# 2D Gaze Estimation Based on Pupil-Glint Vector Using an Artificial Neural Network
## 1 Introduction
Multi-group attempts are conducted to find a training network with optimal performance. In the first attempt, images of only the pupil and cornea are utilized as inputs to ANN. The output units are organized with horizontal and vertical coordinates of the gaze point. A single divided layer is used for training in the ANN architecture. In the second attempt, in order to achieve a better accuracy, the total eye socket (including pupil and glint position) is utilized as an input to ANN. A single continuous hidden layer and a single divided hidden layer are used for training in the ANN architecture. The experimental results show that when the hidden layer units are fewer, the training accuracy of the divided hidden layer is higher than that of the continuous hidden layer. In addition, the training time is short. Furthermore, some of the eye images are employed as training sets and the remainder are employed as testing sets, which provides more accurate experimental results. However, though a higher accuracy can be achieved when the total eye socket (including pupil and glint position) is utilized as an input to ANN, the training sample data is huge and the training time is long. [PERSON] _et al._[66] developed a network-based gaze tracking system. As an auxiliary tool, a strip with black and white bands is mounted on the user's head to facilitate real-time eye detection. Twelve items, consisting of strip edge coordinates at lower ends, eyeball centers coordinates, and eyelid distances, are the input features of the neural network. The \(X\) and \(Y\) coordinate pair of the point the user is looking at on the screen is the output of the neural network. A 25-neuron hidden layer is utilized between the input and output layer. This method requires a large number of input items and a long detection period. The real-time quality needs to be improved. [PERSON] _et al._[67] compare the neural network and linear regression method utilized for estimating gaze direction. The comparison results show that: (1) the calibration procedure of the neural network method is faster as it requires fewer calibration markers, and (2) the neural network method provides higher accuracy. The gaze tracking performance of a neural network is better than that of linear regression. Multi-layer perceptrons (MLPs) are utilized by [PERSON] _et al._[68] to calculate gaze point coordinates based on electro-oculogram (EOG). The number of input nodes depends on the number of data points chosen to represent the saccadic waveforms. The output nodes of the network provide the horizontal and vertical 2D spatial coordinates of the line-of-sight on a particular training or test trial. In order to determine the number of nodes that can provide the optimal outputs, hidden layers containing different numbers of nodes are selected to train MLP ANN. Initial weights trained on another person are referred to in order to reduce training time. The experimental results show that using MLPs for calibration appears to be able to overcome some of the disadvantages of the EOG and provides an accuracy not significantly different from that obtained with the infrared tracker. In addition, [PERSON] _et al._[69] find that MLPs can produce positive effectives: jitter reduction of gaze point estimation and enhancing the calculating stability of gaze points. [PERSON] _et al._[70] utilize multilayer neural feedforward networks (MFNNs) to calculate gaze point coordinates based on pupil-glint vectors. Two separate MFNNs (each one having the same eye features as inputs, with one single output neuron directly estimating one of the \(X\) and \(Y\) coordinates of the POG), each containing 10 neurons in the hidden layer, are employed for training to acquire the outputs. The use of MFNNs overcomes the drawbacks of the model-based EGTSs and the potential reasons for their failure, which sometimes give ANNs an undeservedly poor reputation.