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I found an old thread on the panotools wiki.
https://wiki.panotools.org/User:Klaus/Improving_Hugin
As long as there is no hard vignetting in the lens, the reasoning should work.
Best regards
Klaus
I am using a free service. Downside is that the 2.5 GB will expire there after 48 hours. Files from a Parrot Anafi drone flight are here:
Feel free to upload some or all files to more permanent storage.
Best regards
Klaus
Hallöchen!
klaus...@gmail.com writes:
> I found an old thread on the panotools wiki.
>
> https://wiki.panotools.org/User:Klaus/Improving_Hugin
I find the language hard to understand, sorry. Anyway … what is the
argument against even exponents?
> As long as there is no hard vignetting in the lens, the reasoning
> should work.
How does the vignetting affect distortion?
Am 23.07.2018 um 17:26 schrieb klaus...@gmail.com:
> Non-zero parameters a and c introduce singularities at r=0, something a real lens does not have.
Since the correction function itself doesn't have a singularity at r=0
and all that changes at r=0 is the slope of the curve there is a change
in magnification only in the center. Since a single mathematical point
can't be magnified there is no singularity either. The point in the
center stays in the center.
In the wiki discussion you write "sqrt() has a singularity at 0". This
is not true. sqrt(0) is 0
Am 24.07.2018 um 21:01 schrieb klaus...@gmail.com:
> I found an old thread on the panotools wiki.
>
> https://wiki.panotools.org/User:Klaus/Improving_Hugin
There probably is one problem we didn't consider then: Higher order
polynomials tend to overfit.
That might be the reason why professor
Dersch choose the current model (he's a mathematician after all).
At least that's the opinion of Joost, the maker of PTGui (where this
discussion pops up from time to time, too).
There's nothing gained if we have a "correct" lens distortion model that
can't be safely optimized...
Am 25.07.2018 um 16:38 schrieb klaus...@gmail.com:
> Please compute, in cartesian coordinates, the partial derivative d^2/dxdx
> of the 2-dim mapping function with c=1 as parameter.
> Hint: you'll encounter some x/abs(x) - like terms.
>
>
>
>> In the wiki discussion you write "sqrt() has a singularity at 0". This
>> is not true. sqrt(0) is 0
>>
> In simple language: singularities can be present even if the function is
> continuous.
And how would this affect the image? For no correction at all the
function is linear with a slope of 45°. If there are a, b and c
parameters the d parameter is adjusted such that the curve always goes
through (1,1). For some parameter values it is not 45° at (0,0), but
this results in a different magnification in the center, like to be
expected if you want to correct pincushion or barrel distortion.
My math is too rusty to argue with you, but I would be interested
whether you can estimate how large the error would be?
Will it be as
large or larger than the error f.e. introduced by parallax due to
entrance pupil shift (which is pronounced for fisheye lenses but also
present for rectilinear wide angles).
Hello,I am using a free service. Downside is that the 2.5 GB will expire there after 48 hours. Files from a Parrot Anafi drone flight are here:
Because a spherical lens surface parametrised as z(x,y) is holomorphic.
Then light refraction according to Snell's law also gives holomorphic funktions for the rays. All this if course has a finite convergence radius.
Aspherical corrections are usually even polynomials and hence keep the lens surface holomorphic.
Of course a random lens surface (Flaschenboden) is not holomorphic let alone rotationally symmetric.
Now my point is not to throw out parameters a and c. Leave them in for backward compability. My query is to add two more odd terms. My prediction is that CP errors will go down significantly.
Fine-tuned CPs are good to about 1/10th of a pixel. This is what I found for my cameras in the past.
Best regards
Klaus
Thank you for looking into it. While I was sure the drone drifted barely, and as the photos are taken from 100m height I cannot prove that it is not parallax.
What I can do is to take some photos while not flying. It will not be a 360 degrees panoramic but more like 120 to 150 degs, however I can control the nodal point to a few mm and typical objects are 100+ metres away.
Best regards
Klaus
Am 25.07.2018 um 23:09 schrieb Erik Krause:
>> What I can do is to take some photos while not flying. It will not be
>> a 360 degrees panoramic but more like 120 to 150 degs, however I can
>> control the nodal point to a few mm and typical objects are 100+
>> metres away.
> That would certainly help.
... provided you use the entrance pupil and not the nodal point ;-)
...
The parallax is clearly visible. See the roof of the house move against
the background: http://erik-krause.de/parallax-foehl.gif
Am 26.07.2018 um 13:32 schrieb klaus...@gmail.com:
> This difference image shows the misalignment near the corner:
> http://www.foehl.net/tiff00010002.jpg
This could as well be caused by parallax due to entrance pupil shift.
And it is hard to tell whether chromatic aberration plays a role with
this kind of red-green comparison. Better to use the green channel only.
As you notice, the mathematical lens model, despite its shortcoming, does a halfway decent job at about pixel or half pixel level. In a finished panoramic, you visually notice when images are misaligned at the seam line.
Hugin's sidekick enblend does a really good job in sorting out seam problems.
Barrel correction is mathematically ok. The extra freedom parameters a and c give you work if you spread your CPs out, or in problematic cases you position them nearby the seam line.
Issues do appear when you want to place your seam line away from the geometrical optimum placement. To avoid a car being cut in half for instance.
The limitations also make it necessary that hugin / panotools have to provide different lens models, as rectangular and fisheye lenses cannot be unified. With two more odd polynomials they could. It is amazing how well a Taylor series with four odd terms can approximate tan()...
I think I should do a proper write-up.
But not tonight.
And then there are real world problems like parallax errors, image noise and oversharpened source images. For the latter cases, when CPs become dodgy, hugin is good enough. It is in good cases that its limitations get apparent.
Best regards
Klaus