Eye detection is a preprocessing step in many methods using facial images. Some algorithms to detect eyes are based on the characteristics of the gradient flow in the iris-sclera boundary. These algorithms are usually applied to the whole face and a posterior heuristic is used to remove false positives. In this paper, we reverse that approach by using a Convolutional Neural Network (CNN) to solve a regression problem and give a coarse estimate of the eye regions, and only then do we apply the gradient-based algorithms. The CNN was combined with two gradient-based algorithms and the results were evaluated regarding their accuracy and processing time, showing the applicability of both methods for eye localization.