on Algebraic informatics
Combinatorial view of digital convexity
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Continued fractions and digital lines with irrational slopes
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
On minimal moment of inertia polyominoes
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Consistent digital line segments
Proceedings of the twenty-sixth annual symposium on Computational geometry
Detection of circular arcs in a digital image using chord and sagitta properties
GREC'09 Proceedings of the 8th international conference on Graphics recognition: achievements, challenges, and evolution
Shape decomposition using Farey sequence and saddle points
Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing
Vectorization of thick digital lines using Farey sequence and geometric refinement
Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing
On lazy representations and sturmian graphs
CIAA'10 Proceedings of the 15th international conference on Implementation and application of automata
An arithmetic and combinatorial approach to three-dimensional discrete lines
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Another definition for digital tangents
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Quasi-linear transformations, numeration systems and fractals
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Delaunay properties of digital straight segments
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Computing the characteristics of a subsegment of a digital straight line in logarithmic time
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
A generic and parallel algorithm for 2D digital curve polygonal approximation
Journal of Real-Time Image Processing
Sturmian graphs and integer representations over numeration systems
Discrete Applied Mathematics
Fast guaranteed polygonal approximations of closed digital curves
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Revisiting digital straight segment recognition
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
A generalized preimage for the standard and supercover digital hyperplane recognition
DGCI'06 Proceedings of the 13th international conference on Discrete Geometry for Computer Imagery
Optimal blurred segments decomposition in linear time
DGCI'05 Proceedings of the 12th international conference on Discrete Geometry for Computer Imagery
Sturmian graphs and a conjecture of moser
DLT'04 Proceedings of the 8th international conference on Developments in Language Theory
Linear discrete line recognition and reconstruction based on a generalized preimage
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Digital line recognition, convex hull, thickness, a unified and logarithmic technique
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
PACE: polygonal approximation of thick digital curves using cellular envelope
ICVGIP'06 Proceedings of the 5th Indian conference on Computer Vision, Graphics and Image Processing
Discrete Applied Mathematics
On covering a digital disc with concentric circles in Z2
Theoretical Computer Science
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A digital arc is called 'straight' if it is the digitization of a straight line segment. Since the concept of digital straightness was introduced in the mid-1970s, dozens of papers on the subject have appeared; many characterizations of digital straight lines have been formulated, and many algorithms for determining whether a digital arc is straight have been defined. This paper reviews the literature on digital straightness and discusses its relationship to other concepts of geometry, the theory of words, and number theory.