Gaze tracking is crucial for studying driver’s attention, detecting fatigue, and improving driver assistance systems, but it is difficult in natural driving environments due to nonuniform and highly variable illumination and large head movements. Traditional calibrations that require subjects to follow calibrators are very cumbersome to be implemented in daily driving situations. A new automatic calibration method, based on a single camera for determining the head orientation and which utilizes the side mirrors, the rear-view mirror, the instrument board, and different zones in the windshield as calibration points, is presented in this paper. Supported by a self-learning algorithm, the system tracks the head and categorizes the head pose in 12 gaze zones based on facial features. The particle filter is used to estimate the head pose to obtain an accurate gaze zone by updating the calibration parameters. Experimental results show that, after several hours of driving, the automatic calibration method without driver’s corporation can achieve the same accuracy as a manual calibration method. The mean error of estimated eye gazes was less than 5°in day and night driving.

Tewodros Amdeberhan obtained his Ph.D. in mathematics from Temple University under the supervision of Doron Zeiberger. He currently teaches at Tulane University and holds a permanent membership at DIMACS, Rutgers University. Xiao Guan was born in Beijing, China. He is currently a graduate student working under the guidance of V. Moll at Tulane University. Inspired by his advisor, he is currently concentrating on problems related to the evaluation of definite integrals. He is also interested in random matrices. Lin Jiu is a doctoral student working under the supervision of V. Moll at Tulane University. He obtained both bachelor and master degrees in Mathematics at Beijing Institute of Technology. His research interests involve Symbolic Computations, Special Functions and Number Theory.

Abstract. A sequence of coefficients that appeared in the evaluation of a rational integral has been shown to be unimodal. An alternative proof is presented.

Based on the target reflection section defined by The Bidirectional Reflectance Distribution Function, a method of approximate calculation and analysis of the cone and plate’s reflection section in laser-illuminated condition are derived in the paper. With the method, reflection section of cone is calculated and analyzed. Experimental platform was established with 1.319m Nd:YAG laser, measuring the reflection section of cone in diverse incident angle. Curve of the plate, cylinder and cone relative illumination changing in diverse incident angle were measured. The results of this study are helpful for many applications such as weapon designing, target invisible, and system modeling.

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