A. V. Gorevoy, A. S. Machikhin, A. M. Perfilov

Read the full article 
Article in Russian


The problem of non-contact surface defect area measurement at complex-shape objects under videoendoscopic control is considered. Major factors contributing to the measurement uncertainty are analyzed for the first time. The proposed method of accuracy analysis is based on the evaluation of 3D coordinates of surface points from 2D projections under assumption of projective camera model and Mahalanobis distance minimization in the image plane. Expressions for area measurement error caused by sum-of-triangles approximation are obtained analytically for practically important cases of cylindrical and spherical surfaces. It is shown that the magnitude of this error component for a single triangle does not exceed 1% for the real values of parameters of the endoscopic imaging system. Expressions are derived for area measurement uncertainty evaluation on arbitrary shape surfaces, caused by measurement errors of 3D coordinates of individual points with and without a priori information about surface shape. Verification of the obtained expressions with real experiment data showed that area measurement error for a complex figure, given by a set of points, is mainly caused by ignoring the fact that these points belong to the surface. It is proved that the use of a priori information about investigated surface shape, which is often available from the design documentation, in many cases would radically improve the accuracy of surface defects area measurement. The presented results are valid for stereoscopic, shadow and phase methods of video endoscopic measurements and can be effectively used in development of new non-contact measuring endoscopic systems and modernization of existing ones.

Keywords: visual and measuring control, surface area measurement, videoendoscopy, measuring endoscope, measurement accuracy, triangulation

1.     Klyuev V.V., Sosnin F.R., Kovalev A.V. Nerazrushayushchii Kontrol' i Tekhnicheskaya Diagnostika [Non-Destructive Testing and Technical Diagnostics]. Moscow, Mashinostroenie Publ., 2003, 656 p.
2.     Chigorko A.B., Chigorko A.A. Uzly i Sistemy Volokonno-Opticheskikh Endoskopov [Assemblies and Systems of Fiber Optic Endoscopes]. Tomsk, TPUPubl., 2007, 134 p.
3.     Machikhin A.S. Sovremennye tekhnologii vizual'no-izmeritel'nogo kontrolya aviatsionnykh dvigatelei [Modern technology and visual measuring control of aircraft engines]. Dvigatel', 2009, no. 1, pp. 26–28.
4.     Machikhin A.S. Izmeritel'nye vozmozhnosti sovremennykh videoendoskopov [Measurement capabilities of modern video endoscopes]. Dvigatel', 2009, no. 3, pp. 8–9
5.     Schick A., Forster F., Stockmann M. 3D measuring in the field of endoscopy. Proc. SPIE, 2011, vol. 8082, art. no. 808216. doi: 10.1117/12.889167
6.     Ivanov V.A., Marusina M.Ya., Sizikov V.S. Obrabotka izmeritel'noi informatsii v usloviyakh neopredelennostei [Measuring information processing under uncertainty]. Kontrol'. Diagnostika, 2001, no. 4, pp. 40–43.
7.     Hartley R.I., Zisserman A. Multiple View Geometry. 2nd ed. Cambridge, UK: Cambridge University Press, 2000. 670 p.
8.     MarusinaM.Ya. Invariantnyi analiz i sintez v modelyakh s simmetriyami [Invariant analysis and synthesis in models with symmetries]. St. Petersburg, SPbSU ITMO, 2004, 144 p.
9.     Kannala J., Heikkilä J., Brandt S.S. Geometric camera calibration / In: Wah B.W. (ed.) Wiley Encyclopedia of Computer Science and Engineering. Hoboken, USA: Wiley, 2009. P. 1389–1400.
10.  Ramalingam S. Generic Imaging Models: Calibration and 3D Reconstruction Algorithms. Ph. D. thesis. Santa Cruz, USA: Institut National Polytechnique de Grenoble, 2006. 192 p.
11.  Kannala J., Brandt S.S. A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, vol. 28, no. 8, pp. 1335–1340. doi: 10.1109/TPAMI.2006.153
12.  Forsyth D.A., Ponce J. Computer Vision: A Modern Approach. 2nd ed. Upper Saddle River, USA: Prentice-Hall, 2012, 793 p.
13.  Zhang Z. Flexible camera calibration by viewing a plane from unknown orientations. Proc. of IEEE International Conference on Computer Vision, 1999, vol. 1, pp. 666–673.
14.  Kanatani K. Statistical Optimization for Geometric Computation: Theory and Practice. Mineola, USA: Dover Publications, 2005, 528 p.
15.  Volynskii B.A. Sfericheskaya Trigonometriya [Spherical Trigonometry]. Ed. V.V. Klyuev. Moscow, Nauka Publ., 1977, 136 p.
16.  Zhang Z. Determining the epipolar geometry and its uncertainty: a review. International Journal of Computer Vision, 1998, vol. 27, no. 2, pp. 161–195.
17.  Gorevoi A.V., Kolyuchkin V.Ya. Metody otsenki pogreshnosti izmereniya koordinat v kompleksirovannykh sistemakh registratsii trekhmernykh obrazov ob"ektov [Methods for estimating uncertainty of measurement coordinate systems complexed registration of 3D images of objects]. Inzhenernyi Zhurnal: Nauka i Innovatsii,2013, no. 9 (21), p. 45.
18.  Johnson R.A., Wichern D.W. Applied Multivariate Statistical Analysis. 6th ed. Upper Saddle River, USA: Pearson Prentice Hall, 2007, 773 p.
Copyright 2001-2017 ©
Scientific and Technical Journal
of Information Technologies, Mechanics and Optics.
All rights reserved.