Independent and identically distributed data (images)? If it is said that the data must be independent and identically distributed, and the data are images, then what exactly does it mean for images to be "independent and identically distributed"?
 A: I'm using the general meaning of i.i.d. and apply it to images. I.i.d. then means that
(1) images are drawn randomly from the same population of images (this is for example violated if you have access to a number of databases and you decide to draw the same number of images from each, or, even worse, you take 10000 images from your favourite database and 10 from each of the others),
(2) once some images are drawn, these do not contain any information about other images to be drawn, other than information about the general population (this is for example violated if the population you're interested in is general images, let's say all on the web, but you find out from seeing the first 100 images that almost all your images actually show animals).
Note that whether data are i.i.d. to some extent depends on the population you want to make inference about. If your population is all images in one database, and you draw randomly from that database only, this can be taken as i.i.d. However it is not i.i.d. if in fact your population of interest is all images on the web, because then the specific database may not be representative (for example because it has very many animal images) and the fact that all images come from the same database makes them dependent. The difference is that in one case the fact that there are many animal pictures is a feature of the population of interest, and given this the images are independent. In the other case the fact that there are many animal pictures is not a feature of the population, but a result of all your images being from the same database, which makes then dependent relative to the more general population.
PS: Somebody could argue that (1) above implies (2), because if there's dependence as suggested in (2), it actually means that you didn't sample truly randomly from the same population. This objection is true if "random draw" is interpreted accordingly, however I think it's useful to make this distinction to make clearer how identity and independence can go wrong in different ways.
PPS: Note that "i.i.d." is not a property of the images per se, but rather of your way of drawing them from a well-defined population.
A: You can think of the images as realizations of matrix or tensor random variables, even regular vector random variables if you flatten each image to a vector, the same way that we think of any other observations as realizations of random variables. So before we have realizations of the random variables, we just have the random variables.
Once we see images as vector random variables, “iid” means the same as always. Yes, there are relationships between the pixels of an individual image, same as there are relationships between the components of a multivariate normal distribution with a non-diagonal covariance matrix. The “independent” and “identical” means across observations, not within.
