The Circle Experiment

The existing data could not clarify whether Fitts’ law holds for the eyes. This was the reason to set up another experiment. The paper of Sibert and Jacob [Sibert, Jacob 2000] describes an experiment, which the authors called the circle experiment. The experiment presents circles on the screen and the test subject has to look at them. Their experiment used a single circle size. The authors suggested repeating the experiment with different circle sizes to measure Fitts’ law. The setup for the experiment presented here was mostly the same as in [Sibert, Jacob 2000] with the difference that no dwell time (zero dwell time) was used. The user study was stopped after measuring five participants. One reason to stop the user study was that some participants gave up when the target size was below the eye’s accuracy. Typically, when the participants realized that they were not able to hit the target they started to shake the head. With a liberal head fixation by a chin rest only, this spoiled the calibration and worsened the problem. Another reason was that the data did not allow an evaluation for Fitts’ law as explained later. Nevertheless, some of the data are presented here because they give some insights on the topic. Figure 37 shows the gaze paths of one participant recorded during the circle experiment.

When thinking about a positioning task for the eye the first question is whether the eye hits the target with a single saccade or in a sequence of saccades. A sequence of saccades would lead to a scenario as used for the derivation of Fitts’ law (see 3.4.2) but with the difference that the steps are not constant in time. The time for a saccade depends on the length (see 3.3.3) and this would lead to a different formula.

Figure 37 shows that the gaze moves to a target with a single saccade as long as the target size is bigger than the eye’s accuracy. Small saccades happen mostly within the target and not very often in between the targets. Consequently, the question is whether the amplitude-time relation of a saccade obeys Fitts’ law.

Figure 37 also shows that the gaze does not move to the centre of the targets – it moves to the edge of the targets. This means that it is questionable whether it makes sense to offer the eye a big target – the eye searches its own target size area. It seems that the concept of target size for pointing tasks with the eye has problems. At the beginning of the pointing task the target lies in the area of peripheral vision where the resolution is low. This brings up the question what the eye will recognize as a target and how it estimates its size. It is questionable whether the eye tries to position its view to the centre of a target. It seems more likely that the eye tries to position its view to a spot and the demand for the positioning task is that this spot finally will be within the size of the fovea. Consequently, the target size for the positioning task is the size of the fovea. It also means that the speed of the positioning task is independent of the target size. The evaluations in 3.4.6 are built on this understanding.

The fact that the gaze does not move to the target centre also caused the problem of evaluating the data. The performance time for the first three target sizes was nearly equal for all participants, however, with a small tendency to higher execution time for smaller targets. The grid size for the targets stayed constant and consequently the distance of the target centres stayed constant too for different target sizes. The small increase in performance time for smaller targets could be used as an argument for a positioning time dependent on the target size. However as the gaze moved from edge to edge the total distance covered by the gaze increases with smaller targets as the gaps between the targets become bigger. In this situation the result of the evaluation depends on the

definition of the distance – task defined distance or performed distance. Changing the definitions after looking at the data is not a scientific approach.

Figure 37: Gaze paths (starting at the dark target) for seven different target sizes (radius of 70, 60, 50, 40, 30, 20, and 15 pixels) in the circle experiment. The last three sizes are below the accuracy limit.

Although the presented experiment does not give a proof, it indicates that the performance time for a positioning task for the eye does not depend on the target size. This is in accordance to the opinion of psychologists. A personal email to Professor Deubel [Deubel@], asking whether Fitts’ law applies to eye movements, brought the answer that the time for a saccade depends only on its amplitude. This answer did not encourage setting up a redesigned user study to find out something already known.

As shown in 3.3.2, the ERICA eye tracker does not report eye movements below the 16-pixel threshold and saccades with lengths up to 28 pixels are not reported correctly. The property of the eye tracker to damp the noise disallows fine positioning with the eye, even if the eye could do it. If the eye tries to get closer to the target, the eye tracker first does not report any movement and finally reports a movement to the other side of the target; the reported gaze position jumps across small targets. Therefore, the problems hitting the small targets are mainly an effect of the limited eye tracker’s accuracy. The last three sizes in the circle experiment seem to be affected by the eye tracker’s inaccuracy. In the case of missing the target, the participant’s eye moved away from the target and tried to hit the target again. After some attempts the eyes hit the target by chance. The situation is similar to throwing a stone at a small target and this picture describes the situation (for this type of eye tracker) in the circle experiment for small targets below the accuracy quite well. Of course, it is possible to give a relation for the expected time for a successful hit depending on the target size and distance. However, the character of such a stochastic process is very different from a feedback-controlled process.

The existence of an accuracy limit creates a situation which differs from the experiments conducted by Fitts. Fitts used a stylus as a pointing device with a nearly perfect tip. It is not possible to do the same for the eye. It does not make sense to do positioning tasks for targets smaller than the accuracy of the pointer. When doing so the effective width of the target is the accuracy of the pointer. A pointing task with the fingertip has an accuracy of about ±0.5 cm because of the size of the fingertip. Pressing buttons with sizes of 0.1 cm, 0.2 cm, 0.4 cm, and 0.8 cm with the finger will not reflect target sizes but the size of the fingertip plus the size of the target. See Figure 38 for an illustration.

Figure 38: Target sizes and accuracy for pointing tasks for a pointer of a fixed size.