Randomization (uniqueization) of a photo on the fly, how to implement it?

Question

Photo

The task is to perform a uniqueization of the image, which is located locally on the server, running cent os 6, it is necessary to execute (generate) on the fly, i.e. at each request, so that there is no storage of these photos in fact on the machine.
In short: let's say there is a file named 1.jpg, which is located locally on the server, one of the scripts ( ImageMagick , NConvert , or some similar) needs to make the image unique, for example, beat pixels, crop n-% from the random side, change the date photo, name, etc. (the above software does all this very quickly)
Further, this random action is generated every time you access a link / links.
I managed to see such randomization in action, which gave different results for the same link, figuratively, you need to get the uniqueness of the original photo when clicking on links like domain.ru/cat/rnd (for example, domain.ru/ cat/123 , domain.ru / cat/321 , domain.ru/ cat/abc , etc.). Most likely, some prescribed catalog gave a command to randomly select the original photo and throw out the finished result, each time a new one, even when accessing the same address, and it all worked exactly according to a specific catalog on the site, i.e. index.php was available as usual, this is important!
I would like to get a script (for example .sh) + configuration / upload to the server for quick deployment on a new server.I am ready to pay for such a set if it is a reasonable amount of money and not a quick solution to such a problem.