1. A digital camera, comprising: an imaging unit that receives and images a light from a subject transmitted to a photographing optical system; a recognition unit that recognizes a feature region of the subject using an image obtained by imaging with the imaging unit; a detection unit that detects a size of the feature region that is recognized with the recognition unit; a distance calculation unit that calculates a distance to the subject according to the size of the feature region; and a speed calculation unit that calculates a moving speed of the subject according to a temporal change of the distance to the subject, and a control unit that predicts a distance to the subject after a predetermined period of time according to the size of the feature region, wherein the control unit predicts the distance to the subject based on the distance to the subject calculated with the distance calculation unit and the moving speed of the subject calculated with the speed calculation unit, and controls the photographing optical system so as to focus on the subject, and wherein the imaging unit, the recognition unit, the distance calculation unit, the speed calculation unit and the control unit are all part of a single same digital camera.