## 1 Introduction  
Recently, wearable gaze tracking devices (or called eye trackers) have started to become more widely used in human-computer interaction (HCI) applications. To evaluate people's attention deficit, vision, and cognitive information and processes, gaze tracking devices have been well-utilized in this field [1; 2; 3; 4; 5; 6]. In [4], the eye-tracking technology was a vastly applied methodology to examine hidden cognitive processes. The authors developed a program source code debugging procedure that was inspected by using the eye-tracking method. The eye-tracking-based analysis was elaborated to test the debug procedure and record the major parameters of eye movement. In [5], the eye-movement tracking device was used to observe and analyze a complex cognitive process for C# programming. By evaluating the knowledge level and eye movement parameters, the test subjects were involved to analyze the readability and intelligibility of the query and method at the Language-Integrated Query (LINQ) declarative query of the C# programming language. In [6], the forms and efficiency of debugging parts of software development were observed by tracking eye movements with the participation of test subjects. The routes of gaze for the test subjects were observed continuously during the procedure, and the coherences were decided by the assessment of the recorded metrics.  
Many up-to-date consumer products have applied embedded gaze tracking technology in their designs. Through the use of gaze tracking devices, the technology improves the functions and applications of intuitive human-computer interaction. Gaze tracking designs use an image sensor based on near-infrared (NIR), which was utilized in [7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. Some previous eye-tracking designs used high-contrast eye images, which are recorded by active NIR image sensors. NIR image sensor-based technology can achieve high accuracy when used indoors. However, the NIR-based design is not suitable for use outdoors or with sunlight. Moreover, long-term operation may have the potential to hurt the user's eyes. When eye trackers are considered for general and long-term use, visible-light pupil tracking technology becomes a suitable solution.  
Due to the characteristics of the selected sensor module, the contrast of the visible-light eye image may be insufficient, and the nearfield eye image may contain some random types of noise. In general, visible-light eye images usually include insufficient contrast and large random noise. In order to overcome this inconvenience, some other methods [17; 18; 19] have been developed for visible-light-based gaze tracking design. For the previous wearable eye tracking design in [15; 19] with the visible-light mode, the estimation of pupil position was easily disturbed by light and shadow occlusion, and the prediction error of the pupil position, thus, becomes serious. Figure 1 illustrates some of the visible-light pupil tracking results by using the previous ellipse fitting-based methods in [15; 19]. Thus, a large pupil tracking error will lead to inaccuracy of the gaze tracking operation. In [20; 21], for indoor applications, the designers developed eye tracking devices based on visible-light image sensors. A previous study [20] performed experiments indoors, but showed that the device could not work normally outdoors. When the wearable eye-tracking device is correctly used in all indoor and outdoor environments, the method based on the visible-light image sensor is sufficient.