In the last decade, the development of technologies and tools for eye tracking has been a constantly growing area. Detecting the center of the pupil, using image processing techniques, has been an essential step in this process. A large number of techniques have been proposed for pupil center detection using both traditional image processing and machine learning-based methods. Despite the large number of methods proposed, no comparative work on their performance was found, using the same images and performance metrics. In this work, we aim at comparing four of the most frequently cited traditional methods for pupil center detection in terms of accuracy, robustness, and computational cost. These methods are based on the circular Hough transform, ellipse fitting, Daugman's integro-differential operator and radial symmetry transform. The comparative analysis was performed with 800 infrared images from the CASIA-IrisV3 and CASIA-IrisV4 databases containing various types of disturbances. The best performance was obtained by the method based on the radial symmetry transform with an accuracy and average robustness higher than 94%. The shortest processing time, obtained with the ellipse fitting method, was 0.06 s.