Curvature estimation along noisy digital contours by approximate global optimization

Pattern Recognition

Volumn 42, Issue 10, 2009, Pages 2265-2278

  Kerautret, B ^a   Lachaud, J O ^b  

^a LORIA   (France)

^b UNIVERSITÉ DE SAVOIE   (France)

Author keywords

Curvature estimation; Digital contours; Discrete geometry; Feature detection; Robustness to noise

Indexed keywords

CURVATURE ESTIMATION; DIGITAL CONTOURS; DISCRETE GEOMETRY; FEATURE DETECTION; ROBUSTNESS TO NOISE;

CURVE FITTING; GEOMETRY; GLOBAL OPTIMIZATION;

ESTIMATION;

EID: 67349174673     PISSN: 00313203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.patcog.2008.11.013     Document Type: Article

References (25)

1. M. Marji, On the detection of dominant points on digital planar curves, Ph.D. Thesis, Wayne State University, Detroit, Michigan, 2003.
2. Klette R., and Rosenfeld A. Digital Geometry-Geometric Methods for Digital Picture Analysis (2004), Morgan Kaufmann, San Francisco, CA
3. F. de Vieilleville, J.-O. Lachaud, Convex shapes and convergence speed of discrete tangent estimators, in: Proceedings of the International Symposium on Visual Computing (ISVC'2006), Lake Tahoe, Nevada, in: Lecture Notes in Computer Science, vol. 4292, Springer, Berlin, 2006.
4. J.-O. Lachaud, Espaces non-euclidiens et analyse d'image: modèles déformables riemanniens et discrets, topologie et géométrie discrète, Habilitation à diriger des recherches, Université Bordeaux 1, Talence, France, 2006 (in French).
5. Huxley M.N. Exponential sums and lattice points. Proceedings of the London Mathematical Society 60 (1990) 471-502
6. Klette R., and Žunić J. Multigrid convergence of calculated features in image analysis. Journal of Mathematical Imaging and Vision 13 (2000) 173-191
7. T. Asano, Y. Kawamura, R. Klette, K. Obokata, Minimum-length polygons in approximation sausages, in: C. Arcelli, L.P. Cordella, G. Sanniti di Baja (Eds.), Proceedings of the Fourth International Workshop on Visual Form (IWVF4), Capri, Italy, in: Lecture Notes in Computer Science, vol. 2059, Springer, Berlin, 2001, pp. 103-112.
8. V. Kovalevsky, S. Fuchs, Theoretical and experimental analysis of the accuracy of perimeter estimates, in: W. Förster, S. Ruwiedel (Eds.), Proceedings of Robust Computer Vision, 1992, pp. 218-242.
9. F. Sloboda, B. Zaťko, J. Stoer, On approximation of planar one-dimensional continua, in: R. Klette, A. Rosenfeld, F. Sloboda (Eds.), Proceedings of Advances in Digital and Computational Geometry, 1998, pp. 113-160.
10. D. Coeurjolly, Algorithmique et géométrie pour la caractérisation des courbes et des surfaces, Ph.D. Thesis, Université Lyon 2, December 2002, (in French).
11. J.-O. Lachaud, A. Vialard, F. de Vieilleville, Analysis and comparative evaluation of discrete tangent estimators, in: E. Andrès, G. Damiand, P. Lienhardt (Eds.), Proceedings of International Conference Discrete Geometry for Computer Imagery (DGCI'2005), Poitiers, France, in: Lecture Notes in Computer Science, vol. 3429, Springer, Berlin, 2005, pp. 140-251.
12. Lachaud J.-O., Vialard A., and de Vieilleville F. Fast, accurate and convergent tangent estimation on digital contours. Image and Vision Computing 25 10 (2007) 1572-1587
13. de Vieilleville F., Lachaud J.-O., and Feschet F. Maximal digital straight segments and convergence of discrete geometric estimators. Journal of Mathematical Imaging and Vision 27 2 (2007) 471-502
14. S. Hermann, R. Klette, A comparative study on 2d curvature estimators, Research report CITR-TR-183, CITR, The University of Auckland, New Zealand, 2006.
15. F. Brunet, Convolutions binomiales et dérivation de fonctions discrètes bruitées, Master's thesis, LAIC. University of Clermont-Ferrand, France, 2007 (in French).
16. Kass M., Witkin A., and Terzopoulos D. Snakes: active contour models. International Journal of Computer Vision 1 4 (1988) 321-331
17. Caselles V., Catté F., Coll T., and Dibos F. A geometric model for active contours in image processing. Numerische Mathematik 66 1 (1993) 1-31
18. F. Feschet, L. Tougne, Optimal time computation of the tangent of a discrete curve: application to the curvature, in: Proceedings of the Eighth International Conference Discrete Geometry for Computer Imagery (DGCI'99), in: Lecture Notes in Computer Science, vol. 1568, Springer, Berlin, 1999, pp. 31-40.
19. P.-G. Ciarlet. Introduction à l'analyse numérique et à l'optimisation, in: Sciences Sup., Dunod, Paris, 1998.
20. Debled-Rennesson I., Feschet F., and Rouyer-Degli J. Optimal blurred segments decomposition of noisy shapes in linear times. Computers & Graphics 30 1 (2006) 30-36
21. L. Buzer, An elementary algorithm for digital line recognition in the general case, in: E. Andrès, G. Damiand, P. Lienhardt (Eds.), Proceedings of International Conference Discrete Geometry for Computer Imagery (DGCI'2005), Poitiers, France, in: Lecture Notes in Computer Science, vol. 3429, Springer, Berlin, 2005, pp. 299-310.
22. T. Roussillon, L. Tougne, I. Sivignon, Computation of binary objects sides number using discrete geometry application to automatic pebbles shape analysis, in: Proceedings of the 14th International Conference on Image Analysis and Processing (ICIAP), 2007.
23. T.P. Nguyen, I. Debled-Rennesson, Curvature estimation in noisy curves, in: Proceedings of CAIP, in: Lecture Notes in Computer Science, vol. 4673, Springer, Berlin, 2007, pp. 474-481.
24. B. Kerautret, J.-O. Lachaud, Robust estimation of curvature along digital contours with global optimization, in: D. Coeurjolly, I. Sivignon, L. Tougne, F. Dupont (Eds.), Proceedings of the 14th International Conference Discrete Geometry for Computer Imagery (DGCI'2008), Lyon, France, in: Lecture Notes in Computer Science, vol. 4992, Springer, Berlin, 2008, pp. 334-345.
25. T. Kanungo, Document degradation models and a methodology for degradation model validation, Ph.D. Thesis, University of Washington, 1996.