## How to Estimate the Gaze Point?

Now let’s see how we can map the pupil position to the gaze point in the fixation plane. In fact, the graph here is showing a 2 dimensional view of the problem but the results can be generalized to 3D. In Figure 1 you can see a point called Pupil_y. There is also a vector connecting PoR and the point Pupil_y. This vector indicates the the location of the pupil center inside the eye image for each fixation point. This vector is in fact the input of the gaze tracking system which is obtained from the eye image. Rotate the eye in the figure and see how this vector changes for different gaze points.

In this figure you can also see another vector indicating the height of the PoR. This will be the output of the system. The output is the position of the gaze point in the fixation plane (y) and in reality this would be a point with two coordinates (x, y). A simple gaze estimation can be done by mapping the Pupil_y (input) to the y (PoR) or the output. When you rotate the eye in the Figure 1, you can see the trace of the point Pupil_y. This trace is actually the mapping function we need to use for the gaze mapping. We can either consider this function f(Pupil_y) as a line or a polynomial curve. Let’s assume that it is a linear function for now. Then it can be obtained by taking two sample points. This is done via a calibration procedure. We ask the subject to fixate at two different target points in the fixation plane. This gives us two points along the line which is enough for finding the mapping function.

Use the buttons in the figure, take the first sample point, rotate the eye and take the second sample. You will see a yellow line after the calibration. This is the mapping function that the gaze tracker uses for gaze estimation. This function works fine as long as the position of the eyeball (head position) is fixed relative to the camera. If you move the eye slightly you see that the mapping function will not align with the actual trace of the Pupil_y point.

Figure 1: Main elements of the gaze estimation process using only the pupil center.

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