1. An approaching-object detector for detecting an object approaching an own vehicle, the approaching-object detector comprising: a memory; and a processor configured to perform a process including extracting a plurality of corresponding feature points from chronologically captured images, which are obtained by capturing the object using an imaging device provided for the own device, detecting a behavior among the captured images in regard to each of the plurality of feature points by detecting an optical flow in regard to each of the plurality of feature points from the chronologically captured images, determining whether or not the behavior is random in regard to each of the plurality of feature points based on an amount of a temporal change in a direction of the optical flow, and determining whether or not the object is approaching the own vehicle based on a behavior of a feature point whose behavior is determined to be not random among the plurality of feature points, and outputting a result of the determination.