Joint iris boundary detection and fit: a real-time method for accurate pupil tracking

A range of applications in visual science rely on accurate tracking of the human pupil's movement and contraction in response to light. While the literature for independent contour detection and fitting of the iris-pupil boundary is vast, a joint approach, in which it is assumed that the pupil has a given geometric shape has been largely overlooked. We present here a global method for simultaneously finding and fitting of an elliptic or circular contour against a dark interior, which produces consistently accurate results even under non-ideal recording conditions, such as reflections near and over the boundary, droopy eye lids, or the sudden formation of tears. The specific form of the proposed optimization problem allows us to write down closed analytic formulae for the gradient and the Hessian of the objective function. Moreover, both the objective function and its derivatives can be cast into vectorized form, making the proposed algorithm significantly faster than its closest relative in the literature. We compare methods in multiple ways, both analytically and numerically, using real iris images as well as idealizations of the iris for which the ground truth boundary is precisely known. The method proposed here is illustrated under challenging recording conditions and it is shown to be robust.