Digital straightness

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-1970’s, 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.

[1]  S. H. Y. Hung,et al.  On the Straightness of Digital Arcs , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Seymour Shlien,et al.  Segmentation of digital curves using linguistic techniques , 1983, Comput. Vis. Graph. Image Process..

[3]  Arnold W. M. Smeulders,et al.  Decomposition of discrete curves into piecewise straight segments in linear time , 1991 .

[4]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[5]  AZRIEL ROSENFELD,et al.  Digital Straight Line Segments , 1974, IEEE Transactions on Computers.

[6]  Ugo Montanari,et al.  A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance , 1968, J. ACM.

[7]  Jovisa D. Zunic,et al.  On the Number of Linear Partitions of the (m, n)-Grid , 1991, Inf. Process. Lett..

[8]  Reinhard Klette,et al.  Determination of the Convex Hull of a Finite Set of Planar Points Within Linear Time , 1981, J. Inf. Process. Cybern..

[9]  Mohamed Tajine,et al.  Recognizing arithmetic straight lines and planes , 1996, DGCI.

[10]  Ching Y. Suen,et al.  An optimal O(n) algorithm for identifying line segments from a sequence of chain codes , 1995, Pattern Recognit..

[11]  Samiran Chattopadhyay,et al.  A new method of analysis for discrete straight lines , 1991, Pattern Recognit. Lett..

[12]  Alfred M. Bruckstein,et al.  The number of digital straight lines on an N×N grid , 1990, IEEE Trans. Inf. Theory.

[13]  Jean-Pierre Reveillès Géométrie discrète, calcul en nombres entiers et algorithmique , 1991 .

[14]  Jerome Rothstein,et al.  Parallel and sequential specification of a context sensitive language for straight lines on grids , 1976 .

[15]  K. Voss Discrete Images, Objects, and Functions in Zn , 1993 .

[16]  Dominique Gouyou-Beauchamps,et al.  Sur les Facteurs des Suites de Sturm , 1990, Theor. Comput. Sci..

[17]  Li-De Wu,et al.  On the Chain Code of a Line , 1982, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Chul E. Kim,et al.  Representation of digital line segments and their preimages , 1985, Comput. Vis. Graph. Image Process..

[19]  Ugo Montanari,et al.  A note on minimal length polygonal approximation to a digitized contour , 1970, CACM.

[20]  Giovanni B Reggiori,et al.  Digital Computer Transformations for Irregular Line-Drawings , 1972 .

[21]  Chul E. Kim On cellular straight line segments , 1982, Comput. Graph. Image Process..

[22]  V. A. Kovalevsky New definition and fast recognition of digital straight segments and arcs , 1990, [1990] Proceedings. 10th International Conference on Pattern Recognition.

[23]  Isabelle Debled-Rennesson,et al.  A Linear Algorithm for Segmentation of Digital Curves , 1995, Int. J. Pattern Recognit. Artif. Intell..

[24]  Filippo Mignosi,et al.  On the Number of Factors of Sturmian Words , 1991, Theor. Comput. Sci..

[25]  Murray H. Loew,et al.  Analysis and modeling of digitized straight-line segments , 1988, [1988 Proceedings] 9th International Conference on Pattern Recognition.

[26]  R. Brons,et al.  Linguistic Methods for the Description of a Straight Line on a Grid , 1974, Comput. Graph. Image Process..

[27]  Hans-Ullrich Döhler,et al.  Compact contour codes for convex binary patterns , 1985 .

[28]  M. C. Irwin Geometry of continued fractions , 1989 .

[29]  Jack Bresenham,et al.  Algorithm for computer control of a digital plotter , 1965, IBM Syst. J..

[30]  Reinhard Klette,et al.  Cell complexes through time , 2000, SPIE Optics + Photonics.

[31]  Azriel Rosenfeld,et al.  How a Digital Computer can Tell whether a Line is Straight , 1982 .

[32]  Rachad M. Shoucri,et al.  Note on the determination of a digital straight line from chain codes , 1985, Comput. Vis. Graph. Image Process..

[33]  Reinhard Klette,et al.  The Length of Digital Curves , 1999 .

[34]  Jack Sklansky,et al.  Fast polygonal approximation of digitized curves , 1980, Pattern Recognit..

[35]  Theodosios Pavlidis,et al.  Structural pattern recognition , 1977 .

[36]  Christian Ronse A simple proof of Rosenfeld's characterization of digital straight line segments , 1985, Pattern Recognit. Lett..

[37]  E. Creutzburg,et al.  Geometric methods for on-line recognition of digital straight-line segments , 1988 .

[38]  Michael Lindenbaum,et al.  A New Parameterization of Digital Straight Lines , 1991, IEEE Trans. Pattern Anal. Mach. Intell..

[39]  W.G Kropatsch,et al.  Detecting the straightness of digital curves in O(N) steps , 1989, Comput. Vis. Graph. Image Process..

[40]  Klaus Voss Coding of digital straight lines by continued fractions , 1991 .

[41]  Jean Berstel,et al.  Random generation of finite Sturmian words , 1996, Discret. Math..

[42]  Albrecht Hübler Diskrete Geometrie für die digitale Bildverarbeitung , 1989 .

[43]  David Thomas,et al.  The Art in Computer Programming , 2001 .

[44]  C. Arcelli,et al.  Regular Arcs in Digital Contours , 1975 .

[45]  Robert P. W. Duin,et al.  Spirograph Theory: A Framework for Calculations on Digitized Straight Lines , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.