1. A moving object detection apparatus comprising: an image acquisition device for acquiring continuously taken images; a motion vector calculation device for calculating a motion vector showing a size and direction of movement of an object based on two images with different imaging times among the images acquired by the image acquisition device; a first moving object detection device for detecting existence/nonexistence of a moving object based on the motion vector calculated by the motion vector calculation device; a difference image generation device for generating a difference image between the two images with the different imaging times among the images acquired by the image acquisition device; a second moving object detection device for detecting existence/nonexistence of the moving object based on the difference image generated by the difference image generation device; and an integration device for integrating a detection result by the first moving object detection device and a detection result by the second moving object detection device and determining that the moving object is detected in a case where the moving object is not detected by at least the first moving object detection device and the moving object is detected by the second moving object detection device.