The BEST way to do it, and I do it all the time, is to take a "blank shot" and then divide your image by it.
In other words, take a picture of that white stuff (assuming it's truly flat and uniform, like a sheet of paper), without the yellow stuff. This will give you the pattern of exposure due to the combination of lens shading and lighting non-uniformity. So let's say some pixel in the corner had 90% as much light reaching the sensor as at the middle. Well, you'd want to divide by 90% to bring the value up to what it's supposed to be, wouldn't you? (Note, radiographs and fluorescence images might also need a subtraction). OK, now you need to get rid of small defects in the image like scratches, specks, video noise, etc. So you can either blur the image or fit it to a 2-D polynomial to get the perfect, noise-free background (I do the latter). Now you normalize your noise-free image so that it goes between 0 and 1. It will be 1 at the brightest point and the min, in the corners, will be whatever it is, like 0.6 or 0.8 or whatever, depending on how severe your shading it. The severity of lens shading varies greatly with manufacturers. We've tried stock lenses from manufacturers like Nikon and Canon and they show severe shading - they're junk. You'll get much flatter fields from specialty (non mass market) lens makers like Schneider (my favorite) and Linos. But their lenses cost twice as much. Obviously it's better to start with a better image than a crummy image if you're going to try to fix it. OK, now you just divide your actual image by the test image to get the flat field image:
correctedImage = double(testImage) ./ backgroundImage;
There are ways to improve upon that and be even more accurate, but I don't want to deliver my whole class on it here. They're more complicated and I think this may be enough for you.
If you can't get a blank shot, there are ways to estimate the background with that yellow spot still in there. You just have to remove it as best you can and fit the background to what's left. A simple way to do that is attached in the demo, but I'd actually do it a somewhat different way.
