1. An object detecting device comprising: a detection unit that is installed in a vehicle with a direction crossing the longitudinal direction of the vehicle as the central direction of detection and that detects the relative velocity of an object, which exists in the lateral direction of the vehicle, with respect to the vehicle; a velocity calculating unit that calculates the absolute velocity of the object in the vehicle width direction with respect to the traveling direction of the vehicle on the basis of a detection signal of the detection unit; and a determination unit that is configured to determine: (i) whether the object is an approaching moving object on the basis of the relative velocity of the object with respect to the vehicle detected by the detection unit and a velocity component of the vehicle velocity in the direction from the vehicle to the object, and (ii) whether the object is an approaching moving object on the basis of the absolute velocity of the object in the vehicle width direction with respect to the traveling direction of the vehicle calculated by the velocity calculating unit, wherein when it is determined that the object is not approaching based on the relative velocity of the object, the determination unit determines whether the object is an approaching object based on the absolute velocity of the object.