1. An object detection device, comprising: image recognition circuitry configured to detect an object being recognized in an input frame image, and identify a position of a detected object which is detected as the object being recognized in the input frame image; storage configured to store a position of a first past detected object which is detected as the object being recognized in a first past frame image which is input immediately before the input frame image; distance calculation circuitry configured to calculate a first distance from the position of the first past detected object to the position of the detected object which is detected in the input frame image; first determination circuitry configured to determine that the detected object which is detected in the input frame image is identical to the first past detected object if the first distance is smaller than a first reference distance which is previously set; frame-number comparison circuitry configured to determine whether or not the number of frame images in each of which the object being recognized is detected, out of the input frame image and a first predetermined number of past frame images which are input before the input frame image, is equal to or larger than a first threshold when the object being recognized is not detected in the input frame image; and second determination circuitry configured to determine that the object being recognized is present in the input frame image if the number of frame images in each of which the object being recognized is detected is equal to or larger than the first threshold.