So given for example a challenge with rather specific input and varying output (i.e. image-processing challenges) is it considered "fair play" to copy input processing logic from other answers? (for example logic to load an image to memory).
It's usually OK, if you credit the author
There were countless challenges, where some users made their on algorithms, but then someone else came (usually Martin Büttner or Dennis), and made a new, very short algorithm. After this, others began using that algorithm.
It's usually OK, if..
...the original author don't mind it.
...You credit the original author of the code/algorithm.
Copying part of an answer is a matter of good taste
Consider a previous challenge where users had to convert text to camel case. Nearly all of the solutions had a regex, and most of the answers used identical or similar regexes.
While regex can certainly be golfed (and was in in the previous example), the regex portion of the answer was small enough that we were OK if it got duplicated across answers.
So, in response to your question:
Is input processing a core part of the question? If so, then don't copy. If not, then you should be fine.
What is considered "core" can be different between people, so if you are unsure, ask.