An iterative procedure for robust circle fitting. (English) Zbl 07551090
Summary: The problem of fitting circles and circular arcs to observed points arises in many areas of science. However, the fitting results by using most geometric and algebraic methods are not usually acceptable in the presence of outliers. An iterative procedure for robust circle fitting is proposed. During the iteration, Taubin’s method is employed to obtain the center and radius. And then the geometric distances from the data points to the circle are computed, with which outliers are identified and removed. Numerical examples demonstrate that the proposed iterative procedure can alleviate the corrupted effect of outliers on the circle parameter estimates.
MSC:
| 62-XX | Statistics |
References:
| [1] | Al-Sharadqah, A.; Chernov, N., Error analysis for circle fitting algorithms, 2009. Electronic Journal of Statistics, 3, 886-911 · Zbl 1268.65022 · doi:10.1214/09-EJS419 |
| [2] | Barnett, V.; Lewis, T., 1994. Outliers in statistical data., New York: Wiley, New York · Zbl 0801.62001 |
| [3] | Bassani, M.; Marinelli, G.; Piras, M., Identification of horizontal circular arc from spatial data sources, 2016. Journal of Surveying Engineering, 142, 4, 04016013 · doi:10.1061/(ASCE)SU.1943-5428.0000186 |
| [4] | Chernov, N., 2010. Circular and linear regression: Fitting circles and lines by least squares., Boca Raton, FL: CRC Press, Boca Raton, FL |
| [5] | Chernov, N., MATLAB code for circle fitting algorithms, 2012 (2017) |
| [6] | Chernov, N.; Sapirstein, P. N., Fitting circles to data with correlated noise, 2008. Computational Statistics and Data Analysis, 52, 12, 5328-5337 · Zbl 1452.62041 · doi:10.1016/j.csda.2008.05.025 |
| [7] | Guo, J., The case-deletion and mean-shift outlier models: Equivalence and beyond, 2013. Acta Geodaetica et Geophysica, 48, 2, 191-197 · doi:10.1007/s40328-013-0017-5 |
| [8] | Huber, P. J., 1981. Robust statistics., New York: Wiley, New York · Zbl 0536.62025 |
| [9] | Huber, P. J.; Ronchetti, E. M., 2009. Robust statistics, New York: Wiley, New York · Zbl 1276.62022 |
| [10] | Kåsa, I., A circle fitting procedure and its error analysis, 1976. IEEE Transactions on Instrumentation and Measurement, 25, 1, 8-14 · doi:10.1109/TIM.1976.6312298 |
| [11] | Koch, K. R., 1999. Parameter estimation and hypothesis testing in linear models., Berlin: Springer, Berlin · Zbl 0921.62080 |
| [12] | Ladrón de Guevara, I.; Muñoz, J.; de Cózar, O. D.; Blázquez, E. B., Robust fitting of circle arcs, 2011. Journal of Mathematical Imaging and Vision, 40, 2, 147-161 · Zbl 1255.68245 · doi:10.1007/s10851-010-0249-8 |
| [13] | Landau, U. M., Estimation of a circular arc center and its radius, 1987. Computer Vision, Graphics, and Image Processing, 38, 3, 317-326 · doi:10.1016/0734-189X(87)90116-2 |
| [14] | Leys, C.; Ley, C.; Klein, O.; Bernard, P.; Licata, L., Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median, 2013. Journal of Experimental Social Psychology, 49, 4, 764-766 · doi:10.1016/j.jesp.2013.03.013 |
| [15] | Pratt, V., Direct least-squares fitting of algebraic surfaces, 1987. Computer Graphics, 21, 4, 145-152 · doi:10.1145/37402.37420 |
| [16] | Rousseeuw, P. J.; Leroy, A. M., 1987. Robust regression and outlier detection., New York: Wiley, New York · Zbl 0711.62030 |
| [17] | Späth, H., Least-squares fitting by circles, 1996. Computing, 57, 2, 179-185 · Zbl 0860.65005 · doi:10.1007/BF02276879 |
| [18] | Taubin, G., Estimation of planar curves, surfaces and nonplanar space curves defined by implicit equations, with applications to edge and range image segmentation, 1991. IEEE Transactions on Pattern Analysis, 13, 11, 1115-1138 · doi:10.1109/34.103273 |
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