[CREATE] Lens correction database

[Gerhard Kulzer]

Am Thursday 23 August 2007 schrieb Andrew Zabolotny:
> Hello again!
>
> In the continuation of the theme.
>
> The current draft of the database is based on the panotools lens
> aberration model which is described here:
>
> http://wiki.panotools.org/Lens_correction_model
>
> This model involves a 4-order polynome for modelling both TCA and
> distortion: rd = a * ru^4 + b * ru^3 + c * ru^2 + d * ru, where rd is
> the distance from the image center to the distorted pixel, ru - to the
> undistorted pixel.
>
> However, there is at least one another lens distortion model that is
> used by the Imatest software which is used by some sites (e.g.
> photozone.de) when testing lenses. The model is described here:
>
> http://www.imatest.com/docs/distortion.html
>
> Also the Paul van Walree's page on lens distortion:
>
> http://www.vanwalree.com/optics/distortion.html
>
> seems to like this lens model. It uses a 5-th order polynomial but uses
> only odd terms, e.g. rd = k1 * ru^3 + k2 * ru^5. In simple cases the
> 5th order term may be omitted, e.g. rd = k1 * ru^3, like in this
> paper:
>
> http://etoile.berkeley.edu/~jrg/Aberrations/node10.html
>
> This model is very suitable for real-time computations, since it does
> not require computing a square root per pixel, which is a very
> expensive operation:
>
> rd/ru = k2 * ru^4 + k1 * ru^2,
> ru = sqrt (dx^2 + dy^2) =>
> rd/ru = k2 * (dx^2 + dy^2)^2 + k1 * (dx^2 + dy^2)
>
> and then you just have to multiply dx and dy by rd/ru to get the
> distorted x and y.
>
> I would like to see the lens correction formulas suitable for realtime
> applications, since a) If the lens database will contain e.g. VCR
> lenses and such, some software may want to process video in realtime;
> b) In software such as UFRaw the user would like to see the effect of
> changing distortion and TCA sliders in realtime, with a minimal delay.
>
> Also a side effect could be that we could use calibration data from
> Imatest in the lens database.
>
> One problem is that the current database has a lot of data for lenses
> in Panotools format, and switching lens model would mean we can lose
> all of it.
>
> I see several solutions here:
>
> a) Just extend the current model of a, b, c and d with yet another
> coefficient for ru^5:
>
> rd = c5 * ru^5 + c4 * ru^4 + c3 * ru^3 + c2 * ru^2 + c1 * ru
> (where c4 == a, c3 == b, c2 == c, c1 == d)
>
> and select the appropriate algorithm depending on which coefficients are
> non-zero. However, this would mean that some lenses would be described
> with the "fast" polynom and some with the "slow" one, which will lead to
> inconsistent program behavior.
>
> b) Approximate the a,b,c polynom with a k1,k2 polynom. I wrote a
> Octave script which tries to do that, and the results are questionable.
> I have to see yet how this looks on a real-world image.
>
> Right now the same approach is used in Hugin to describe both distortion
> and TCA, although Paul van Walree here
> (http://www.vanwalree.com/optics.html) suggests that lateral color
> depends only of the distance, e.g:
>
> rd = ru * c
>
> I'm not sure if that's always true, have to check it on some real-world
> images again.
>
> So to generalize:
>  - Lens distortion is tied to the focal distance of the lens (for
> zooms). A programmatically optimal model for it is k1 * r^5 + k2 *
> r^3. An additional parameter like 'd' can be added to provide
> image scaling.
>  - Transverse chromatic aberrations are tied to the focal distance of
> the lens. It is possible that it can be modelled with the simple
> equation k * r (to be checked). Would be nice to have them in database
> too.
>  - Vignetting depends of the focal distance, and according to Paul van
> Walree also depends on the distance to subject. That's quite
> unfortunate since distance to subject is not a standard EXIF item, and
> besides there are still alot of manual-focus lenses in use. So perhaps
> the parameters for vignetting could be measured at several distances
> and then present the user a slider with which he can select the
> approximated distance to the subject, interpolating between existing
> parameters. I just hope that in practice vignetting does not change too
> much with the focused distance (to be checked).
>
> Comments anyone?

I have a seemingly stupid question: If we settled for the 5th order model but 
used the 4th order data until our DB would fill up, then we also can used the 
fast 3rd order preview mode? Since the 3rd order is available in both models. 
Or am I wrong here? If not this mixed start-up look ideal to me.

Gerhard
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