Vignetting, discussion about methods of resolution Options

[Tman]

Hi Nirgal and all, I would like to discuss about vignetting and methods of resolution for it. I'm mainly interested in mathematical methods that could automatically calculate and adjust the right grey value for each pixel in a single picture.

My current method works with more or less transparent layers over the original picture that so roughly are able to balance the grey values. A perfect layer have to be the exact inverted brightness difference of each picture with this shadow effects. This method is very effective if you get the correct inverted values. These shots of the Mars sky come nearly at such a perfect mask, but not always. And of course the center of the pictures lose much of theirs original brightness/luminance sadly.

I have in mind a mathematical method that can adjust each grey value in a pic in order to obtain a completely balanced brightness over the entire picture. But I'm not in the position to reach that. I only know one have to start with the calculation of the grey values in the center of the picture. In the center are quasi the reference values of the whole picture, if I'm correct.
Is there a possibility (mathematical method) to get (roughly) the same brightness and luminance like in the center over the whole picture from the MERs?

Greetings, Peter

[Nirgal]

Hi Tman,

mathematically, we can describe vignetting effects as a very low frequency
change in pixel brightness.
Unfortunately there is no "perfect" algorithm that could always distinguish the
Vignetting from other low frequency brightness variations that belong to the
"real" picture content and are therefore not to be canceled out.
So I'm afraid that there will be no better method than to use the
complete reference frames where the camera points to a uniformly bright sky.
So actually I think your method of using the Navcam reference sky-images is
already quite good !
The only problem that I can see is that the sky is probably not uniform and
that, if there is a time span between the reference image and the actual
shot, it may not work well because of intermediate changes n light conditions.

As for my "unstrip" program I had to choose a different approach, because it
is mainly intended to remove the dark "strips" (at the frame seams) in already stitched conplete panoramas.

The algorithm works as follows (simplified)

0. convert the image to LAB color space to handle color and luminance independently
1. try to find a *horizontal* strip in the image that is as uniform in brightness as possible.
2. apply a gaussian smoothing filter to each line of the reference area
3. "merge" step: calculate the reference line as an average of all lines in the reference area.
4. take the avreage brightness of the reference area as the reference luminance.
5. we now have our horizontal "brightness correcting curve", but it may still have
undesired high frquency variations (despite the smoothing)
6. so,as a last step I create a b-spline (or linear) interpolated version of the
correction curve.
7. apply the correction curve to each individual line in the image
(i.e. brightness(pixel(x,y)) = brightness(pixel(x,y)) + brightness(correction-curve(x))