Hallöchen!

Okay, now for the definitive, thoroughly calculated solution.  Sorry
for the confusion.

Helmut Jarausch writes:

> [...]
>
> - using Octave I fitted a polynomial of the form    
> r*(d+r*(c+r*(b+r*a))) to the data using a smoothed maximum norm

Let me write this in a different way:

r_d = a·r⁴ + b·r³ + c·r² + d·r

r:   Radius in the undistorted target image
r_d: Radius in the distorted original image

r is allowed to be scaled; this causes a mere scaling of the
result.  r_d must not be scaled.

If I use e·r instead of r for the look-up, I simply scale down the
target image uniformly by the factor e:

r_d = a·e⁴·r⁴ + b·e³·r³ + c·e²·r² + d·e·r

With the Lensfun+PanoTools constraint

d·e = 1 − a·e⁴ − b·e³ − c·e²

I have an equation for e.

> [...]
>
> Here are my results:
>
> The focal lengthes here are scaled by the crop factor
>
> focal length     d          c            b           a
>      25         0.997913   0.0213096   -0.102825    0.0261528

Let's take this example.

The scaling e is 1.069413355 (solved the above equation numerically,
taking the only real solution).  Thus the Lensfun coefficients are:

a = 0.03420586726
b = -0.1257579729
c = 0.02437061587

If you use this in Lensfun, the correction should work equally well
(plus a global uniform scaling of the resulting image).

Tschö,
Torsten.

-- 
Torsten Bronger    Jabber ID: [email protected]


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