I have the fundamental matrix F =

0.0000158837883646 -0.0000152334359882 -0.0002570398792159

0.0000189358888747 0.0000186621982721 -0.0041565797291696

-0.0049716099165380 -0.0040264814160764 1.0000000000000000

I want camera matrices on the canonical form P1 = [ I | 0 ], P2 = [ E*F | e

], where E is the skew-symmetric cross-product form of e and e is the left

epipole defined by e*F = 0. This is better explained on p.256 in "Multiple

View Geometry".

Could someone calculate e and P2 for me so I can see how they are supposed

to look like?

I get e = [ 0.11755536 0.99305763 0.00415794 ]

and P2 =

-0.00493717 -0.00399861 0.99307491 0.11755536

0.00058451 0.00047327 -0.11755643 0.99305763

-0.00001355 0.00001732 -0.00023337 0.00415794

but P2 doesn't seem right...

-Jostein

2008/12/27 Jostein Austvik Jacobsen <

[hidden email]>

> I'm trying to implement the optimal triangulation method (Algorithm 12.1

> from "Multiple View Geometry<

http://books.google.no/books?id=si3R3Pfa98QC&printsec=frontcover&dq=Multiple+View+Geometry+in+Computer+Vision>"),

> but I'm having some trouble getting the results I want.

>

> I haven't found many examples of fundamental matrices and on on the web, so

> I'm wondering if someone has got a set of a fundamental matrix, two camera

> matrices (one of which is the 3x4 identity matrix), and a few points in 2D

> and 3D for me to test with.

>

> In my implementation, I get to the last point "(xi) The 3-space point X may

> then be obtained by the homogeneous method of 12.2". This, however, requires

> two camera matrices. As suggested in the same book, I use P1 = [1 0 0 0; 0 1

> 0 0; 0 0 1 0] and P2 = [e2x * F | e2] where F is the fundamental matrix, e2

> is the left epipole from e2' * F = 0 and e2x is the skew-symmetric matrix

> form of e2. Using cvSVD to find e2 from F, and the input images left01.jpg

> and right01.jpg from the repositories (in /opencv/samples/c/*) I obtain the

> following e2 and P2:

>

> F: ( 3 x 3 )

> 0.00000041 -0.00003567 0.00938759

> 0.00003563 -0.00000333 -0.03538222

> -0.01032410 0.03462822 1.00000000

>

> e2: ( 1 x 3 )

> 0.95907376

> 0.28315455

> 0.00101525

>

> P2: ( 4 x 3 )

> -0.00292335 0.00980514 0.28319047 0.95907376

> 0.00990157 -0.03321106 -0.95906423 0.28315455

> 0.00003406 0.00000691 -0.03659230 0.00101525

>

> I believe this camera matrix P2 is the problem. Shouldn't P2(0,0) and

> P2(1,1) be closer to 1.0 ?

>

> Of course, if anyone has a finished implementation which does this already

> (which they'd like to share), I'd be happy to use that instead :)

>

> -Jostein

>

[Non-text portions of this message have been removed]