A Comparative Evaluation of Length Estimators of Digital Curves

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 26, Issue 2, 2004, Pages 252-258

  Coeurjolly, David ^a   Klette, Reinhard ^b  

^a UNIVERSITÉ LUMIÈRE LYON 2   (France)

^b UNIVERSITY OF AUCKLAND   (New Zealand)

Author keywords

Curve length; Digital geometry; Length estimator; Multigrid convergence

Indexed keywords

ALGORITHMS; ANALOG TO DIGITAL CONVERSION; ASYMPTOTIC STABILITY; CODES (STANDARDS); COMPUTATIONAL GEOMETRY; ESTIMATION; IMAGE SEGMENTATION; METRIC SYSTEM; OPTIMIZATION; TOPOLOGY;

CURVE LENGTHS; DIGITAL GEOMETRY; LENGTH ESTIMATORS; MULTIGRID CONVERGENCE;

IMAGE ANALYSIS;

ALGORITHM; ARTICLE; AUTOMATED PATTERN RECOGNITION; COMPARATIVE STUDY; COMPUTER ASSISTED DIAGNOSIS; COMPUTER GRAPHICS; EVALUATION; IMAGE ENHANCEMENT; MATHEMATICAL COMPUTING; METHODOLOGY; QUALITY CONTROL; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; STANDARD; VALIDATION STUDY;

ALGORITHMS; BENCHMARKING; COMPUTER GRAPHICS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; PATTERN RECOGNITION, AUTOMATED; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED;

EID: 0742268829     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2004.1262194     Document Type: Article

References (35)

1. H. Freeman, "Techniques for the Digital Computer Analysis of Chain-Encoded Arbitrary Plane Curves," Proc. Nat'l Electronics Conf., vol. 17, pp. 421-432, 1961.
2. A. Rosenfeld, "Digital Straight Line Segments," IEEE Trans. Computers, vol. 23, pp. 1264-1269, 1974.
3. J. Sklansky and D.F. Kibler, "A Theory of Nonuniformly Digitized Binary Pictures," IEEE Trans. Systems, Man, and Cybernetics, vol. 6, pp. 637-647, 1976.
4. T.J. Ellis, D. Proffitt, D. Rosen, and W. Rutkowski, "Measurement of the Lengths of Digitized Curved Lines," Computer Graphics and Image Processing, vol. 10, pp. 333-347, 1979.
5. A. Hübler, R. Klette, and K. Voss, "Determination of the Convex Hull of a Finite Set of Planar Points within Linear Time," EIK (Elektronische Informationsverarb. Kybernetik), vol. 17, pp. 121-140, 1981.
6. E. Creutzburg, A. Hübler, and V. Wedler, "On-Line Erkennung Digitaler Geradensegmente in Linearer Zeit," Proc. GEOBILD '82, pp. 48-65, 1982.
7. C.E. Kim, "On Cellular Straight Line Segments," Computer Graphics and Image Processing, vol. 18, pp. 369-391, 1982.
8. L.D. Wu, "On the Chain Code of a Line," IEEE Trans. Pattern Analysis Machine Intelligence, vol. 4, pp. 347-353, 1982.
9. A.M. Vossepoel and A.W.M. Smeulders, "Vector Code Probabilities and Metrication Error in the Representation of Straight Lines of Finite Length," Computer Graphics and Image Processing, vol. 20, pp. 347-364, 1982.
10. B.L. van der Waerden, Geometry and Algebra in Ancient Civilizations. Berlin: Springer, 1983.
11. T.A. Anderson and C.E. Kim, "Representation of Digital Line Segments and Their preimages," Computer Vision, Graphics, Image Processing, vol. 30, pp. 279-288, 1985.
12. G. Borgefors, "Distance Transformations in Digital Images," Computer Vision, Graphics, and Image Processing, vol. 34, pp. 344-371, 1986.
13. L. Dorst and A.W.M. Smeulders, "Length Estimators for Digitized Contours," Computer Vision, Graphics, and Image Processing, vol. 40, pp. 311-333, 1987.
14. J. Koplowitz and A.M. Bruckstein, "Design of Perimeter Estimators for Digitized Planar Shapes," IEEE Trans. Pattern Analysis Machine Intelligence, vol. 11, pp. 611-622, 1989.
15. V.A. Kovalevsky, "New Definition and Fast Recognition of Digital Straight Segments and Arcs," Proc. 10th Int'l Conf. Pattern Recognition, pp. 31-34, 1990.
16. L. Dorst and A.W.M. Smeulders, "Discrete Straight Line Segments: Parameters, Primitives, and Properties," Contemporary Math., R. Melter, P. Bhattacharya, and A. Rosenfeld, eds., vol. 119, pp. 45-62, 1991.
17. J.-P. Reveillès, "Géométrie Discrète, Calcul en Nombres Entiers et Algorithmique," Thèse d'état, Univ. Louis Pasteur, Strasbourg, 1991.
18. B. Verwer, "Local Distances for Distance Transformations in Two and Three Dimensions," Pattern Recognition Letters, vol. 12, pp. 671-682, 1991.
19. V. Kovalevsky and S. Fuchs, "Theoretical and Experimental Analysis of the Accuracy of Perimeter Estimates," Robust Computer Vision, Wichmann, Karlsruhe, pp. 218-242, 1992.
20. I. Debled-Rennesson and J. Reveillès, "A Linear Algorithm for Segmentation of Digital Curves," Inl'l J. Pattern Recognition and Artificial Intelligence, vol. 9, pp. 635-662, 1995.
21. J. Françon, J.-M. Schramm, and M. Tajine, "Recognizing Arithmetic Straight Lines and Planes," Proc. Sixth Int'l Workshop Discrete Geometry for Computer Imagery, pp. 141-150, 1996.
22. 2," technical report, Inst. of Control Theory and Robotics, Bratislava, 1996.
23. A. Vialard, "Geometrical Parameters Extraction from Discrete Paths," Discrete Geometry for Computer Imagery, pp. 24-35, 1996.
24. A. Jonas and N. Kiryati, "Length Estimation in 3-D Using Cube Quantization," J. Math. Imaging and Vision, vol. 8, pp. 215-238, 1998.
25. F. Sloboda, B. Zatko, and J. Stoer, "On Approximation of Planar One-Dimensional Continua," Advances in Digital and Computational Geometry, R. Klette, A. Rosenfeld, and F. Sloboda, eds., pp. 113-160, 1998.
26. F. Feschet and L. Tougne, "Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature," Discrete Geometry for Computer Imagery, pp. 31-40, 1999.
27. R. Klette, V. Kovalevsky, and B. Yip, "Length Estimation of Digital Curves," SPIE Proc. Vision Geometry VIII, pp. 117-129, July 1999. (expanded version available: Machine Graphics & Vision, vol. 9, pp. 673-703, 2000.)
28. R. Klette, V. Kovalevsky, and B. Yip, "Length Estimation of Digital Curves," SPIE Proc. Vision Geometry VIII, pp. 117-129, July 1999. (expanded version available: Machine Graphics & Vision, vol. 9, pp. 673-703, 2000.)
29. T. Asano, Y. Kawamura, R. Klette, and K. Obokata, "A New Approximation Scheme for Digital Objects and Curve Length Estimations," Proc. Image and Vision Computing, pp. 26-31, 2000.
30. R. Klette and T. Bülow, "Minimum-Length Polygons in Simple Cube-Curves," Discrete Geometry for Computer Imagery, pp. 467-478, 2000.
31. R. Klette and J. Zunic, "Multigrid Convergence of Calculated Features in Image Analysis," J. Math. Imaging Vision, vol. 13, pp. 173-191, 2000.
32. T. Asano, Y. Kawamura, R. Klette, and K. Obokata, "Minimum-Length Polygons in Approximation Sausages," Proc. Fourth Int'l Workshop Visual Form, pp. 103-112, 2001.
33. D. Coeurjolly, I. Debled-Rennesson, and O. Teytaud, "Segmentation and Length Estimation of 3D Discrete Curves," Proc. Digital and Image Geometry, pp. 299-317, 2001.
34. D. Coeurjolly and O. Teytaud, "Multigrid Convergence of Discrete Differential Estimators: Discrete Tangent and Length Estimation," Research Report Laboratoire ERIC, Universite Lumiere Lyon, France, RR-0101, http://eric.univ-lyon2.fr/RR/RR-0101.ps.gz, 2001.
35. R. Klette, "Multigrid Convergence of Geometric Features," Proc. Digital and Image Geometry, pp. 318-338, 2001.