Curve Digitization Variability

This paper presents a study on the set of digitizations generated by the action of a group of transformations on a continuous curve before the digitization step. An upper bound for the cardinal of this digitization set under the translation group action is exhibited. Then this bound is tested on several functions. Finally, a representation of this digitization set is proposed and an illustration of its potential use is given on a length estimator.

[1]  Rémy Malgouyres,et al.  Convergence of binomial-based derivative estimation for C2 noisy discretized curves , 2011, Theor. Comput. Sci..

[2]  François de Vieilleville,et al.  Analysis and Comparative Evaluation of Discrete Tangent Estimators , 2005, DGCI.

[3]  Jovisa D. Zunic,et al.  The Number of N-Point Digital Discs , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  François de Vieilleville,et al.  Experimental Comparison of Continuous and Discrete Tangent Estimators Along Digital Curves , 2008, IWCIA.

[5]  Mohamed Tajine,et al.  About the frequencies of some patterns in digital planes. Application to area estimators , 2009, Comput. Graph..

[6]  Jacques-Olivier Lachaud,et al.  Curvature estimation along noisy digital contours by approximate global optimization , 2009, Pattern Recognit..

[7]  Laure Tougne,et al.  Discrete Curvature Based on Osculating Circle Estimation , 2001, IWVF.

[8]  Reinhard Klette,et al.  Multigrid Convergence of Calculated Features in Image Analysis , 2000, Journal of Mathematical Imaging and Vision.

[9]  Mohamed Tajine,et al.  Patterns for multigrid equidistributed functions: Application to general parabolas and length estimation , 2011, Theor. Comput. Sci..

[10]  Mohamed Tajine,et al.  Patterns in Discretized Parabolas and Length Estimation , 2009, DGCI.

[11]  Reinhard Klette,et al.  A Comparative Evaluation of Length Estimators of Digital Curves , 2004, IEEE Trans. Pattern Anal. Mach. Intell..

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

[13]  Étienne Baudrier,et al.  About Multigrid Convergence of Some Length Estimators , 2014, DGCI.

[14]  Reinhard Klette,et al.  Evaluation of curve length measurements , 2000, Proceedings 15th International Conference on Pattern Recognition. ICPR-2000.

[15]  Nahum Kiryati,et al.  Chain code probabilities and optimal length estimators for digitized three-dimensional curves , 1995, Pattern Recognit..