Pupil detection plays a key role in eye and gaze video-based tracking algorithms. Various algorithms have been proposed through the years in order to improve the performances or the robustness in real-world scenarios. However, the development of an algorithm which excels in both execution time and pupil detection precision is still an open challenge. This paper presents a novel, feature-based eye-tracking algorithm for pupil detection. Morphological operators are used to remove corneal reflections and to reduce noise in the pupil area prior to the pupil detection step: this solution allows to significantly reduce the computational overhead without lowering the tracking precision. Moreover, a shape validation step is performed after the elliptical fitting and, if the elliptical shape is not detected properly, a set of additional steps is performed to improve the pupil estimation. The proposed solution, Pupil Detection after Isolation and Fitting (PDIF), has been compared with other state-of-the-art tracking algorithms that use morphological operations such as ElSe (Ellipse Selection) and ExCuSe (Exclusive Curve Selector) to evaluate both speed and robustness; the proposed algorithm has been tested over numerous datasets offering different pupil detection challenges. Obtained results show how PDIF provides comparable tracking precision at a significantly lower computational cost compared to ElSe and ExCuSe.