# 2D Gaze Estimation Based on Pupil-Glint Vector Using an Artificial Neural Network
## 1 Introduction  
Human beings acquire 80%-90% of outside information through the eyes. Humans' visual perception of information can be acquired through eye gaze tracking [1; 2; 3; 4]. With the increasing development of computer/machine vision technology, gaze tracking technology has been more and more widely applied in the fields of medicine [5], production tests [6], human-machine interaction [7; 8], military aviation [9; 10], _etc._  
According to differences in dimension of gaze direction estimation, gaze tracking technology can be divided into 2D gaze tracking [11; 12; 13; 14; 15; 16; 17; 18; 19] and 3D gaze tracking [20; 21; 22; 23; 24; 25; 26; 27]; according to differences in ways of wearing, gaze tracking technology can be classed as intrusive (head-mounted) [12; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37] or non-intrusive (head-free) [20; 23; 38; 39; 40; 41; 42; 43; 44]. For different gaze tracking systems, gaze tracking methods mainly contain Limbus Tracking [45; 46; 47], Pupil Tracking [48; 49; 50], Pupil-glint Vector [51; 52; 53; 54; 55], Purkinje Image [56; 24; 57], _etc._  
For 2D gaze estimation methods, mapping function between gaze points and target plane or regions of interest is firstly established. The mapping function solved is then further utilized to calculate the gaze point on certain targets or regions. For 3D gaze estimation methods, a human eyeballmodel is employed to determine the absolute position of eyes in the test space. On this basis, 3D gaze is calculated to acquire the specific staring location or fixation targets of human eyes in the space. The main purpose of this paper is to estimate the gaze point of the human eye on a monitor screen fixed to the head. The mapping function between gaze points and fixation targets is from plane to plane. Therefore, a novel 2D gaze estimation method based on pupil-glint vector is proposed to calculate the gaze direction. In conventional 2D gaze estimation methods, the most widely utilized calculation methods can be divided into two groups: linear regression (direct least squares regression) [58; 59; 60; 61; 62; 63; 64] and nonlinear regression (generic artificial neural network) [65; 66; 67; 68; 69]. In [58; 59; 60; 61], [PERSON] _et al._ utilize least squares to calculate the mapping function between calibration markers and corresponding pupil-glint vectors. Overdetermined linear equations for solving mapping function are composed by a series of 2 nd-order polynomials. The number of polynomials depends on the number of calibration markers. Corresponding coordinates of calibration markers, pupil and glint centers are determined through a calibration process. The pupil-glint vector is calculated through the subtraction of pupil and glint center coordinates. [PERSON] _et al._[62] propose an adaptive calibration method. A second time calibration is employed for error correction. A polynomial transformation of higher order is utilized to model mapping function by applying a mean square error criterion. The result of single calibration shows that the gaze estimation accuracy will increase with the enhancement of the polynomial order. However, through experimental analyses, [PERSON] _et al._[63; 64] point out that the gaze estimation accuracy of a gaze tracking system will not increase with the enhancement of polynomial order owing to the factors of head motion, number of calibration markers, and calculating method of pupil-glint vector, _etc._ When applied for solving mapping function, 2 nd-order linear polynomial is the most widely used linear regression solution method with the advantages of fewer calibration markers and better approximation effect. An artificial neural network is the most widely used nonlinear regression method for solving the mapping function between calibration markers and corresponding pupil-glint vectors (or pupil centers, eye movements information, _etc._). Early in 1994, [PERSON] and [PERSON] [65] proposed the method using simple artificial neural network (ANN) to estimate gaze direction.