1. A motion sensor comprising: a processor configured to: extract, from each of a first image representing a detection target object and generated by a camera and a second image representing the detection-target object and generated after the first image by the camera, an object area including the detection-target object; detect, from each of the first image and the second image, a reference point indicating a boundary between a moving part of the detection-target object and a fixed part of the detection-target object, the moving part moving when the detection-target object performs a certain motion, the fixed part not moving compared to the moving part when the detection-target object performs the certain motion; set a first area located on a side including the moving part with respect to the reference point; obtain, for each of the first image and the second image, a position of the moving part of the object area in the first area; and determine that the certain motion has been performed, when a difference between the position of the moving part in the first image and the position of the moving part in the second image corresponds to a movement of the detection-target object during the certain motion, wherein detection of the reference point includes calculating, for each pixel line parallel to an end of the first image with which the object area is in contact, a width of the object area at the pixel line and detecting the reference point on the first image based on a variation of the width of the object area along a direction across the end of the first image.