1. A moving object detection apparatus comprising: an image acquisition device that acquires continuously taken images; and a processor and a non-transitory memory device storing instructions executed by the processor to: calculate a motion vector of an object, the motion vector showing a level and direction of movement, the motion vector being calculated based on two images with different imaging times among the images acquired by the image acquisition device; generate a difference image between two images with the different imaging times among the images acquired by the image acquisition device; detect a first existence/nonexistence of a moving object based on the calculated motion vector; detect a second existence/nonexistence of the moving object based on existence/nonexistence of a moving object region detected based on the generated difference image; and integrate the detected first existence/nonexistence of the moving object and the detected second existence/nonexistence of the moving object and determine that the moving object is detected, (a) in a case where the moving object is not detected by the first existence/nonexistence detecting step because the moving object is moving too fast for the motion vector calculating step to calculate the motion vector of the moving object and the moving object is detected by the second existence/nonexistence detecting step, and (b) in a case where the moving object is detected by the first existence/nonexistence detecting step and the moving object is not detected by the second existence/nonexistence detecting step because the moving object is moving too slow for the difference image generating step to generate the difference image.