1. A target tracking apparatus comprising: a target detecting device for detecting a target, which is to be tracked, within a detection area of a subject image represented by image data which is obtained by imaging a subject continuously and is displayed on a screen of an imaging device; a detection area updating device, responsive to detection of the target by said target detecting device, for updating the detection area in such a manner that the detected target will occupy the center thereof; a motion detecting device, wherein said motion detecting device is responsive to the target no longer being detected by said target detecting device in one frame and the motion detecting device detects magnitude and direction of motion of the overall subject image in which the target is no longer detected, wherein said motion of the overall subject image in which the target is no longer detected represents a motion of the imaging device; a detection area setting device for setting the detection area in a following frame when the target is no longer being detected by said target detecting device in said one frame, wherein if the motion of the imaging device detected by said motion detecting device is equal to or greater than a prescribed magnitude, the imaging device is following the moving target, and the detection area setting device then sets the detection area at a central portion of the subject image in said following frame, and if the motion of the imaging device detected by said motion detecting device is less than the prescribed magnitude, the imaging device is not following the moving target, and the detection area setting device then sets the detection area, whose size differs from the size of the detection area set at the central portion, at an edge of the subject image in a direction opposite the direction of motion of the overall subject image which has been detected by said motion detecting device; and a control device for controlling said target detecting device, said detection area updating device, said motion detecting device and said detection area setting device so as to repeat processing for detecting the target, processing for updating the detection area, processing for detecting the magnitude and direction of the motion, and processing for setting the detection area.