© The Institution of Engineering and Technology
The estimation of a fundamental matrix between two views is of great interest for a number of computer vision and robotics tasks. There exist well-known algorithms for this problem: such as normalised eight-point algorithm, fundamental numerical scheme (FNS), extended FNS (EFNS), and heteroscedastic errors-in-variable (HEIV). The Levenberg–Marquardt (LM) method can also be employed to estimate a fundamental matrix; however, for some unknown reason, it was unfairly treated in the literature so that it was reported to have inferior performance. In this study, the authors concentrate on the application of the LM method for fundamental matrix estimation. Particularly, a new Gauss–Newton approximation of the Hessian matrix is presented, when the Sampson error is minimised; and the rank-two constraint of a fundamental matrix is automatically enforced by revitalising a particular parameterisation. An evaluation of algorithms is presented, showing the advantage of these two techniques.
References
-
-
1)
-
Kanatani, K., Sugaya, Y.: `High accuracy fundamental matrix computation and its performance evaluation', 17thBritish Machine Vision Conf., 2006, p. 217–226.
-
2)
-
W. Chojnacki ,
M.J. Brooks ,
A. van den Hengel ,
D. Gawley
.
From FNS to HEIV: A link between two vision parameter estimation methods.
IEEE Trans. Pattern Anal. Mach. Intell.
,
2 ,
264 -
268
-
3)
-
Z. Zhang
.
Determining epipolar geometry and its uncertainty: a review.
Int. J. Comput. Vis.
,
2 ,
161 -
195
-
4)
-
B. Matei ,
P. Meer
.
Estimation of nonlinear errors-in-variables models for computer vision applications.
IEEE Trans. Pattern Anal. Mach. Intell.
,
10 ,
1537 -
1552
-
5)
-
A. Bartoli ,
P. Sturm
.
Nonlinear estimation of fundamental matrix with minimal parameters.
IEEE Trans. Pattern Anal. Mach. Intell.
,
3 ,
426 -
432
-
6)
-
S. Baker ,
I. Matthews
.
Lucas–Kanade 20 years on: a unifying framework.
Int. J. Comput. Vis.
,
221 -
255
-
7)
-
Z. Zhang
.
On the optimization criteria used in two-view motion analysis.
IEEE Trans. Pattern Anal. Mach. Intell.
,
7 ,
717 -
729
-
8)
-
G.H. Golub ,
C.F. Van Loan
.
(1989)
Matrix computations.
-
9)
-
Kanatani, K., Sugaya, Y.: `High accuracy computation of rank-constrained fundamental matrix', 18thBritish Machine Vision Conf., 2007, p. 72390Q-1-72390Q-12.
-
10)
-
W.H. Press ,
S.A. Teukolsky ,
W.T. Vetterling ,
B.P. Flannery
.
(1996)
Numerical recipes in C.
-
11)
-
R.I. Hartley
.
In defense of the eight-point algorithm.
IEEE Trans. Pattern Anal. Mach. Intell.
,
6 ,
580 -
593
-
12)
-
W. Chojnacki ,
M.J. Brooks ,
A. van den Hengel ,
D. Gawley
.
Fns, cfns and heiv: ‘a unifying approach.
J. Math. Imaging Vis.
,
2 ,
175 -
183
-
13)
-
W. Chojnacki ,
M.J. Brooks ,
A. van den Hengel ,
D. Gawley
.
On the fitting of surfaces to data with covariances.
IEEE Trans Pattern Anal. Mach. Intell.
,
11 ,
1294 -
1303
-
14)
-
http://www.robots.ox.ac.uk/~vgg/data.html.
-
15)
-
R. Hartley
.
(2003)
Multiple view geometry in computer vision.
-
16)
-
Migita, T., Shakunaga, T.: `One-dimensional search for reliable epipole estimation', IEEE Pacific-Rim Symp. on Image and Video Technology, 2006, p. 1215–1224.
-
17)
-
K. Kanatani
.
Statistical optimization for geometric fitting: theoretical accuracy bound and high order error analysis.
Int. J. Comput. Vis.
,
2 ,
167 -
188
-
18)
-
G. Chesi ,
A. Garulli ,
A. Vicino ,
R. Cipolla
.
Estimating the fundamental matrix via constrained least-squares: a convex approach.
IEEE Trans. Pattern Anal. Mach. Intell.
,
3 ,
397 -
401
-
19)
-
W. Chojnacki ,
M.J. Brooks ,
A. van den Hengel ,
D. Gawley
.
A new approach to constrained parameter estimation applicable to some computer vision problems.
Image Vis. Comput.
,
2 ,
85 -
91
-
20)
-
Kanatani, K.: `Unified computation of strict maximum likelihood for geometric fitting', Proc. IS&T/SPIE 21st Annual Symp., EI103: 3D Imaging Meteorology, 2009.
-
21)
-
Kanatani, K., Sugaya, Y.: `Compact fundamental matrix computation', Proc. 2009 IEEE Pacific-Rim Symp. on Image and Video Technology, 2009, p. 179–190.
-
22)
-
Migita, T., Shakunaga, T.: `Evaluation of epipole estimation methods with/without rank-2 constraint across algebraic/geometric error functions', Proc. Computer Vision and Pattern Recognition, 2007.
-
23)
-
Kanatani, K., Sugaya, Y.: `Extended fns for constrained parameter estimation', Proc. Tenth Meeting Image Recog. Understand., 2007, p. 219–226.
-
24)
-
Y. Leedan ,
P. Meer
.
Heteroscedastic regression in computer vision: problems with bilinear constraint.
Int. J. Comput. Vision
,
2 ,
127 -
150
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cvi.2009.0146
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