Accurate Curvature Estimation along Digital Contours with Maximal Digital Circular Arcs

We propose in this paper a new curvature estimator based on the set of maximal digital circular arcs. For strictly convex shapes with continuous curvature fields digitized on a grid of step h, we show that this estimator is mutligrid convergent if the discrete length of the maximal digital circular arcs grows in Ω(h-1/2). We indeed observed this order of magnitude. Moreover, experiments showed that our estimator is at least as fast to compute as existing estimators and more accurate even at low resolution.

[1]  Longin Jan Latecki,et al.  Digitizations preserving topological and differential geometric properties , 1995, Other Conferences.

[2]  Stina Svensson,et al.  Estimation of Curvature along Curves with Application to Fibres in 3D Images of Paper , 2003, SCIA.

[3]  Rémy Malgouyres,et al.  Convergence of Binomial-Based Derivative Estimation for C2 Noisy Discretized Curves , 2009, DGCI.

[4]  Gerald Sommer,et al.  A Novel Curvature Estimator for Digital Curves and Images , 2010, DAGM-Symposium.

[5]  Marcel Worring,et al.  Digital curvature estimation , 1993 .

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

[7]  Laure Tougne,et al.  On Three Constrained Versions of the Digital Circular Arc Recognition Problem , 2009, DGCI.

[8]  Christophe Fiorio,et al.  Curvature Estimation for Discrete Curves Based on Auto-adaptive Masks of Convolution , 2010, CompIMAGE.

[9]  Wenyu Liu,et al.  A Unified Curvature Definition for Regular, Polygonal, and Digital Planar Curves , 2008, International Journal of Computer Vision.

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

[11]  Azriel Rosenfeld,et al.  Digital geometry - geometric methods for digital picture analysis , 2004 .

[12]  Reinhard Klette,et al.  A Comparative Study on 2D Curvature Estimators , 2007, 2007 International Conference on Computing: Theory and Applications (ICCTA'07).

[13]  Valentin E. Brimkov,et al.  Computational modeling of objects represented in images , 2011, Graph. Model..

[14]  Leszek Wojnar,et al.  Image Analysis , 1998 .

[15]  Gabriella Sanniti di Baja,et al.  Visual Form 2001 , 2001, Lecture Notes in Computer Science.

[16]  Anne Vialard.  Geometrical parameters extraction from discrete paths , 1996, DGCI.

[17]  Laure Tougne,et al.  Optimal Time Computation of the Tangent of a Discrete Curve: Application to the Curvature , 1999, DGCI.

[18]  François de Vieilleville,et al.  Fast, accurate and convergent tangent estimation on digital contours , 2007, Image Vis. Comput..

[19]  Florent Brunet,et al.  Binomial Convolutions and Derivatives Estimation from Noisy Discretizations , 2008, DGCI.