# Entropy of a system

1. Nov 3, 2007

### LeoYard

Let's consider an image of a natural scene ;we 've got some individuals (pixels) that may differ one from another (different colors).
the entropy E of the system is E=sigma(-p.logp), where the sum is computed over the colors and p is the probability of occurence of a given color.
the issue here is that E simply does not depend on the location of the pixels within the image and thus does not depend on the "shapes" or "object" that one can perceive in the image (tress, etc): E only depends on the histogram of the pixels but not on the geometry of the image...

can anyone suggest a way to estimate the complexity of images of the world?

2. Nov 3, 2007

### marcusl

That's because you have defined a "color entropy" that, by definition, is geometry independent. That doesn't mean that your color entropy completely defines a scene.

3. Nov 3, 2007

### Chris Hillman

Entropy Measures

You wrote down the Shannon entropy; computing this would require you to know the "probability of c" for each color c, whatever that mean. Fortunately there are numerous other entropy measures you can consider which might be more appropriate, depending on what application you have in mind.