Distortion parameters "a,b,c" to "k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]]" (OpenCV)

[Finfa811]

Hi there,

I've calibrated my camera and estimated the a,b,c lens distortion parameters, and now I would like to apply some OpenCV code to my images.

How do I convert my a,b,c parameters to OpenCV style "k_1, k_2, p_1, p_2[, k_3[, k_4, k_5, k_6]]"?

Thanks.

[Erik Krause]

Am 29.06.2016 um 14:22 schrieb Finfa811:

> How do I convert my a,b,c parameters to OpenCV style "k_1, k_2, p_1, p_2[,
> k_3[, k_4, k_5, k_6]]"?

The a,b,c parameters define a polynomial curve which describes the
distortion of the image. See
http://wiki.panotools.org/Lens_correction_model for details.

OpenCV apparently uses a different polynomial. As far as I know there is
no easy way to transform one polynomial into another. Your best bet is
probably to use hugin to correct for lens distortion...

--
Erik Krause
http://www.erik-krause.de

[Finfa811]

I've found a solution in the following link:

http://www.panotools.org/dersch/barrel/barrel.html

• a = k₂ * (width/2)³
• b = 0
• c = k₁* (width/2)
• d = 1

The minimum input that OpenCV uses for its polynomial is k1k2p1p2 (4 parameters). In my case, just the parameter c was not zero (other than d), so only k1 will be used. The result is pretty much the same.

Thank you for your help anyway.

[Torsten Bronger]

Hallöchen!

Finfa811 writes:

> I've found a solution in the following link:
>

> *http://www.panotools.org/dersch/barrel/barrel.html*
>
> - a = k2 * (width/2)3
> - b = 0
> - c = k1* (width/2)
> - d = 1

>
> The minimum input that OpenCV uses for its polynomial is k1k2p1p2
> (4 parameters). In my case, just the parameter c was not zero
> (other than d), so only k1 will be used. The result is pretty much
> the same.

I'm suprised that this works.

First, the only coefficients of the same power in r in both models
are b and k1. Both apply to r^3. OpenCV's k2 and k3 apply to r^5
and r^7, respectively, both of which don't have counterparts in
Hugin.

Secondly, d in Hugin is 1-a-b-c rather than 1. The difference is
noticable for real-world lenses in my experience.

I think the only way to make both compatible is to use only b in
Hugin for calibration, take the different coordinate system into
account (i.e. scaling factor to the power of 3), and take d!=1 into
account by dividing the resulting k1 by (1-b)^3.

(Beware that I haven't checked the calculation, and one can easily
make mistakes in these things.)

Tschö,
Torsten.

--
Torsten Bronger Jabber ID: torsten...@jabber.rwth-aachen.de

[Bruno Postle]

Yes, there is no direct conversion possible unless you limit the
parameters. However given the two formulas, this is a curve fitting
problem - it ought to be possible to get a very good approximation
with a spreadsheet solver.

--
Bruno

[bugbear]

'Bruno Postle' via hugin and other free panoramic software wrote:
> Yes, there is no direct conversion possible unless you limit the
> parameters. However given the two formulas, this is a curve fitting
> problem - it ought to be possible to get a very good approximation
> with a spreadsheet solver.
>

If they are both good and useful models of the same
distortions, they should indeed map onto each other,
"somehow", at least for realistic and/or common cases.

BugBear

[Finfa811]

In my case it is working, maybe it's just coincidence because I've checked the polynomials and you are right. Probably the ccd width value is the correct one that returns a valid solution in my case.

In any case it would be nice to try with different lenses. 

[Torsten Bronger]

Hallöchen!

'Bruno Postle' via hugin and other free panoramic software writes:

> Yes, there is no direct conversion possible unless you limit the
> parameters. However given the two formulas, this is a curve fitting
> problem - it ought to be possible to get a very good approximation
> with a spreadsheet solver.

In case of non-matching powers, I failed to achieve this. I tried
to convert Adobe's ACM model (Lightroom) to Hugin by re-sampling the
Adobe polynomial. The results were unusable. I suspected this was
due to the fact that two terms with different powers are orthogonal.

However, if all powers are availiable in the destination model, you
have a fighting chance, even to convert exactly.

We recently had a similar problem on the Lensfun mailing list.
There, a general a,b,c,d model should be mapped to Hugin's
a,b,c,(1-a-b-c) model. This works exactly because you have scaling
as one degree of freedom. This way, one coefficient (no matter
which!) can be set to an arbitrary non-zero value. The conversion
is not easy, though.