Answer:
The correct answer is: his brain is retrieving information about your appearance that was encoded the last time he saw you.
Gus recognizes you as soon as you walk in the door because his brain has stored the information about your appearance from previous encounters. Dogs have the ability to remember and recognize familiar faces, scents, and other sensory information. When you return home after being away for three months, Gus's brain retrieves the stored information about your appearance and matches it with the sensory input he receives in the present moment, allowing him to recognize you.