"No, the image to be tested would stay on the sender's computer and be compared there with images downloaded from the regulator."
I don't think you've thought this through. You seem to be suggesting the regulator will send you illegal images, all of them, burying you in data and automatic crime.
The images can be encrypted with the regulator's public key. The sender's computer would encrypt each of its images using the regulator's public key before comparing it to the downloaded encrypted images. Having these encrypted images would not be illegal because without the regulator's private key they cannot be viewed.
Storage is cheap. It should be possbile to store an encrrypted copy of every image in the regulator's illegal image database on a standard cell phone. If not, the regulator can pay the extra cost.
The way things like this are typically done is you send them a hash of your image and they perform a hash check and respond with a Yes/No. Ignoring the huge potential for misuse here, all it takes is a single pixel/bit change and the hash no longer matches.
It is posible to do a series of Fuzzy Hashes to determine near matches but that begs the question of exactly what is near.
I don't think it is possble to create a fuzzy hash for illegal images that will not either miss some illegal images or incorrectly identify legal images as illegal.