We present a new system for biometric recognition using periocular images. The feature extraction method employed describes neighborhoods around keypoints by projection onto harmonic functions which estimates the presence of a series of various symmetric curve families around such keypoints. The iso-curves of such functions are highly symmetric w.r.t. the keypoints and the estimated coefficients have well defined geometric interpretations. The descriptors used are referred to as Symmetry Assessment by Feature Expansion (SAFE). Extraction is done across a set of discrete points of the image, uniformly distributed in a rectangular-shaped grid positioned in the eye center. Experiments are done with two databases of iris data, one acquired with a close-up iris camera, and another in visible light with a webcam. The two databases have been annotated manually, meaning that the radius and center of the pupil and sclera circles are available, which are used as input for the experiments. Results show that this new system has a performance comparable with other periocular recognition approaches. We particularly carry out comparative experiments with another periocular system based on Gabor features extracted from the same set of grid points, with the fusion of the two systems resulting in an improved performance. We also evaluate an iris texture matcher, providing fusion results with the periocular systems as well.