Fig. 1. Eye structure (Illustration taken from [15]).

Fig. 2. System configuration: a monitor with four IR LEDs attached to the corners and two cameras, one of which is with an IR LED attached to its lens.

Fig. 3. Input images captured by a camera: (A) dark eye image (corneal reflection) and (B) bright eye image.

Fig. 4. The relation between the IR LEDs of the monitor (LED₁, LED₂, LED₃, and LED₄) and the virtual projection points (v₁, v₂, v₃, and v₄). The points are the projection of IR LEDs onto the surface of the cornea. p is the pupil position in an image and g is the gaze point of the eye.

Fig. 5. Geometrical relation of the reflection. r₁, r₂, and c are the glints of LED. v₁ and v₂ are the virtual projection points.

Fig. 6. How to compute a virtual projection point. Σ_c is a coordinate system origin which is located at the optical center of the camera, and Σ_i is an image coordinate system origin.

(A) u_r1.

(B) u_v1.

(C) u_v1/u_r1.

Fig. 7. The variation of the features in the image according to the eye’s location.

Fig. 8. Computation of virtual projection points in an image plane. The white circles (○) are the glints, and the black circles (•) are the virtual projection points of the glints. The cross (+) marks the pupil center.

Fig. 9. How a cross-ratio in an image is computed. u_v1, u_v2,u_v3, and u_v4 are the virtual projection points on the cornea. u_p is the center of the pupil in the image. e is an intersection of diagonal lines of the polygon u_v1,u_v2,u_v3, and u_v4.

Fig. 10. The screen of a monitor. w is the width of the screen and h is its height. g is the estimated eye gaze point and its position is .

Fig. 11. Simulation environment.

(A) Cross-ratio.

(B) Estimated gaze point.

Fig. 12. The variation of the cross-ratio according to the eye’s location. The positions of the glints in the image are used to compute the cross-ratio: (A) the cross-ratio and (B) the estimation result.

(A) Cross-ratio.

(B) Estimated gaze point.

Fig. 13. The variation of the cross-ratio according to the eye’s location. The positions of the virtual projection points are used to compute the cross-ratio.

(A) Cornea center = (152, 112, and 500).

(B) Cornea center = (10, 0, and 500).

Fig. 14. Sensitivity study. The camera is at (152, 0, and 100) and the gaze point is (152, 117).

Fig. 15. Detection of the corneal reflections: (A) dark-eye image, (B) segmented result, and (C) detected glints.

Fig. 16. Segmented results of three cases.

Fig. 17. Ellipse fitting to the edge detected by a Sobel operator. The red ellipse is the fitted result.

Fig. 18. Edge detection of a pupil region by a 1D search.

Fig. 19. Boundary detection results of the examples from Fig. 16. The small circle is an initial position of a simplified active contour. The crosses mark the boundary of the pupil region.

Fig. 20. Fitting results of Fig. 16.

(A) t = 16.

(B) t = 72.

(C) t = 94.

(D) t = 111.

(E) t = 16.

(F) t = 72.

(G) t = 94.

(H) t = 111.

Fig. 21. Face and eye tracking results: (A–D) are the images obtained by a wide-view camera, and (E–H) are the images simultaneously obtained by a high-zoom camera.

Fig. 22. Experimental setup: a monitor with four IR LEDs and two cameras mounted on a pan-tilt unit. A small wide-view camera is attached to the top of the high-zoom camera.

(A) Conventional method.

(B) Proposed method.

Fig. 23. Experimental result. The resolution of the screen was 1024 × 768 and the screen had 5 × 5 target points.

The average, standard deviation, and maximum of the estimation error using the conventional method

The average, standard deviation, and maximum of the estimation error using the proposed method