1. An eyeball parameter estimating device, comprising: a head posture estimating unit that estimates, from a face image of a person photographed by a camera, position data ({right arrow over (t)}) corresponding to three degrees of freedom (x-, y-, z-axes) in a camera coordinate system, of an origin (O′) in a head coordinate system and rotation angle data (R) corresponding to three degrees of freedom (x-, y-, z-axes) of a coordinate axis of the head coordinate system relative to a coordinate axis of the camera coordinate system, as head posture data ({right arrow over (t)}, R) in the camera coordinate system; a head coordinate system eyeball central position candidate setting unit that sets candidates of eyeball central position data ({right arrow over (a)}′) in the head coordinate system based on coordinates of two feature points on an eyeball, which are preliminarily set in the head coordinate system; a camera coordinate system eyeball central position calculating unit that calculates an eyeball central position ({right arrow over (a)}) in the camera coordinate system based on the head posture data ({right arrow over (t)}, R), the eyeball central position candidate data ({right arrow over (a)}′), and pupil central position data detected from the face image; and an eyeball parameter estimating unit that estimates an eyeball central position (O) and an eyeball radius (r) in the head coordinate system based on the eyeball central position ({right arrow over (a)}) in the camera coordinate system so as to minimize deviations of position data of a point of gaze (O″), a pupil center (i), and an eyeball center (O) from a straight line joining original positions of the three pieces of position data.