How do I measure the amount of information within an image?

Question

I'm trying to find some information threshold that is required for performing detection of objects in images. However, I'm not sure how exactly to quantify the amount of information contained within an image.

Thoughts:

I imagine that looking at the gradients/edges of the image would be a good idea, but simply counting the number of edge pixels doesn't seem enough. Maybe looking for patterns within the edge image?

Perhaps I should look at the image in the frequency domain?

I don't think I can just use Shannon's entropy because it doesn't really "look" at the big picture.

Any help/guidance would be appreciated.

My problem with Shannon's entropy is that it is calculated without considering spatial structures. For example, the following two image have the same entropy score:

Answer 1

My problem with Shannon's entropy is that it is calculated without considering spatial structures.

That's not true!

Entropy is the expectation of Information, which is the negative logarithm of probability.

So, if you have correlated pixels (for example, in pictures of the first kind, say, a pixel in anything but the top row always has the same value as the pixel above), then that pixel's info drops to zero.

So, your statement is only true if you assume all pixels to be independent, which they aren't.