Agalmatophilia refers to being sexually aroused or excited by statues or mannequins. Richard Von Krafft-Ebing noted a case in 1877 in Psychopathia Sexualis of a gardener who was found trying to have sex with a statue of the Venus de Milo. There have been more recent cases of agalmatophilia in the news where people have run into trouble with the law while satisfying their sexual interests.
People who are interested in A.S.F.R sometimes include those who eroticize statues or mannequins, or simply the freezing in place of a person (like a robot that has stopped working).
Krafft-Ebing, R. Psychopathia Sexualis. New York: Paperback Library, 1965.
Love, B. Encyclopedia of Unusual Sex Practices. London: Greenwich Editions, 2001.
White, M.J. “The Statue Syndrome: Perversion? Fantasy? Anecdote?” Journal of Sex Research. Volume 14, No. 4 (1978): 246-249.