Statistical methods of estimating the results of coordinate measurements of intricately shaped surfaces from discretized observations are investigated. Recommendations to complement existing methods of regularization of optimization problems in the calculation of the values of the geometric parameters are given.
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D. A. Masterenko, “On different approaches to estimation of parameters on the basis of highly discretized observations,” Vest. MGTU Stankin, No. 3 (11), 88–94 (2010).
D. A. Masterenko, “Selection of the best estimator of a measured quantity on the basis of highly discretized observations,” Izmer. Tekhn., No. 7, 17–20 (2011).
D. A. Masterenko, “Investigatation of estimators of a measured quantity on the basis of highly discretized observations,” Izmer. Tekhn., No. 8, 22–24 (2011).
D. A. Masterenko, “Statistical estimaton of measured quantities on the basis of discretized observations with unknown scale parameter of the random component,” Izmer. Tekhn., No. 6, 40–42 (2012).
D. A. Masterenko, “Investigatation of estimators of the parameters of a linear statistical model on the basis of highly discretized observations,” Vest. MGTU Stankin, No. 3 (22), 89–93 (2012).
S. N. Grigor’ev, D. A. Masterenko, M. G. Koval’skii, and P. N. Yemel’yanov, “Experience of MGTU STANKIN in the development of coordinate-measuring machines of submicron precision,” Kontrol. Diagn., No. 12, 25–30 (2012).
D. A. Masterenko, P. N. Yemel’yanov, M. G. Koval’skii, et al., “Development of a model series of coordinate-measuring machines,” Izmer. Tekhn., No. 12, 23–27 (2013).
S. A. Kononogov, V. G. Lysenko, and S. Yu. Zolotarevskii, “The concept of assuring the uniformity of coordinate measurements of the geometric parameters of intricately shaped surfaces,” Pribory, No. 3, 1–11 (2008).
S. A. Kononogov, V. G. Lysenko, D. V. Gogolev, and S. Yu. Zolotarevskii, “Procedural foundations of 3-D measurements of the geometric parameters of geometric surfaces of complex form,” Pribory, No. 12, 12–18 (2008).
D. V. Gogolev, Development and Investigation of Methods and Means of Assuring the Uniformity of Measurements of the Geometric Parameters of Deviations of the Form of Intricately Shaped Surfaces: Auth. Abstr. Dissert. Cand. Techn. Sci., VNIIMS, Moscow (2009).
V. I. Teleshevskii, A. V. Shulepov, and A. P. Yesin, “Methods of increasing the precision of linear measurements on measuring microscopes by digital processing optical images,” Vest. MGTU Stankin, No. 1, 102–107 (2009).
V. I. Teleshevskii, A. V. Shulepov, and Ye. M. Rozdina, “Method of smart computer microscopy in measurement of the linear and angular dimensions of articles,” Izmer. Tekhn., No. 8, 3–6 (2011).
GOST 24642–81, GSI. Basic Standards of Interchangeability. Tolerances of Form and Position of Surfaces. Basic Terms and Definitions.
D. Umbach and K. N. Jones, “A few methods for fitting circles to data,” IEEE Trans. Instrum. Measur., 52, No. 6, 1881–1885 (2003).
Heng-sheng Wang, Qiang Zhang, and Fu-liang Wang, “Iterative circle fitting based on circular attracting factor,” J. Central. South. Univer., 20, No. 10, 2663–2675 (2013).
I. Kasa, “A circle fitting procedure and its error analysis,” IEEE Trans. Instrum. Measur., IM-25, No. 1, 8–14 (1976).
S. V. Mikhlyaev, “Approximation of a circle in measurement of the diameter of a crystal,” Vychisl. Tekhnol., 12, No. 1, 61–71 (2007).
F. L. Bookstein, “Fitting conic sections to scattered data,” Comp. Vis. Graph. Image Process., No. 9, 56–71 (1979).
P. D. Sampson, “Fitting conic sections to very scattered data – an iterative refinement of the Bookstein algorithm,” Comp. Vis. Graph. Image Process., No. 18, 97–108 (1982).
M. D. Kudryavstev and N. L. Yavorovskaya, “Estimation of the errors of coordinate measurements of geometric parameters under the conditions of an ill-posed measurement problem,” Navigation and Motion Control: Proc. 8th Sci. Techn. Conf. of Young Scientists, St. Petersburg (2006).
V. P. Suslin, A. V. Dzhunkovskii, and M. G. Shuter, “A new method of determining the geometric parameters of objects in measurements on small objects,” Prikl. Zakonodat. Metrol., No. 6, 39–42 (2008).
V. P. Suslin and A. V. Dzhunkovskii, “Use of the method of regularization for the solution of ill-posed problems of coordinate measurements,” Izmer. Tekhn., No. 7, 23–27 (2009).
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Translated from Izmeritel’naya Tekhnika, No. 7, pp. 28–31, July, 2015.
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Masterenko, D.A. Advantages Gained with the Use of Methods of Statistical Processing of Discretized Observations in Coordinate Measurements of Intricately Shaped Surfaces. Meas Tech 58, 766–771 (2015). https://doi.org/10.1007/s11018-015-0791-2
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DOI: https://doi.org/10.1007/s11018-015-0791-2