This paper describes a method for quickly and robustly localizing the iris and pupil boundaries of a human eye in close-up images. Such an algorithm can be critical for iris identification, or for applications that must determine the subject's gaze direction, e.g., human-computer interaction or driver attentiveness determination. A multiresolution coarse-to-fine search approach is used, seeking to maximize gradient strengths and uniformities measured across rays radiating from a candidate iris or pupil's central point. An empirical evaluation of 670 eye images, both with and without glasses, resulted in a 98% localization accuracy. The algorithm has also shown robustness to weak illumination and most specular reflections (e.g., at eyewear and cornea), simplifying system component requirements. Rapid execution is achieved on a 750 MHz desktop processor.