In the course video on “Neural Style Transfer” regarding the “Style Cost Function”, at 3:15, Andrew says that “[…] for them to be uncorrelated […] it means that whenever there is this vertical texture, it probably won’t have that orange-ish tint”.
So, as far as I understand, Andrew uses the term “uncorrelated” to describe that the channels are not related in any way (where information about one channel does not tell you anything about the other). However, in his example, where “vertical textures” indicate absence of “orange-ish tints”, isn’t he rather describing “anti-correlation” (i.e., an inverse relationship)?
If I understand your question correctly, I think Andrew is not trying to discuss “general relationship between two image features (e.g. texture and tints)”, but in my words, less accurate but perhaps more intuitive, it will be “whether two features co-exist or not in an image”.
I think it will help to read this part of the transcript of the lecture again, which is a further elaboration of what we are trying to do with correlation:
if we use the degree of correlation between channels as a measure of the style, then what you can do is measure the degree to which in your generated image, this first channel is correlated or uncorrelated with the second channel and that will tell you in the generated image how often this type of vertical texture occurs or doesn’t occur with this orange-ish tint and this gives you a measure of how similar is the style of the generated image to the style of the input style image.
Two points to bare in mind:
We are comparing the style of two images (generated vs input) in terms of their correlations between the first and the second channel.
The two channels may be correlated in image A (e.g. generated) and uncorrelated in image B (e.g. input).
So, for your quote, for a more intuitive discussion, let’s translate it into "OK, this image does not have vertical text and orange-ish tint at the same time, so our correlation value should be low for this image (let’s call it image A).
If we further this example and another image B has both at the same time, then the correlation value for such pair of features (vertical text and orange-ish tint) should be high.
Because image A has a low value but B is high, their style, in terms of such pair of features, is different.
I think not. Not discussing it as any general relation between two features. It was a discovery in just one instance (image).