1. An image processing device comprising: a feature point derivation unit that derives a plurality of characteristic points in an input moving image obtained by photographing an object; a tracking subject feature point setting unit that sets a feature point within a tracking subject, from the plurality of characteristic points; a background feature point setting unit that sets a group of background feature points from the plurality of characteristic points, the background feature points not being located within the tracking subject; a motion detection unit that detects movement over time of the background feature points within the input moving image; a clip area setting unit that sets a size and a position of a clip area of an image to be employed such that the clip area includes the feature point within the tracking subject, on the basis of the movement of the feature point within the tracking subject and the movement of the background feature points, wherein when the movement of the background feature points decreases or is not detected, the clip area setting unit sets the clip area in a first setting mode, and when the movement of the background feature points is detected and does not decrease, the clip area setting unit sets the clip area in a second setting mode different from the first setting mode.