Take the infamous "Vanishing Commissar" photographs, perhaps the classic example of Stalinist censorship. Among the various state instruments that existed during the Purges, which one(s) would have been responsible for image "corrections" like this? Did it fall under the aegis of the NKVD or one of the other directorates?
Thank you for your time.
There was no special NKVD department who handled it, it was up to the editors of magazines, newspapers, books, albums, etc. where the photographs were published to align them with the ongoing political situation. The people who altered the photos were called "retouchers", every printed edition employed at least one.
How did the editor know who needed to disappear from the photo? Sometimes it was obvious if that person had been declared "enemy of the people", arrested and executed. Sometimes Stalin himself would let his close circle know (never directly) who couldn't be depicted next to him anymore.
For editors, making the right decision was extremely nerve-wrecking as Stalin was unpredictable and even those closest to him couldn't always foresee who he was going to go after next.
Also, if you were a family member of the person who had been censored out of a photograph and you kept the original, if found by authorities, that photo could (and did) send you to a labor camp.
NKVD, on their end, destroyed original photos in their archives, as it happened with Trotsky and many others.