I found a bug in the documentation of the lenscorrection filter:
https://www.ffmpeg.org/ffmpeg-all.html#lenscorrection

It's written there "0.5 means no correction" for the coefficients k1 and k2. This can't be right, or the formula is wrong. It's obvious that the formula makes no correction if k1=k2=0.

The remarks "0.5 means no correction" in the documentation are wrong. This can easily be tested:

ffmpeg -i input.png -vf lenscorrection=k1=0.5:k2=0.5 output.png
It's clearly visible that the output is not the same as the input.

ffmpeg -i input.png -vf lenscorrection=k1=0:k2=0 output.png
Now the output is the same as the input. It is clear that 0 means no correction.

But unfortunately this isn't the only error in the documentation. I haven't yet found out which formula is actually used in the lenscorrection filter, but one thing is absolutely sure: It's not the formula from the documentation.

I've done some tests. The input picture is 5472x3648. Half of the diagonal is 3288.
With k1=0.1, half of the diagonal becomes 3030.
With k1=0.2, half of the diagonal becomes 2856.
With k1=0.3, half of the diagonal becomes 2723.
With k2=0.1, half of the diagonal becomes 3058.

None of these results can be explained by the documented formula.

Michael

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