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Curve and Surface Fitting Techniques in Computer Vision

Kyle Brown

Department of Computer Science, Wright State University, 3640 Colonel Glenn Highway, Dayton, Ohio 45435, USA

E-mail Address: brown.718@wright.edu

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and

Nikolaos Bourbakis

CART Center, Wright State University, 3640 Colonel Glenn Highway, Dayton, Ohio 45435, USA

E-mail Address: nikolaos.bourbakis@wright.edu

Corresponding author.

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https://doi.org/10.1142/S0219467821500418Cited by:2 (Source: Crossref)

Abstract

Curve and surface-fitting are classic problems of approximation that find use in many fields, including computer vision. There are two broad approaches to the problem — interpolation, which seeks to fit points exactly, and regression, which seeks a rougher approximation which is more robust to noise. This survey looks at several techniques of both kinds, with a particular focus on applications in computer vision. We make use of an empirical first-level evaluation approach which scores the techniques on multiple features based on how important they are to users of the technique and developers. This provides a quick summary of the broad applicability of the technique to most situations, rather than a deep evaluation of the performance and accuracy of the technique obtained by running it on several datasets.

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References

1. C. Steger, M. Ulrich and C. Wiedemann , Machine Vision Algorithms and Applications (John Wiley & Sons, 2018). Google Scholar
2. D. K. Prasad, M. K. H. Leung and C. Quek , “Ellifit: An unconstrained, non-iterative, least squares based geometric ellipse fitting method,” Pattern Recogn. 460(5), 1449–1465 (2013). Crossref, Web of Science, Google Scholar
3. A. Tsitsoulis and N. Bourbakis , “A first stage comparative survey on human activity recognition methodologies,” Int. J. Artif. Intell. Tools 22(6) (2013). Link, Web of Science, Google Scholar
4. G. P. Lepage, B. Clark, C. T. H. Davies, K. Hornbostel, P. B. Mackenzie, C. Morningstar and H. Trottier, Constrained curve fitting, arXiv:hep-lat/0110175, 2001. Google Scholar
5. H. Greiner , “A survey on univariate data interpolation and approximation by splines of given shape,” Math. Comput. Model. 15(10), 97–106 (1991). Crossref, Web of Science, Google Scholar
6. M. Gasca and T. Sauer , “Polynomial interpolation in several variables,” Adv. Comput. Math. 12(4), 377 (2000). Crossref, Web of Science, Google Scholar
7. S. Gopalakrishnan and N. Bourbakis , “Curve fitting methods: A survey,” Int. J. Monitor. Surveillance Technol. Res. (IJMSTR) 4(4), 33–53 (2016). Crossref, Google Scholar
8. U. M. Ascher and C. Greif , A First Course in Numerical Methods, Computational Science and Engineering (SIAM, 2011). Crossref, Google Scholar
9. P. O’Leary and M. Harker , “An algebraic framework for discrete basis functions in computer vision,” in 2008 Sixth Indian Conf. Computer Vision, Graphics & Image Processing, pp. 150–157, IEEE, 2008. Crossref, Google Scholar
10. J. Siswantoro and E. Asmawati , “A new framework for measuring volume of axisymmetric food products using computer vision system based on cubic spline interpolation,” in 2016 2nd Int. Conf. Science in Information Technology (ICSITech), pp. 74–78, IEEE, 2016. Crossref, Google Scholar
11. J. Liu, S. Lu, J.-H. Lim, Z. Zhang, T. N. Meng, D. W. K. Wong, H. Li and T. Y. Wong , Photometric correction of retinal images by polynomial interpolation, in 2009 16th IEEE Int. Conf. Image Processing (ICIP), pp. 3893–3896, IEEE, 2009. Crossref, Google Scholar
12. V. Koivunen and R. Bajcsy , “Spline representations in 3-d vision,” in Int. Workshop on Object Representation in Computer Vision, pp. 177–190 (Springer, 1994). Google Scholar
13. C. S. Zhao and R. Mohr, B-spline patches for surface reconstruction in computer vision, 1993. Google Scholar
14. R. Szeliski and J. Coughlan, Hierarchical spline-based image registration, Citeseer, 1994. Google Scholar
15. J.-P. Berrut and L. N. Trefethen , “Barycentric Lagrange interpolation,” SIAM Rev. 46(3), 501–517 (2004). Crossref, Web of Science, Google Scholar
16. E. V. Shikin and A. I. Plis , Handbook on Splines for the User (CRC Press, 1995). Google Scholar
17. C. De Boor , A Practical Guide to Splines (Springer-Verlag, New York, 1978). Crossref, Google Scholar
18. Y. Zhang, J. Cao, Z. Chen, X. Li and X.-M. Zeng , “B-spline surface fitting with knot position optimization,” Comput. Graph. 58, 73–83 (2016). Crossref, Web of Science, Google Scholar
19. D. R. Forsey and R. H. Bartels , “Hierarchical B-spline refinement,” ACM SIGGRAPH Comput. Graph. 22(4), 205–212 (1988). Crossref, Google Scholar
20. S. Yoshizawa, A. Belyaev and H.-P. Seidel , “A fast and simple stretch-minimizing mesh parameterization,” in Proc. Shape Modeling Applications, 2004, pp. 200–208, IEEE, 2004. Crossref, Google Scholar
21. L. A. Piegl and W. Tiller , “Surface approximation to scanned data,” Vis. Comput. 16(7), 386–395 (2000). Crossref, Web of Science, Google Scholar
22. H. Park , “B-spline surface fitting based on adaptive knot placement using dominant columns.” Comput.-Aid. Des. 43(3), 258–264 (2011). Crossref, Web of Science, Google Scholar
23. P. Meer, D. Mintz, A. Rosenfeld and D. Y. Kim , “Robust regression methods for computer vision: A review,” Int. J. Comput. Vis. 6(1), 59–70 (1991). Crossref, Web of Science, Google Scholar
24. L. Hongtao and Z. Qinchuan , “Applications of deep convolutional neural network in computer vision,” J. Data Acquisition Process. 31(1), 1–17 (2016). Google Scholar
25. G. Guo and G. Mu , “Simultaneous dimensionality reduction and human age estimation via kernel partial least squares regression,” In CVPR 2011, pp. 657–664, IEEE, 2011. Crossref, Google Scholar
26. X. Sun, B. Xiao, F. Wei, S. Liang and Y. Wei , “Integral human pose regression,” in Proc. European Conf. Computer Vision (ECCV), pp. 529–545, 2018. Crossref, Google Scholar
27. T. Narihira, M. Maire and S. X. Yu , Direct intrinsics: Learning albedo-shading decomposition by convolutional regression, in Proc. IEEE Int. Conf. Computer Vision, p. 2992, 2015. Crossref, Google Scholar
28. G. Tzimiropoulos , “Project-out cascaded regression with an application to face alignment,” in Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 3659–3667, 2015. Crossref, Google Scholar
29. S. J. Ahn, W. Rauh and H.-J. Warnecke , “Least-squares orthogonal distances fitting of circle, sphere, ellipse, hyperbola, and parabola,” Pattern Recogn. 34(12), 2283–2303 (2001). Crossref, Web of Science, Google Scholar