1. An image processing apparatus comprising: an area acquiring means that acquires image area information expressing an area including an image of a target object acquired from within an image as a range in an image coordinate system; a first transforming means that derives a target spatial area in which the area expressed by the image area information acquired by the area acquiring means is transformed to a corresponding position in a spatial coordinate system that simulates actual space in which the target object is present; a physical model identifying means that identifies a reference physical model that simulates characteristics related to behavior and shape of the target object in the spatial coordinate system; a correcting means that compares the target spatial area and the reference physical model, and corrects position and shape of the target spatial area based on the comparison result; a second transforming means that derives a corrected area in which the target spatial area corrected by the correcting means is transformed to a corresponding position in the image coordinate system; and an output means that outputs corrected area information expressing the corrected area derived by the second transforming means.