Re: What is optimized FOV really?

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