research-article

On Recursive, O(N) Partitioning of a Digitized Curve into Digital Straight Segments

Authors:

A. BrucksteinAuthors Info & Claims

IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume 15, Issue 9

Pages 949 - 953

https://doi.org/10.1109/34.232082

Published: 01 September 1993 Publication History

Abstract

A simple online algorithm for partitioning of a digital curve into digital straight-line segments of maximal length is given. The algorithm requires O(N) time and O(1) space and is therefore optimal. Efficient representations of the digital segments are obtained as byproducts. The algorithm also solves a number-theoretical problem concerning nonhomogeneous spectra of numbers.

References

[1]

{1} A. Rosenfeld, "Digital straight line segments," IEEE Trans. Comput., vol. C-23, pp. 1264-1269, 1974.

[2]

{2} C. E. Kim and A. Rosenfeld, "Digital straight lines and convexity of digital regions," IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-4, pp. 149-153, 1982.

Digital Library

[3]

{3} L. D. Wu, "On the chain code of a line," IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-4, pp. 347-353, 1982.

Digital Library

[4]

{4} L. Dorst and A. W. M. Smeulders, "Discrete representation of straight lines," IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-6, pp. 450-463, 1984.

Digital Library

[5]

{5} S. H. Y. Hung, "On the straightness of digital arcs," IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-7, pp. 203-215, 1985.

Digital Library

[6]

{6} L. Dorst and A. W. M. Smeulders, "Best linear unbiased estimators for properties of digitized straight lines," IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-8, pp. 276-282, 1986.

Digital Library

[7]

{7} J. Koplowitz and A. P. Sundar Raj, "A robust filtering algorithm for subpixel reconstruction of chain coded line drawings," IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, pp. 451-457, 1987.

Digital Library

[8]

{8} C. A. Berenstein, L. N. Kanal, D. Lavine, and E. Olson, "A geometric approach to subpixel registration accuracy," Comput. Vision Graphics Image Processing, vol. 40, no. 3, pp. 334-360, 1987.

Digital Library

[9]

{9} M. Lindenbaum and J. Koplowitz, "Compression of chain codes using digital straight line sequences," Patt. Recogn. Lett., vol. 7, pp. 167-171, 1988.

Digital Library

[10]

{10} M. Werman, A. Y. Wu, and R. A. Melter, "Recognition and characterization of digitized curves," Patt. Recogn. Lett., vol. 5, pp. 207-213, 1987.

Digital Library

[11]

{11} M. D. McIlroy, "A note on discrete representation of lines," AT&T Tech. J., vol. 64, no. 2, pp. 481-490, 1984.

[12]

{12} M. Lindenbaum and J. Koplowitz, "A new parametrization of digital straight lines," IEEE Trans. Patt. Anal. Machine Intell., vol. 13, pp. 847-852, 1991.

Digital Library

[13]

{13} A. Bruckstein, "The selfsimilarity of digital straight lines," in Vision Geometry (Melter, Rosenfeld, and Bhattacharya, Eds.). Contemporary Mathematics, AMS, 1991, pp. 1-20, vol. 119.

[14]

{14} J. Koplowitz, M. Lindenbaum, and A. Bruckstein, "On the number of digital straight lines on an N × N grid," IEEE Trans. Inform. Theory, vol. IT-36, pp. 192-197, 1990.

[15]

{15} C. Ronse, "A bibliography on digital and computational convexity (1961-1988)," IEEE Trans. Patt. Anal Machine Intell., vol. 11, pp. 181-190, 1989.

Digital Library

[16]

{16} B. A. Venkov, Elementary Number Theory, (translated and edited by H. Anderson). Groningen: Wolters-Noordhoff, 1970.

[17]

{17} K. Stolarsky, "Beatty sequences, continued fractions, and certain shift operators," Canadian Math. Bull., vol. 19, no. 4, pp. 473-482, 1976.

[18]

{18} A. S. Fraenkel, M. Mushkin, and U. Tassa, "Determination of {nθ} from its sequence of differences," Canadian Math. Bull., vol. 21, no. 4, pp. 441-446, 1978.

[19]

{19} R. L. Graham, S. Lin, and C. S. Lin, "Spectra of numbers," Math. Mag., vol. 51, pp. 174-176, 1978.

[20]

{20} M. Boshernitzan and A. S. Fraenkel, "A linear algorithm for nonhomogeneous spectra of numbers," J. Algorithms, vol. 5, pp. 187-198, 1984.

[21]

{21} A. W. M. Smeulders and L. Dorst, "Decomposition of discrete curves into piecewise straight segments in linear time," in Vision Geometry (Melter, Rosenfeld and Bhattacharya, Eds.). Contemporary Mathematics, AMS, 1991, pp. 169-195, vol. 119.

[22]

{22} G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. Oxford: Oxford University Press, 1979.

[23]

{23} F. P. Preparata and M. I. Shamos, Computational Geometry, Berlin: Springer Verlag, 1985.

Digital Library

[24]

{24} D. E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms. Reading, MA: Addison-Wesley, 1969.

Digital Library

[25]

{25} L. Dorst and A. W. M. Smeulders, "Length estimators for digital contours," Comput. Vision Graphics Image Processing, vol. 40, pp. 311-333, 1987.

Digital Library

[26]

{26} J. O'Rourke, "An on-line algorithm for fitting straight lines between data ranges," Commun. ACM, vol. 24, no. 9, pp. 574-578, 1981.

Digital Library

Cited By

Gerard Y(2017)About the Decidability of Polyhedral Separability in the Lattice $$\mathbb {Z}^d$$ZdJournal of Mathematical Imaging and Vision10.1007/s10851-017-0711-y59:1(52-68)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1007/s10851-017-0711-y
Lachaud JProvençal X(2011)Dynamic minimum length polygonProceedings of the 14th international conference on Combinatorial image analysis10.5555/2008730.2008753(208-221)Online publication date: 23-May-2011
https://dl.acm.org/doi/10.5555/2008730.2008753
Damiand GCoeurjolly D(2011)A generic and parallel algorithm for 2D digital curve polygonal approximationJournal of Real-Time Image Processing10.1007/s11554-011-0193-x6:3(145-157)Online publication date: 1-Sep-2011
https://dl.acm.org/doi/10.1007/s11554-011-0193-x
Show More Cited By

Index Terms

On Recursive, O(N) Partitioning of a Digitized Curve into Digital Straight Segments
1. Theory of computation
  1. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

Recommendations

Digital Straight Line Segments

It is shown that a digital arc S is the digitization of a straight line segment if and only if it has the "chord property:" the line segment joining any two points of S lies everywhere within distance 1 of S. This result is used to derive several ...
Three-Dimensional Digital Line Segments

Digital arcs in 3-D digital pictures are defined. The digital image of an arc is also defined. A digital arc is defined to be a digital line segment if it is the digital image of a line segment. It is shown that a digital line segment may be ...
A simple proof of Rosenfeld's characterization of digital straight line segments

A digital straight line segment is defined as the grid-intersect quantization of a straight line segment in the plane. Let S be a set of pixels on a square grid. Rosenfeld [8] showed that S is a digital straight line segment if and only if it is a ...

Comments

Information & Contributors

Information

Published In

cover image IEEE Transactions on Pattern Analysis and Machine Intelligence

IEEE Transactions on Pattern Analysis and Machine Intelligence Volume 15, Issue 9

September 1993

125 pages

ISSN:0162-8828

Issue’s Table of Contents

Copyright © Copyright © 1993 IEEE. All Rights Reserved.

Publisher

IEEE Computer Society

United States

Publication History

Published: 01 September 1993

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

21
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 04 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

Gerard Y(2017)About the Decidability of Polyhedral Separability in the Lattice $$\mathbb {Z}^d$$ZdJournal of Mathematical Imaging and Vision10.1007/s10851-017-0711-y59:1(52-68)Online publication date: 1-Sep-2017
https://dl.acm.org/doi/10.1007/s10851-017-0711-y
Lachaud JProvençal X(2011)Dynamic minimum length polygonProceedings of the 14th international conference on Combinatorial image analysis10.5555/2008730.2008753(208-221)Online publication date: 23-May-2011
https://dl.acm.org/doi/10.5555/2008730.2008753
Damiand GCoeurjolly D(2011)A generic and parallel algorithm for 2D digital curve polygonal approximationJournal of Real-Time Image Processing10.1007/s11554-011-0193-x6:3(145-157)Online publication date: 1-Sep-2011
https://dl.acm.org/doi/10.1007/s11554-011-0193-x
Gerard YCoeurjolly DFeschet F(2009)Gift-wrapping based preimage computation algorithmPattern Recognition10.1016/j.patcog.2008.10.00342:10(2255-2264)Online publication date: 1-Oct-2009
https://dl.acm.org/doi/10.1016/j.patcog.2008.10.003
Gerard YFeschet FCoeurjolly D(2008)Gift-wrapping based preimage computation algorithmProceedings of the 14th IAPR international conference on Discrete geometry for computer imagery10.5555/1792454.1792487(310-321)Online publication date: 16-Apr-2008
https://dl.acm.org/doi/10.5555/1792454.1792487
Sivignon IDupont FChassery J(2007)Reversible vectorisation of 3D digital planar curves and applicationsImage and Vision Computing10.1016/j.imavis.2006.06.02225:10(1644-1656)Online publication date: 1-Oct-2007
https://dl.acm.org/doi/10.1016/j.imavis.2006.06.022
Brimkov VCoeurjolly DKlette R(2007)Digital planarity-A reviewDiscrete Applied Mathematics10.1016/j.dam.2006.08.004155:4(468-495)Online publication date: 20-Feb-2007
https://dl.acm.org/doi/10.1016/j.dam.2006.08.004
de Luca ADe Luca A(2006)Some characterizations of finite Sturmian wordsTheoretical Computer Science10.1016/j.tcs.2006.01.036356:1(118-125)Online publication date: 5-May-2006
https://dl.acm.org/doi/10.1016/j.tcs.2006.01.036
Coeurjolly DZerarga L(2006)Supercover model, digital straight line recognition and curve reconstruction on the irregular isothetic gridsComputers and Graphics10.1016/j.cag.2005.10.00930:1(46-53)Online publication date: 1-Feb-2006
https://dl.acm.org/doi/10.1016/j.cag.2005.10.009
Debled-Rennesson IFeschet FRouyer-Degli J(2006)Optimal blurred segments decomposition of noisy shapes in linear timeComputers and Graphics10.1016/j.cag.2005.10.00730:1(30-36)Online publication date: 1-Feb-2006
https://dl.acm.org/doi/10.1016/j.cag.2005.10.007
Show More Cited By

View Options

View options

Media

Figures

Other

Tables

View Issue’s Table of Contents