1. A method for eye tracking, comprising: under control of a hardware processor: generating an eye-box over an eye in an eye image for determining an eye pose of the eye in the eye image, wherein the eye pose comprises a direction toward which the eye is looking, wherein the eye-box has an upper edge and a lower edge, wherein the upper edge overlays a portion of an upper eyelid of the eye, and wherein the lower edge overlays a portion of a lower eyelid of the eye; generating a plurality of radial lines extending from approximately the center of the eye-box to the upper edge or the lower edge; determining candidate points on the plurality of radial lines using an edge detector; determining parameters of a parabolic fit curve from a subset of the candidate points, wherein the parabolic fit curve is an estimation of an eyelid shape of the eye in the eye image; determining a score of the parabolic fit curve is above a threshold score using the parameters of the parabolic fit curve; determining that the parabolic fit curve is a preferred estimation of the eyelid shape of the eye in the eye image; and determining the eye pose of the eye in the eye image using parameters of the preferred estimation of the eyelid shape; and tracking the eye in the eye image using the eye pose of the eye in the eye image.