Regarding the situations where a ground truth iris area cannot be defined due to heavy noise, and a tracked iris area cannot be found due to a shortage of the tracking algorithm, we define operations as follows: Display Formula
(23)Then, the recall and precision measures of the tracked eye image sequence are defined as Display Formula
(25)where is the matching function, taking into account a successful track, i.e., Display Formula
(26)The harmonic mean (HM) of recall and precision which emphasizes the minimum of the two performance values is defined as follows: Display Formula
(27)Since it is unrealistic to mark all ground truth iris areas in a real-time application, the real-time tracking confidence is defined and measured as follows. Let be the boundary area of a partial iris decided by the Hough transform and partial circle ranges as discussed in Sec. 2 and be the actual number of boundary iris pixels detected in the area. Given , let and . The real-time tracking mean (RM) at the time-step (i.e., at image frame ) is defined as the mean of successfully tracked adjacent frames between the time-steps delta and , where is a parameter used for control the smoothness of the RM. The effect of different is discussed in Sec. 6.2. The RM is then calculated using the frame sequence as follows: Display Formula
(28)where the success of eye tracking at image frame is defined using the constraint of the real-time matching threshold as follows: Display Formula
(29)where is determined experimentally as 0.625 based on the threshold determination method41 and the details can be found in Sec. 6.2.