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Abstract
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.
Highlights
One approach to boundary localization in gray-level images to is to find a set of points that define the object by an edge-detecting mechanism and proceed to find a geometric curve that best fits that set, see for example [1,2,3] and [4]
With the notable exception of the integro-differential operator method for circles [6] and for elliptical contours [7], global methods—which enforce a priori knowledge of the geometric curve describing the boundary—have been mostly overlooked
In having to localize the full iris, those procedures often make use of the limbic boundary to help localize the pupillary boundary, which is usually much less pronounced. To overcome these problems we have developed a global method that assumes a priori that the pupil boundary has a certain geometrical shape with a dark interior, so it can be found and fit simultaneously
Summary
One approach to boundary localization in gray-level images to is to find a set of points that define the object by an edge-detecting mechanism and proceed to find a geometric curve that best fits that set, see for example [1,2,3] and [4]. In these approaches no prior assumption is made as to what shape the boundary might have, even if later one tries to fit a simple geometric curve to the set of points found to describe it. Preprocessing has the potential to increase the number of parameters in the procedure to a level similar to those in find and fit methods, eroding its attractiveness for simple shapes
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