Unified computation of strict maximum likelihood for geometric fitting

Journal of Mathematical Imaging and Vision

Volumn 38, Issue 1, 2010, Pages 1-13

  Kanatani, Kenichi ^a   Sugaya, Yasuyuki ^b  

^a OKAYAMA UNIVERSITY   (Japan)

^b TOYOHASHI UNIVERSITY OF TECHNOLOGY   (Japan)

Author keywords

Ellipse fitting; Fundamental matrix; Geometric fitting; Maximum likelihood; Stereo image triangulation

Indexed keywords

ELLIPSE FITTING; FUNDAMENTAL MATRIX; GEOMETRIC FITTING; STEREO IMAGE TRIANGULATION; STEREO-IMAGE;

DISTANCE MEASUREMENT; GEOMETRY; MATRIX ALGEBRA; OPTIMIZATION; TRIANGULATION;

MAXIMUM LIKELIHOOD;

EID: 77952590115     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-010-0206-6     Document Type: Article

References (30)

1. S.J. Ahn W. Rauh H.S. Cho H.-J. Warecke 2002 Orthogonal distance fitting of implicit curves and surfaces IEEE Trans. Pattern Anal. Mach. Intell. 24 620 638 10.1109/34.1000237 (Pubitemid 34550430)
2. A. Atieg G.A. Watson 2003 A class of methods for fitting a curve or surface to data by minimizing the sum of squares of orthogonal distances J. Comput. Appl. Math. 158 277 296 1034.65007 10.1016/S0377-0427(03)00448-5 2000302 (Pubitemid 37142094)
3. A. Bartoli P. Sturm 2004 Nonlinear estimation of fundamental matrix with minimal parameters IEEE Trans. Pattern Anal. Mach. Intell. 26 426 432 10.1109/TPAMI.2004.1262342
4. Björck, A.: Numerical Methods for Least Squares Problems. SIAM, Philadelphia, PA (1996)
5. Boyd, S., Vandenberghe, L.: Convex Optimization. Cambridge University Press, Cambridge (2004)
6. N. Chernov C. Lesort 2004 Statistical efficiency of curve fitting algorithms Comput. Stat. Data Anal. 47 713 728 05374078 10.1016/j.csda.2003.11. 008 2101548
7. W. Chojnacki M.J. Brooks A. van den Hengel D. Gawley 2000 On the fitting of surfaces to data with covariances IEEE Trans. Pattern Anal. Mach. Intell. 22 1294 1303 10.1109/34.888714
8. W. Chojnacki M.J. Brooks A. van den Hengel D. Gawley 2004 A new constrained parameter estimator for computer vision applications Image Vis. Comput. 22 85 91 10.1016/S0262-8856(03)00140-9
9. Föstner, W.: On weighting and choosing constraints for optimally reconstructing the geometry of image triplets. In: Proc. 6th Eur. Conf. Comput. Vision, Dublin, Ireland, June/July 2000, vol. 2, pp. 669-701
10. W. Gander H. Golub R. Strebel 1994 Least-squares fitting of circles and ellipses BIT 34 558 578 0817.65008 10.1007/BF01934268 1430909
11. Harker, M., O'Leary, P.: First order geometric distance (The myth of Sampsonus). In: Proc. 17th Brit. Mach. Vision Conf., Edinburgh, UK, September 2006, vol. 1, pp. 87-96
12. R.I. Hartley 1997 In defense of the eight-point algorithm IEEE Trans. Pattern Anal. Mach. Intell. 19 580 593 10.1109/34.601246
13. Hartley, R., Kahl, F.: Optimal algorithms in multiview geometry. In: Proc. 8th Asian Conf. Comput. Vision, Tokyo, Japan, November 2007, vol. 1, pp. 13-34
14. R.I. Hartley P. Sturm 1997 Triangulation Comput. Vis. Image Underst. 68 146 157 10.1006/cviu.1997.0547 (Pubitemid 28127056)
15. Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004)
16. Kanatani, K.: Statistical Optimization for Geometric Computation: Theory and Practice. Elsevier Science, Amsterdam (1996); reprinted Dover, New York, 2005
17. K. Kanatani 1998 Cramer-Rao lower bounds for curve fitting Graph. Models Image Process. 60 93 99 10.1006/gmip.1998.0466
18. K. Kanatani 2008 Statistical optimization for geometric fitting: theoretical accuracy analysis and high order error analysis Int. J. Comput. Vis. 80 167 188 10.1007/s11263-007-0098-0
19. K. Kanatani N. Ohta 2003 Comparing optimal three-dimensional reconstruction for finite motion and optical flow J. Electron. Imaging 12 478 488 10.1117/1.1579018
20. K. Kanatani Y. Sugaya 2007 High accuracy fundamental matrix computation and its performance evaluation IEICE Trans. Inf. Syst. E90-D 579 585 10.1093/ietisy/e90-d.2.579 (Pubitemid 46279833)
21. Kanatani, K., Sugaya, Y.: Extended FNS for constrained parameter estimation. In: Proc. Meeting Image Recognition and Understanding, Hiroshima, Japan, July-August 2007, pp. 219-226
22. K. Kanatani Y. Sugaya 2007 Performance evaluation of iterative geometric fitting algorithms Comput. Stat. Data Anal. 52 1208 1222 05560224 10.1016/j.csda.2007.05.013 2418557 (Pubitemid 47552619)
23. K. Kanatani Y. Sugaya 2010 Compact fundamental matrix computation IPSJ Trans. Comput. Vision Appl. 2 59 70 10.2197/ipsjtcva.2.59
24. Kanatani, K., Sugaya, Y., Niitsuma, H.: Triangulation from two views revisited: Hartley-Sturm vs. optimal correction. In: Proc. 19th British Machine Vision Conf., Leeds, UK, September 2008, pp. 173-182
25. Y. Leedan P. Meer 2000 Heteroscedastic regression in computer vision: Problems with bilinear constraint Int. J. Comput. Vis. 37 127 150 0985.68627 10.1023/A:1008185619375
26. B.C. Matei P. Meer 2006 Estimation of nonlinear errors-in-variables models for computer vision applications IEEE Trans. Pattern Anal. Mach. Intell. 28 1537 1552 10.1109/TPAMI.2006.205 (Pubitemid 46405076)
27. Mikhail, E.M., Ackermann, F.: Observations and Least Squares. University Press of America, Lanham (1976)
28. P.D. Sampson 1982 Fitting conic sections to "very scattered" data: an iterative refinement of the Bookstein algorithm Comput. Graph. Image Process. 18 97 108 10.1016/0146-664X(82)90101-0
29. Sturm, P., Gargallo, P.: Conic fitting using the geometric distance. In: Proc. 8th Asian Conf. Comput. Vision, Tokyo, Japan, November 2007, vol. 2, pp. 784-795
30. Triggs, B., McLauchlan, P.F., Hartley, R.I., Fitzgibbon, A.: Bundle adjustment-a modern synthesis. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) Vision Algorithms: Theory and Practice, pp. 298-375. Springer, Berlin (2000)