| | This Article | |
| |
| |
| | Share | |
| |
| |
| | Bibliographic References | |
| |
| |
| | Add to: | |
| |
 Digg
 Furl
 Spurl
 Blink
 Simpy
 Google
 Del.icio.us
 Y!MyWeb
| |
| | Search | |
| |
| |
| | |
From FNS to HEIV: A Link between Two Vision Parameter Estimation Methods
February 2004 (vol. 26 no. 2)
pp. 264-268
Abstract—Problems requiring accurate determination of parameters from image-based quantities arise often in computer vision. Two recent, independently developed frameworks for estimating such parameters are the FNS and HEIV schemes. Here, it is shown that FNS and a core version of HEIV are essentially equivalent, solving a common underlying equation via different means. The analysis is driven by the search for a nondegenerate form of a certain generalized eigenvalue problem and effectively leads to a new derivation of the relevant case of the HEIV algorithm. This work may be seen as an extension of previous efforts to rationalize and interrelate a spectrum of estimators, including the renormalization method of Kanatani and the normalized eight-point method of Hartley.
[1] 264 O.D. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint. Cambridge, Mass.: MIT Press, 1993.[2] M.J. Brooks, W. Chojnacki, and L. Baumela, Determining the Egomotion of an Uncalibrated Camera from Instantaneous Optical Flow J. Optical Soc. Am. A, vol. 14, no. 10, pp. 2670-2677, 1997.[3] A. Fitzgibbon, M. Pilu, and R.B. Fisher, “Direct Least Square Fitting of Ellipses,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 21, no. 5, pp. 476-480, May 1999.[4] K. Kanatani, Statistical Optimization for Geometric Computation: Theory and Practice. Amsterdam: Elsevier, 1996.[5] W. Chojnacki, M.J. Brooks, A. van den Hengel, and D. Gawley, On the Fitting of Surfaces to Data with Covariances IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 22, no. 11, pp. 1294-1303, Nov. 2000.[6] M. Brooks, W. Chojnacki, D. Gaeley, and A. can den Hengel, What Value Covariance Information in Estimating Vision Parameters? Proc. IEEE Eighth Int'l Conf. Computer Vision, pp. 302-308, 2001.[7] Y. Leedan and P. Meer, Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint Int'l J. Computer Vision, vol. 37, no. 2, pp. 127-150, 2000.[8] B. Matei and P. Meer, “A General Method for Errors-in-Variables Problems in Computer Vision,” Proc. Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 18-25, June 2000.[9] B. Matei, Heteroscedastic Errors-in-Variables Models in Computer Vision PhD dissertation, Dept. Electrical and Computer Eng., Rutgers Univ., New Brunswick, N.J., May 2001, http://www.caip.rutgers.edu/riul/research theses.html.[10] W. Chojnacki, M.J. Brooks, A. van den Hengel, and D. Gawley, A New Approach to Constrained Parameter Estimation Applicable to Some Computer Vision Problems Proc. Statistical Methods in Video Processing Workshop, held in conjunction with ECCV2002, pp. 43-48, 2002.[11] A. van den Hengel, W. Chojnacki, M.J. Brooks, and D. Gawley, A New Constrained Parameter Estimator: Experiments in Fundamental Matrix Computation Proc. 13th British Machine Vision Conf., vol. 2, pp. 468-476, 2002.[12] W. Chojnacki, M.J. Brooks, A. van den Hengel, Rationalising the Renormalisation Method of Kanatani J. Math. Imaging and Vision, vol. 14, no. 1, pp. 21-38, 2001.[13] W. Chojnacki, M.J. Brooks, A. van den Hengel, and D. Gawley, Revisiting Hartley's Normalized Eight-Point Algorithm IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, no. 9, pp. 1172-1177, Sept. 2003.[14] B.N. Parlett, The Symmetric Eigenvalue Problem. Englewood Cliffs, N.J.: Prentice-Hall, 1980.[15] R. Halír and J. Flusser, Numerically Stable Direct Least Squares Fitting of Ellipses Proc. Sixth Int'l Conf. Computer Graphics and Visualization, vol. 1, pp. 125-132, 1998, http://wscg.zcu.cz/wscg98wscg98.htm.[16] http://www.caip.rutgers.edu/riul/research code.html. 2003.[17] http://www.cs.adelaide.edu.au/~hengel/Vision/ Codeindex.html. 2003.
Index Terms:
Statistical methods, maximum likelihood, (un)constrained minimization, fundamental matrix, epipolar equation.
Citation:
Wojciech Chojnacki, Michael J. Brooks, Anton van den Hengel, Darren Gawley, "From FNS to HEIV: A Link between Two Vision Parameter Estimation Methods," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 26, no. 2, pp. 264-268, Jan. 2004, doi:10.1109/TPAMI.2004.1262197
