Abstract
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 \(\Omega(h^{-\frac{1}{2}})\). 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.
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References
Coeurjolly, D., Miguet, S., Tougne, L.: Discrete curvature based on osculating circle estimation. In: Arcelli, C., Cordella, L.P., Sanniti di Baja, G. (eds.) IWVF 2001. LNCS, vol. 2059, pp. 303–312. Springer, Heidelberg (2001)
Coeurjolly, D., Svensson, S.: Estimation of curvature along curves with application to fibres in 3D images of paper. In: Bigun, J., Gustavsson, T. (eds.) SCIA 2003. LNCS, vol. 2749, pp. 247–254. Springer, Heidelberg (2003)
Esbelin, H.-A., Malgouyres, R.: Convergence of binomial-based derivative estimation for c2- noisy discretized curves. In: Brlek, S., Reutenauer, C., Provençal, X. (eds.) DGCI 2009. LNCS, vol. 5810, pp. 57–66. Springer, Heidelberg (2009)
Feschet, F., Tougne, L.: Optimal time computation of the tangent of a discrete curve: Application to the curvature. In: Bertrand, G., Couprie, M., Perroton, L. (eds.) DGCI 1999. LNCS, vol. 1568, pp. 31–40. Springer, Heidelberg (1999)
Fiorio, C., Mercat, C., Rieux, F.: Curvature estimation for discrete curves based on auto-adaptive masks of convolution. In: Barneva, R.P., Brimkov, V.E., Hauptman, H.A., Natal Jorge, R.M., Tavares, J.M.R.S. (eds.) CompIMAGE 2010. LNCS, vol. 6026, pp. 47–59. Springer, Heidelberg (2010)
Fleischmann, O., Wietzke, L., Sommer, G.: A Novel Curvature Estimator for Digital Curves and Images. In: Goesele, M., Roth, S., Kuijper, A., Schiele, B., Schindler, K. (eds.) DAGM 2010. LNCS, vol. 6376, pp. 442–451. Springer, Heidelberg (2010)
Gross, A., Latecki, L.: Digitizations preserving topological and differential geometric properties. Comput. Vis. Image Underst. 62(3), 370–381 (1995)
Hermann, S., Klette, R.: A comparative study on 2d curvature estimators. In: Proc. ICCTA, pp. 584–589 (2007)
Kerautret, B., Lachaud, J.-O.: Curvature estimation along noisy digital contours by approximate global optimization. Pattern Recognition 42(10), 2265–2278 (2009)
Klette, R., Rosenfeld, A.: Digital Geometry - Geometric Methods for Digital Picture. Morgan Kaufmann, San Francisco (2004)
Lachaud, J.-O., Vialard, A., de Vieilleville, F.: Fast, accurate and convergent tangent estimation on digital contours. Image and Vis. Comput. 25(10), 1572–1587 (2007)
Liu, H., Latecki, L., Liu, W.: A unified curvature definition for regular, polygonal, and digital planar curves. Int. Jour. of Comput. Vis. 80, 104–124 (2008)
Malgouyres, R., Brunet, F., Fourey, S.: Binomial convolutions and derivatives estimation from noisy discretizations. In: Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds.) DGCI 2008. LNCS, vol. 4992, pp. 370–379. Springer, Heidelberg (2008)
Marji, M.: On the detection of dominant points on digital planar curves. PhD thesis, Wayne State University, Detroit, Michigan (2003)
Roussillon, T., Sivignon, I., Tougne, L.: On three constrained versions of the digital circular arc recognition problem. In: Brlek, S., Reutenauer, C., Provençal, X. (eds.) DGCI 2009. LNCS, vol. 5810, pp. 34–45. Springer, Heidelberg (2009)
Vialard, A.: Geometrical parameters extraction from discrete paths. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 24–35. Springer, Heidelberg (1996)
Worring, M., Smeulders, A.W.M.: Digital curvature estimation. CVGIP: Image Understanding 58(3), 366–382 (1993)
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Roussillon, T., Lachaud, JO. (2011). Accurate Curvature Estimation along Digital Contours with Maximal Digital Circular Arcs. In: Aggarwal, J.K., Barneva, R.P., Brimkov, V.E., Koroutchev, K.N., Korutcheva, E.R. (eds) Combinatorial Image Analysis. IWCIA 2011. Lecture Notes in Computer Science, vol 6636. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21073-0_7
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DOI: https://doi.org/10.1007/978-3-642-21073-0_7
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