# 2D Gaze Estimation Based on Pupil-Glint Vector Using an Artificial Neural Network
## 1 Introduction
[PERSON] and [PERSON] [71] utilize generalized regression neural networks (GRNNs) to calculate a mapping function from pupil parameters to screen coordinates in a calibration procedure. The GRNN topology consists of four layers: input layer, hidden layer, summation layer, and output layer. Six factors including pupil-glint vector, pupil ellipse orientation, _etc._ are chosen as the input parameters of GRNNs. The output nodes represent the horizontal and vertical coordinates of the gaze point. Though the use of hierarchical classification schemes simplifies the calibration procedure, the gaze estimation accuracy of this method is not perfect. [PERSON] and [PERSON] [72] utilize two single radial basis function neural networks (RBFNNs) to map the complex and non-linear relationship between the pupil and glint parameters (inputs) to the gaze point on the screen (outputs). Both of the networks have 11 inputs including \(x\) and \(y\) coordinates of left and right pupils, pupil-to-glint vectors of the left and right eyes, _etc._ The number of network output nodes depends on the number of calibration regions in the horizontal and vertical direction. The weights of the network are stored as calibration data for every subsequent time the user operates the system. As is the case with GRNNs, the gaze estimation accuracy of RBFNNs is not high enough. [PERSON] _et al._[73] employ the Active Appearance Model (AAM) to represent the eye image features, which combines the shape and texture information in the eye region. The support vector machine (SVM) is utilized to classify 36 2D eye feature points set (including eye contour, iris and pupil parameters, _etc._) into eye gazing direction. The final results show the independence of the classifications and the accurate estimation of the gazing directions. In this paper, considering the high speed of direct least squares regression and the high accuracy of artificial neural network, we propose an improved artificial neural network based on direct least squares regression (DLSR-ANN) to calculate the mapping function between pupil-glint vectors and actual gaze points. Different from general artificial neural networks, coefficient matrix elements of direct least squares regression are employed as connection coefficients in the input and hidden layers of DLSR-ANN. The error cost function and continuous-time learning rule of DLSR-ANN are defined and calculated according to the constraint condition of solving direct least squares regression. The initial condition of an integrator associated with the learning rule of DLSR-ANN is acquired through linear polynomial calculation of direct least squares regression. The learning rate parameter is limited to a range determined by the maximal eigenvalue of auto-correlation matrix composed by input vector of direct least squares regression. The proposed method contains advantages of both direct least squares regression and artificial neural network. The remainder of this paper is organized as follows: Section 2 presents the proposed neural network method for gaze estimation in detail. Section 3 describes the experimental system and shows the results. Section 4 concludes the whole work. The experimental results show that the training process of the proposed method is stable. The gaze estimation accuracy of the proposed method in this paper is better than that of conventional linear regression (direct least squares regression) and nonlinear regression (generic artificial neural network). The proposed method contributes to enhance the total accuracy of a gaze tracking system.