1. An image processing device for identifying a characteristic of an eye from a face image of a person, the image processing device comprising: a first differentiation unit configured to differentiate an eye region where the eye of the face image exists in a crosswise direction of the eye to obtain a first luminance gradient; a first edge extraction unit configured to extract a first edge point corresponding to a boundary at which a left side is brighter than a right side and a second edge point corresponding to a boundary at which the left side is darker than the right side as edge points from the eye region according to the first luminance gradient; a voting unit configured to vote for an ellipse that is a voting target at each edge point using a Hough transform while changing a weight of the voting with respect to the ellipse according to one of the first edge point and the second edge point and according to a positional relationship between the ellipse and the edge point; a pupil outline identification unit configured to identify an ellipse expressing a pupil outline based on a voting result of the voting unit; a second differentiation unit configured to obtain a second luminance gradient by differentiating the eye region in at least a vertical direction of the eye; a second edge extraction unit configured to extract a third edge point with respect to the eye region according to the second luminance gradient; a curve identification unit configured to identify a curve, which is expressed by a control point and both end points and fits to the third edge point, as a curve expressing an upper-eyelid outline or a lower-eyelid outline, the end points being an inner corner point of eye and a tail point of eye; and a pupil region identification unit configured to identify a pupil region of the face image based on the ellipse expressing the pupil outline, the curve expressing the upper-eyelid outline, and the curve expressing the lower-eyelid outline, wherein the curve expressed by both the end points and the control point is a B-spline curve or a Bezier curve, wherein the curve identification unit is configured to identify the curve fitting to the third edge point located on the upper side of the inner corner point of eye or the tail point of eye as a curve expressing the upper-eyelid outline, and identifies the curve fitting to the third edge point located on the lower side of the inner corner point of eye or the tail point of eye as a curve expressing the lower-eyelid outline.