Hi everybody,

I got curious about how radial correction is computed and did a small test.

>From Helmut's description  (remember, he implemented the code):
http://www.all-in-one.ee/~dersch/barrel/barrel.html I learned that the
correction is

dd + cr + br^2 + ar^3 (found in the function radial).

Noticed the first parameter dd. In the page above is referred as d,
but d in panotools has a different meaning.

As he explains, to avoid scaling the sum of dd + c + b + a = 1.

This is supported by the code. dd is computed from a, b and c to
satisfy the invariant.

Now, look at the following test:

http://turingmachine.org/~dmg/temp/test_grid.zip

It looks as if, in the case of the 2 rectangular images, there is
scaling, but not in the squarish image.

In the code, the scale of the image is normalized as 1/2 the smallest
of dimensions. This means the image is not scaled with respect to the
longest dimension,
but it is scaled with respect to the shortest dimension. Now, this
example is a bit extreme because the ration width to length is 2. But
even if it was 1.5 (as with
36mm cameras) the different is significant.

I suspect helmut did this because most people shoot panoramas with the
camera in portrait mode. This way the "horizontal" field of view,
remains unchanged
after the correction has been applied.

With this information we should be able to computer a, b and c
parameters from imatest data (such as the ones published at photozone:
http://www.photozone.de/canon-eos/336-canon-ef-35mm-f14-test-report--review?start=1)

What about the samyang 8mm lens? This radial correction is made before
the photo is remapped to its native projection. One would need to
either: calibrate the lens using the typical methods, or do some math
and approximations
to come to the estimation of these parameters based on the formulas
above. Remember, the lens is closer to stereographic (which we have
implemented in panotools), do not use for this one a typical
equidistant.

Samyang should donate us a couple of lenses to be able to properly
test the code. It has never been used.

--dmg

---
Daniel M. German
http://turingmachine.org

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