p u2032 can be interpreted as the probability that a pixel is part of the red pupil given the pixel 39 s redness value p the value of bias red 520 determines the value of p at which p u2032 0 5 the center point of the sigmoid function the value of gain red influences the steepness of the transition of the soft threshold function 510 parameters for an ellipse representing a candidate pupil are estimated in a search circle that completely contains a candidate pupil and does not contain other stray red pixels the candidate pupil ellipse parameters are estimated using the first and second order spatial moments of p u2032 m xx u03c3 p u2032 x 2 u03c3 p u2032 u2212 m x 2 m xy u03c3 p u2032 x y u03c3 p u2032 u2212 m x m y and m yy u03c3 p u2032 y 2 u03c3 p u2032 u2212 m y 2 where x and y are the image coordinates of the pixel having the value p u2032 the summations are over the pixels contained in the search circle as shown in fig6 the general ellipse 610 used to model the candidate pupil is determined by five parameters x 0 y 0 r x r y and alpha the point x 0 y 0 is the center of the ellipse 610 the parameters r x and r y are the horizontal and vertical radii of the image axis aligned bounding box 620 that encloses the ellipse 610 the alpha parameter abs alpha lt 1 determines the skew of the ellipse 610 in terms of this parameterization the implicit formula for the ellipse 610 is the estimated candidate pupil ellipse parameters can be checked to verify that the parameters are reasonable for a physical.