Drowsiness is the intermediate state between wakefulness and sleep. It is characterized by impairments of performance, which can be very dangerous in many activities and can lead to catastrophic accidents in transportation or in industry. There is thus an obvious need for systems that are able to continuously, objectively, and automatically estimate the level of drowsiness of a person busy at a task. We have developed such a system, which is based on the physiological state of a person, and, more specifically, on the values of ocular parameters extracted from images of the eye (photooculography), and which produces a numerical level of drowsiness. In order to test our system, we compared the level of drowsiness determined by our system to two references: (1) the level of drowsiness obtained by analyzing polysomnographic signals; and (2) the performance of individuals in the accomplishment of a task. We carried out an experiment in which 24 participants were asked to perform several Psychomotor Vigilance Tests in different sleep conditions. The results show that the output of our system is well correlated with both references. We determined also the best drowsiness level threshold in order to warn individuals before they reach dangerous situations. Our system thus has significant potential for reliably quantifying the level of drowsiness of individuals accomplishing a task and, ultimately, for preventing drowsiness-related accidents.