Abstract
A discrete polynomial curve is defined as a set of points lying between two polynomial curves. This paper deals with the problem of fitting a discrete polynomial curve to given integer points in the presence of outliers. We formulate the problem as a discrete optimization problem in which the number of points included in the discrete polynomial curve, i.e., the number of inliers, is maximized. We then propose a method that effectively achieves a solution guaranteeing local maximality by using a local search, called rock climging, with a seed obtained by RANSAC. Experimental results demonstrate the effectiveness of our proposed method.
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References
Aiger, D., Kenmochi, Y., Talbot, H., Buzer, L.: Efficient Robust Digital Hyperplane Fitting with Bounded Error. In: Domenjoud, E. (ed.) DGCI 2011. LNCS, vol. 6607, pp. 223–234. Springer, Heidelberg (2011)
Fischler, M.A., Bolles, R.C.: Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Communications of the ACM 24(6), 381–395 (1981)
Gérard, Y., Provot, L., Feschet, F.: Introduction to Digital Level Layers. In: Domenjoud, E. (ed.) DGCI 2011. LNCS, vol. 6607, pp. 83–94. Springer, Heidelberg (2011)
Provot, L., Gérard, Y.: Estimation of the Derivatives of a Digital Function with a Convergent Bounded Error. In: Domenjoud, E. (ed.) DGCI 2011. LNCS, vol. 6607, pp. 284–295. Springer, Heidelberg (2011)
Rousseeuw, P.: Least median of squares regression. Journal of the American Statistical Association, 871–880 (1984)
Zrour, R., Kenmochi, Y., Talbot, H., Buzer, L., Hamam, Y., Shimizu, I., Sugimoto, A.: Optimal consensus set for digital line and plane fitting. International Journal of Imaging Systems and Technology 21(1), 45–57 (2011)
Zrour, R., Largeteau-Skapin, G., Andres, E.: Optimal Consensus Set for Annulus Fitting. In: Domenjoud, E. (ed.) DGCI 2011. LNCS, vol. 6607, pp. 358–368. Springer, Heidelberg (2011)
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Sekiya, F., Sugimoto, A. (2012). Discrete Polynomial Curve Fitting to Noisy Data. In: Barneva, R.P., Brimkov, V.E., Aggarwal, J.K. (eds) Combinatorial Image Analaysis. IWCIA 2012. Lecture Notes in Computer Science, vol 7655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34732-0_5
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DOI: https://doi.org/10.1007/978-3-642-34732-0_5
Publisher Name: Springer, Berlin, Heidelberg
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