It is surmised that the Romans used a template for their facial portraits. The same art style is seen on the famous Egyptian mummie casings.
The evidence for templates is with the heavily accentuated eyes, but look at multiple of these portraits, if you separate the face into bands, such as the forehead, eyebrows, eyes, nose etc., it does emerge that the individuals share features.
The portraits are stunningly beautiful nevertheless.
The funeral pictures shown in the post are at the end of the Egyptian collection at the Met. The Roman and Greek collections are at the other end of museum. They are a rare example of encaustic painting and are probably very close to their original condition after two-thousand years. Encaustic is the technique of painting in pigmented hard wax. The artist has to work very quickly before the wax sets and traditional brush strokes are not possible. I had an art professor who did an encaustic painting as an experiment. After he finished the work, he threw it on the roof of his studio in Baltimore and left it out in the sun, rain, and snow for two years. Amazingly, it was not affected in any way, aside from being a bit dirty.