Brightness of two images

I have two images. The one which is correct is brighter at the center of the image and darker at the limits. The other one is the opposite. I want to change the brightness in a way that the second image would be brighter at the center and darker at the limits. Is there a way to do so?

Thanks

[Image Analyst]

I'm adding the images that were posted later (in a comment to Massimo) so they'll be at the top of this discussion:

Answer 1

[Massimo Zanetti]

If the second image (call it A) has values between [0,1], just consider B=1-A; This one has opposite brightness. If A is 8-bit, consider B=255-A, etc for other image depths.

[Efstathios Kontolatis]

Thanks for the reply. However, the two images are different. I don't want to change the second image. I want to change its brightness distribution so as this be the same as the first image's.

[Massimo Zanetti]

Then I suggest you to use HISTOGRAM MATCHING technique, which is specific for this purpose. https://it.mathworks.com/help/images/ref/imhistmatch.html

Given the histogram of one image, it stretches the values of another image to get the same histogram.

[Efstathios Kontolatis]

These are the two images

The imhistmatch just increased the brightness of the second image. I don't want that. I want the brightness to be increased at the center of the second image just like the first.

[Massimo Zanetti]

Ok, now is more clear what you need (looking at the images). I have to say there is no "standard" method to do what you have to do.

One thing that comes to my mind, is to get (in some way) a raw scale envelope of the illumination in the first image, and then transfer this envelope to the second image. I think this can be done by approximating the first image whith a very smooth surface.

See this surface as a function of x,y that in the z value contains the level of illumination catched in A1. There could be different ways to do this.

[Image Analyst]

It looks like your signal is just plain missing from a huge portion of your second image. Under what conditions were the two images taken? Specifically, what was different when you snapped the bottom image as opposed to the top image?

[Efstathios Kontolatis]

Thanks. What is A1? And suppose I manage to find a surface how can I apply it to the second image? Also I need a way to extract the equation z=f(x,y).

[Massimo Zanetti]

A1=first image A2=second image.

One simple way can be just adding the values of the illumination surface to A2 (and possibly normalizing the values to stay in the range and avoiding saturation).

[Image Analyst]

You didn't answer my question. If your image is just constant/saturated then no amount of post processing can fix it. And yes, it is possible for cameras to saturate at values other than 0 and 255.

[Massimo Zanetti]

The second image Efstathios displayed was the image he got by matching his A2 image with histogram of A1, not the real A2. He is not starting by a constant image. (as far as I could understand)

[Efstathios Kontolatis]

Image Analyst these images are after processing with a gaussian filter. The mean intensity difference of the original images were about 3%. The problem is that the first image with the gaussian filter is good but the mean intensity difference from the second image is now 150%(!). So I want to increase the illumination of the second image to see what's behind the dark.

[Massimo Zanetti]

AAAAH. That is very different to what you asked in the original question........

If you want to see behind the dark, just stretch the image.

[Efstathios Kontolatis]

No I don't want to resize the image. I want the lighter part to be at the center of the image(with some offsetting or something like that).A1 image is not a constant one but that doesn't matter as far as I want to post process only the second image. Is there a way to take the equation from an,let's say interpolation of the illumination of the first image and use this as an elementwise multiply for the second image?

[Massimo Zanetti]

Stretching doesn't mean resizing image. Image stretching is technique to increase contrast (visibility) in image (very roughly speaking...):

https://it.mathworks.com/help/images/ref/stretchlim.html

[Efstathios Kontolatis]

That's the image I take with imadjust(A2,stretchlim(A2),[]). Still not what I want to do

Answer 2

[Image Analyst]

Yes. You can multiply it by some function, like a Gaussian or quadratic or something. Use meshgrid() to create X and Y arrays,

[rows, columns, numberOfColorChannels] = size(originalImage);
[X, Y] = meshgrid(1:columns, 1:rows);

then calculate z = f(X, Y) according to some function, then

brightImage = originalImage .* z;
imshow(brightImage, []);

[Efstathios Kontolatis]

Thanks. Is there a way to find brightness distribution of the first image and then apply it to the second image(I want to do it for a series of images so I cannot check it one by one)?

[Image Analyst]

Try imadjust() or imhistmatch().

For a color image, see this: http://www.cl.cam.ac.uk/~mg290/Portfolio/ColorHistogramWarp.html