The main objective of gaze trackers is to provide an accurate estimate of the user’s gaze by using the eye tracking information. Gaze, in its most general form, can be considered to be the line of sight or line of gaze, as 3D (imaginary) lines with respect to the camera, or as the point of regard (also termed the point of gaze). This chapter introduces different gaze estimation techniques, including geometry-based methods and interpolation methods. Issues related to both remote and head mounted trackers are discussed. Different fixation estimation methods are also briefly introduced. It is assumed that the reader is familiar with basic 3D geometry concepts as well as advanced mathematics, such as matrix manipulation and vector calculus.
TopGaze Estimation Techniques
To calculate eye movements, a connection between the features provided by the technology (i.e., eye tracking results) and gaze must be established. Our eyes are constantly in motion. As we look around, the eyes perform different movements so that the informative parts of the scene are sensed by the fovea. When fixating on an object, the eye performs specific micro-movements from which the stable point of fixation can be deduced. Gaze estimation is defined as the function connecting eye image and gaze (PoR/LoS) (see Figure 1). The success of this task depends largely on the technology selected, on the algorithms used to extract the specific eye features from the image, on the gaze estimation method employed, and on the fixation-estimation algorithm used.
Figure 1. Gaze estimation attempts to find a relationship between image analysis results and gaze
Gaze estimation is not a trivial task, and, so far, no single solution to the problem has emerged (i.e., a method for determining gaze that is clearly the best). An acceptable gaze estimation method should, preferably, be accurate (with an error of <1º), robust, and tolerant to head movement. The third characteristic in particular has been one of the most sought-after features in recent years. In head-mounted systems, head movement tolerance is not a problem, as the gaze tracking system moves with the head; however, there are other problems with head-mounted systems, as described later in this chapter, in the section ‘Head-mounted Gaze Trackers’. Head movements are particularly important for remote eye tracking systems, in which the subject can move more freely with respect to the camera.
The connection between image and gaze is not self-evident, and different approaches have been proposed in recent decades. In attempting to find this connection two main approaches can be distinguished:
• Geometry-based methods
• Interpolation methods
Geometry-based methods express the relationship between the image and gaze in terms of the geometry of the gaze tracking system in combination with modelling of the visual fixation mechanism. Thus 3D models (for the eyeball and system framework) are constructed. In the same manner, the mathematical basis of the image-formation process must be explored. Alternatively, interpolation methods, largely arising during the last few decades, represent the relationship between the image and gaze via a general-purpose function, such as linear or quadratic polynomials, based on unknown (empirical) coefficients and a vector containing the image features and their possible products. For a more extensive description of this topic refer to the work of Hansen and Ji (2010).
In this chapter, the basic theory underlying gaze estimation methods is presented. Additional sections focus on the problems of head-mounted eye trackers and fixation-estimation methods.
TopGeometry Based Methods
Geometry-based methods use the geometry of the system and the eye to estimate gaze. Consequently, the geometric relationships between system elements must be known and implemented properly. Analytical deduction of gaze is challenging; hence, geometry-based gaze estimation methods are difficult to derive. However, they provide a useful theoretical basis for system behaviour that allows for the heuristic analysis of the system. These kinds of methods permit the measurement of alternative factors of system performance, such as the sensitivity of the system to different variables (e.g., image resolution) and the possibility of quantifying errors theoretically, among other elements.