It comes down to the characterizing architecture of convolutional nets, that is weight sharing, and the assumption on data this makes. If by image one means som

It comes down to the characterizing architecture of convolutional nets, that is weight sharing, and the assumption on data this makes. If by image one means something where you can expect any pattern (at some level in the hierarchy) being equally likely to occur anywhere across an input dimension, then yes this is true. Personally I would say that this is too narrow of a definition of an image (too great of an assumption), and, interestingly enough, perhaps too broad too. I am not a pro. [Edit] Too broad in the sense that, intuitively, there is perhaps an implied assumption of continuity of the input function defining the image. Note that such assumptions can be made explicit with various so-called statistical priors incorporated in the network.