There are a few similarities. First, there's the aspect of an individual having a very distinct and almost inhumane trait, like the main character's super - sensitive sense of smell in the story, which could be compared to real - life criminals with extreme and abnormal characteristics. Second, the connection between the actions of the character (murder in the story) and their underlying psychological state is similar to how real - life criminals' actions are often linked to their mental states. However, it's important to remember that the story is highly fictionalized and these are just broad similarities.
One similarity could be the concept of an individual with an unusual fixation. In the real - life cases that might have inspired it and in the story, there is someone with an abnormal preoccupation, in this case related to scents. Another similarity could be the general idea of the criminal's motives being something beyond the ordinary, something that is deeply psychological.
The main similarity is the idea of a person whose actions are driven by an extreme sense. In the true stories that may have influenced it, there could have been individuals with abnormal senses or obsessions that led them to commit abnormal acts. In 'Perfume: The Story of a Murderer', the main character's extraordinary sense of smell and his need to capture scents through murder is a similar concept. Also, the general air of mystery and the exploration of the darker side of human nature might be similar to real - life criminal cases.