Abstract
We propose a method that we call auto-adaptive convolution which extends the classical notion of convolution in pictures analysis to function analysis on a discrete set. We define an averaging kernel which takes into account the local geometry of a discrete shape and adapts itself to the curvature. Its defining property is to be local and to follow a normal law on discrete lines of any slope. We used it together with classical differentiation masks to estimate first and second derivatives and give a curvature estimator of discrete functions.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Andres, E.: Modélisation Analytique Discrète d’Objets Géométriques. Habilitation à diriger des recherches, UFR Sciences Fondamentale et Appliquées, Université de Poitiers, France (2000)
Billingsley, P.: Convergence of probability measures, 2nd edn. Wiley Series in Probability and Statistics. John Wiley & Sons Inc., New York (1999)
Coeurjolly, D., Debled-Rennesson, I., Teytaud, O.: Segmentation and length estimation of 3D discrete curves. In: Bertrand, G., Imiya, A., Klette, R. (eds.) Digital and Image Geometry. LNCS, vol. 2243, pp. 299–317. Springer, Heidelberg (2002)
Coeurjolly, D., Klette, R.: A comparative evaluation of length estimators of digital curves. IEEE Trans. Pattern Anal. Mach. Intell. 26(2), 252–257 (2004)
Coeurjolly, D., Sivignon, I., Tougne, L., Dupont, F. (eds.): DGCI 2008. LNCS, vol. 4992. Springer, Heidelberg (2008)
Debled-Rennesson, I., Reveillès, J.P.: A linear algorithm for segmentation of digital curves. IJPRAI 9(4), 635–662 (1995)
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)
Fourey, S., Malgouyres, R.: Normals and curvature estimation for digital surfaces based on convolutions. In: Coeurjolly, D., et al. (eds.) [5], pp. 287–298
Gebal, K., Bærentzen, J.A., Aanæs, H., Larsen, R.: Shape Analysis Using the Auto Diffusion Function. Computer Graphics Forum 28(5), 1405–1413 (2009)
Konrad, P., Marc, A., Michael, K. (eds.): Symposium on Graphics Processing. Eurographics Association (2009)
Lachaud, J.O., Vialard, A., de Vieilleville, F.: Fast, accurate and convergent tangent estimation on digital contours. Image Vision Comput. 25(10), 1572–1587 (2007)
Malgouyres, R., Brunet, F., Fourey, S.: Binomial convolutions and derivatives estimation from noisy discretizations. In: Coeurjolly, et al. (eds.) [5], pp. 370–379
Matas, J., Shao, Z., Kittler, J.: Estimation of curvature and tangent direction by median filtered differencing. In: Braccini, C., Vernazza, G., DeFloriani, L. (eds.) ICIAP 1995. LNCS, vol. 974, pp. 83–88. Springer, Heidelberg (1995)
Nguyen, T.P., Debled-Rennesson, I.: Curvature estimation in noisy curves. In: Kropatsch, W.G., Kampel, M., Hanbury, A. (eds.) CAIP 2007. LNCS, vol. 4673, pp. 474–481. Springer, Heidelberg (2007)
Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Experiment. Math. 2(1), 15–36 (1993)
Reveillès, J.P.: Géométrie Discrète, Calcul en Nombres Entiers et Algorithmique. Ph.D. Thesis, Université Louis Pasteur, Strasbourg, France (1991)
Rosenfeld, A.: Digital straight line segments. IEEE Transactions on Computers 23(12), 1264–1269 (1974)
Sun, J., Ovsjanikov, M., Guibas, L.: A concise and provably informative multi-scale signature based on heat diffusion. In: Konrad, et al. (eds.) [10], pp. 1383–1392, http://www.eg.org/EG/DL/CGF/volume28/issue5/v28i5pp1383-1392.pdf
Worring, M., Smeulders, A.W.: Digital curvature estimation. CVGIP: Image Understanding 58(3), 366–382 (1993)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fiorio, C., Mercat, C., Rieux, F. (2010). 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) Computational Modeling of Objects Represented in Images. CompIMAGE 2010. Lecture Notes in Computer Science, vol 6026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12712-0_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-12712-0_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12711-3
Online ISBN: 978-3-642-12712-0
eBook Packages: Computer ScienceComputer Science (R0)