1. An impersonation detector comprising: a memory; and a processor coupled to the memory and configured acquire an image including a face of a person; acquire depth information of the face in the image from a distance measuring module; set a deficient area indicating an area where the depth information fails to be acquired; detect a face area from the image; acquire a reference image generated based on a probability set to the deficient area in the image, and calculate a degree of similarity between the face area where the deficient area is set and the reference image; and determine whether the image is impersonation based on the degree of similarity.