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Re: What is optimized FOV really?

by Aron H :: Rate this Message:

On Jul 3, 4:08 am, Klaus Foehl <k...@...> wrote:

> Hello,
>
> Quick addition and summary from my side.
>
> 1) Barrel distortion correction: panotools uses r* = a*r^4 + b*r^3 +
> c*r^2 + d*r,
> with r being the normalised radius. If it were not for the condition a
> +b+c+d=1
> this parameter d would be fully collinear with the focal length.
> focal_length_panotools * d = true_focal_length
>
> 2)http://www.vision.caltech.edu/bouguetj/calib_doc/htmls/parameters.html
> x_d=x_n * (1+kc(1)*r^2+kc(2)*r^4+kc(5)*r^6) +dx, dx=[...]
> Looking at the distortion formulas the Bouguet model looks
> mathematically
> sound to me, as the parameters x_d and dx only use odd and even
> powers,
> respectively, of (r,x,y) polynomial expressions.
> That respects the lense symmetry. Parameters a and c in panotools do
> not.

I've looked through Bouguet's site for an explanation of the symmetry
issue, and I think he pushes it off to publications. I guess I don't
know what the argument is, except perhaps that r^2 and r^4 distortion
are expected from the lens design, and the r and r^3 are not. The
formulas only deal with positive r values, and apply distortion
totally in the radial direction, so they are 'symmetric' in that
sense. Is there a good explanation of this somewhere?

>
> 3) In the xd formula 1 is equivalent to d, kc(1)=b/d, kc(2) and kc(5)
> are unaccounted for. (N.B. I suggested a few times to include
> a kc(2) type parameter into hugin/panotools).

Note, however, that the 'r' parameter is scaled differently in Hugin
and Bouguet. I'll write up the derivation....

>
> 4) Sheer parameters are available in panotools but are not shown
> in the hugin GUI. There are two parameters, and combined with
> the roll parameter I suspect that this set of three only spans
> a two-dimensional configuration space, save for possibly a
> higher order correction that results in non-square-like pixels.
>
> 5) Tangential distortion vectors, kc(3) and kc(4) in Bouguet,
> I have not seen such in hugin/panotools.
>
> 6) Principal point cc in Bouguet are parameters e and f
> in panotools, in the GUI labelled x and y.
>
> 7) Rectangular non-square pixels, Bouguet using fc(1) and fc(2),
> are not there in the hugin/panotools model.
>
> Summary: models are reasonably similar, Bouguet is more powerful,
> and parameters a and c of hugin/panotools, the only ones
> I cannot find a match in Bougues, have a maths symmetry issue.
>
> Cheers
> Klaus

I agree with the rest, thanks for the nice summary,
Aron
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