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