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It is difficult to demarcate the limbus borders in standard intensity images of the eye since the transition from the cornea (iris) to sclera is gradual. Non-parametric techniques that are currently used for this task are not sufficiently precise to be adopted in those ophthalmic applications where high precision in determining the limbus/pupil characteristics is required. This is the case, for example, in customized refractive corrections. Another aspect of limbus corneae characterization is the inability of measuring in vivo the outer outline of the limbus annulus without specialized illumination techniques. To overcome these limitations, we propose a parametric approach that utilizes a sigmoidal function fitted to radial intensity profiles of the limbus corneae. By the way of simulations, we show the superiority of the proposed parametric approach when compared to an optimized nonparametric technique. Further, we review the techniques for fitting ellipses to the estimated points of the limbus annulus and discuss clinical aspects of the proposed methodology. Initial clinical experiments showed close agreement between the proposed approach and limbus corneae estimates manually obtained by experienced clinicians.