Pie menus offer several features which are advantageous especially for gaze control. Although the optimal number of slices per pie and of depth layers has already been established for manual control, these values may differ in gaze control due to differences in spatial accuracy and congitive processing. Therefore, we investigated the layout limits for hierarchical pie menu in gaze control. Our user study indicates that providing six slices in multiple depth layers guarantees fast and accurate selections. Moreover, we compared two different methods of selecting a slice. Novices performed well with both, but selecting via selection borders produced better performance for experts than the standard dwell time selection.
Twelve volunteers participated in the study, aged between 23 and
30 (26 in mean). All reported normal or corrected-to-normal vision
and were familiar with computer usage. Two of them had prior
experience with eye tracking and pie menus.
The study took place in a room without windows under indirect arti-
ﬁcial lightning. The pie menus were presented on a 21 Sony GDM-
F520 CRT display with a resolution of 1280x960 at a frame rate
of 75Hz. The eye tracking device used was a head-mounted Eye-
link2. The spatial resolution of this set-up, considering the nominal
tracking resolution of 0.5◦ , was about 12 pixels.
Figure 2: Example trial and selection procedure. After selecting
the last slice (d), the next trial starts (e).
Independent variables throughout the study were the number of
slices per pie (width), the number of hierarchical layers per pie 4.1 Width
(depth), and the method of selection. These factors were varied
blockwise. In total, 13 blocks by 32 trials were to be performed Selection time: For investigating the effects of menu width, blocks
with the conﬁguration and selection method described in Table 1. with menus of four, six, eight, and twelve slices were compared. All
these menus consisted of two depth layers. For four slices, IST took
Table 1: Menu layout, selection method and visualization condition 667.141 ms (standard error se=31.18). For six slices, IST was in
for all 13 blocks. mean 786.35 ms (se=38.60), for eight slices 907.01 ms (se=54.37),
and for twelve slices 933.11 ms (se=40.31) (see Fig. 3). These
Block # Width Depth Sel. Method Visualization differences were of signiﬁcance (F(3,33)=27.52, p < .001). Post
1 4 2 sel. borders yes hoc comparisons revealed that all numbers of slices differed signif-
2 8 2 sel. borders yes icantly from each other except eight and twelve slices.
3 6 2 sel. borders yes
4 12 2 sel. borders yes
5 4 2 sel. borders yes
Mean Item Selection Time (ms)
6 4 3 sel. borders yes 900
7 4 4 sel. borders yes 850
8 4 2 sel. borders yes 750
9 4 2 sel. borders no 700
10 4 2 sel. borders yes 650
11 4 2 dwell time yes 550
12 8 3 sel. borders yes 500
4 6 8 12
13 8 3 dwell time yes
Number of items
Errors and item selection times (ISTs, measured from the onset of
the pie until the selection of one slice) served as dependent vari- Figure 3: Effect of the number of slices on item selection times.
ables. ISTs were computed instead of the usual task completion
times in order to compare performance between the different menu
layouts. An error was deﬁned as every single false selection. For
Error rate: For four slices, 5.62% errors were produced (se=1.04).
example, for the task “N - O”, the selection of “N - W” or “O - O”
With six slices, the error rate reached 9.58% (se= 1.40), with
was counted as one, the selection of “W- N” as two errors.
eight slices 21.51% (se=3.67), and with twelve slices 22.62%
(se=3.68). Also for the error rate, menu width had a signiﬁcant
3.5 Procedure effect F(3,33)=16.77, p <.001. Again, this effect was due to differ-
ences between all numbers of slices except eight and twelve slices.
The task was to select as fast and as accurate as possible objects
through a pie menu, which were depicted above the centre top of These data indicate that six slices seem to be the maximal number
the screen. After ﬁxating the start button the pie menu popped up of slices which can be suggested for using pie menus in gaze control
(see Fig. 2a and 2b). Each selection was accompanied by a click both, in terms of fast and accurate performance.
sound [Majaranta et al. 2006]. With a selection, either the next
pie layer popped up or, the menus were closed and the start button 4.2 Depth layers
appeared again together with a new task until the block was ﬁnished
(see Fig. 2).
Selection time: For examining the effects of number of layers,
menus of two, three, and four layers were compared, all based on
4 Results pies of four slices. IST was 667.14 ms (se=31.18) for two layers,
749.85 ms (se=48.02) for three layers, and 746.83 ms (se=31.76)
IST and errors were entered into ANOVAs for repeated measures. for four layers (see Fig. 4). These differences were of signiﬁcance
Except for the investigation of learning effects, data for the menu of (F(2,22)=9.13, p <.001). Post hoc analysis showed that this effect
four slices presented in two layers were taken from the second run. was due to the faster IST with two layers relative to three and four.
1000 performance between the steps of both layers should not differ. If,
Mean Item Selection Time (ms)
however, users solve this task step by step, in the marking ahead
850 condition the ﬁrst selection might still succeed whereas the second
may be more error-prone and/or slower.
650 Selection time: Performance between the very ﬁrst block and
600 the block without visual presentation did only marginally differ
(F(1,11)=4.04, p =.07). In addition, the IST for the ﬁrst menu layer
2 3 4 was with 951.09 ms (se= 90.18) slower than for the second layer
(824.31 ms, se=79.53; F(1,11)=11.29, p <.01, see Fig. 6). How-
ever, there was no interaction between both variables suggesting
that there were no speciﬁc differences between both blocks (F<1).
Figure 4: Effect of the number of layers on item selection time.
1200 Pie Menu
Mean Item Selection Time (ms)
1100 Marking Menu
Error rate: Errors were as high as 5.62% (se=1.04) for two, 6.03% 1000
(se=1.04) for three, and 6.06% (se=1.26) for four layers. The effect 900
of menu depth on IST was not signiﬁcant (F<1). 800
These results show that the depth of a pie menu is not as crucial in 600
gaze control as is the width. This is in contrast to the data provided 500
for manual control by Kurtenbach and Buxton . 1 2
Figure 6: Item selection times for the ﬁrst and second menu layer
Selection time: Effects of learning were investigated comparing separately for the very ﬁrst block of the marking menu and the
performance for the menu of four slices arranged in two layers, marking ahead condition.
which was repeated four times throughout the whole experiment.
In the ﬁrst run, users took 817.03 ms (se=61.81) per item. This
was reduced to 667.14 ms (se= 31.18) in the second, to 633.46 ms Error rate: In errors, performance between the very ﬁrst run and
(se=30,36) in the third, and to 586.88 ms (se=28.19) in the fourth the marking block did not differ (F<1). As in selection times, the
run (see Fig. 5). The effect of learning was statistically signiﬁcant menu layers (i.e., ﬁrst versus second selection) produced a signiﬁ-
(F(3,33)=17.14, p <.001). Each run produced signiﬁcantly faster cant effect (F1,11)= 14.63, p <.01). This was due to more errors
selection times, except the second and third (p =.15). The decrease in the second (9.5% se=1.31) than in the ﬁrst menu layer (5.88%,
from the third to the fourth run was marginally signiﬁcant (p =.06). se=.83). There was no interaction between both variables (F<1).
4.5 Selection Method
Mean Item Selection Time (ms)
850 Selection time: The investigation of whether selection via selection
800 borders can actually compete with the standard selection procedure
using dwell times (400 ms) was performed on two menu designs:
650 A small menu of four slices and two depth layers and a larger menu
of eight slices and three depth layers. The statistical comparison re-
vealed a main effect of menu size (F(1,11)=58.04, p <.001) where
1 2 3 4 selection took less time in the small menu (663.37 ms, se=25.29)
relative to the larger one (887.59 ms, se=45.42). However, there
was neither a main effect of selection method (F<1) nor an interac-
tion with it (F<1), indicating that in terms of selection speed, both
Figure 5: Effect of learning on selection times per item. selection methods can be regarded as equally useable.
Error rate: In errors, learning let to a decrease from 16.05% Error rate: In errors, there was also an effect of menu size
(se=2.73) over 5.62% (se=1.04) and 3.30% (se=.82) to 5.72% (F(1,11)=19.56, p <.001. Here were, with 10.55% (se=2.02), less
(se=1.24). These differences were also of signiﬁcance (F(3, errors per selection for the small pie menu as for the large (21.43%,
33)=18.63, p <.001). Post hoc comparisons revealed that perfor- se=3.49) (see Fig. 7). Selection via selection borders was with
mance in the ﬁrst session was worse than in all further sessions. 11.72% (se=1.67) more effective than selection via dwell times
(20.27%, se=3.91; F(1,11)=7.55, p <.02). Again, there was no
interaction between both variables (F<1).
4.4 Marking Ahead Selection
In order to further investigating learning, one block without visual 5 Discussion and Conclusion
feedback was performed. The assumption of the marking ahead
strategy is that users have a complete mental conception of the When designing pie menus for gaze control the number of items
whole series of actions. In order to test this assumption, perfor- per layer in a pie menu seems to be the most crucial factor. As
mance in this marking ahead block was compared to performance our data revealed, up to six slices per pie can be effectively and
on the very ﬁrst run. Importantly, we included the menu layer (i.e., efﬁciently selected with eye trackers with about 0.5◦ of spatial ac-
selection in the ﬁrst versus in the second layer) as a further vari- curacy (i.e. professional eye tracking equipment). Of course the ra-
able: If users have a mental conception of the whole task, then dius (180 px in our study) may affect the optimal number of slices
30 Border Sel. tions by dwelling on an item produced more errors than selections
25 by borders. One might thus improve the accuracy by increasing the
dwelling time. However, dwell time was perceived as a “more nat-
Errors in %
ural”, “intuitive” but also “slower” selection method among partici-
pants without prior experience in gaze control. Taken together, one
might suppose that selection by selection borders provides a bet-
5 ter performance for selecting items in a pie menu than dwell times.
0 The arrangement of the pie menus might also be responsible for
the superiority of selection by borders: Since all new layers were
centred around the outer border of the current pie, selection by bor-
ders already brings the eye towards the centre of the next pie menu.
Figure 7: Effect of the selection method on error rates. Hence, with other designs like centring the pie around the current
ﬁxation position, dwell time selection might compete with selec-
tion by borders. However, as already discussed above, respective
designs may be of disadvantage for the usability and learnability of
and should thus be investigated in further experiments. Addition- pie menus.
ally, one should take into consideration that the tasks for the vari-
ous numbers of slices varied in difﬁculty: For four and eight slices, To sum up, pie menus are a suitable and promising interfaces for
tasks were given with cardinal points, and for six and twelve slices, gaze interaction can allocate up to six items in width and multiple
they were given using the clock. We suppose cardinal points to be depth layers, allowing a fast and accurate navigation through hier-
more difﬁcult: Some subjects confused “W” with “O” and vice- archical levels by using or combining multiple selection methods.
versa (like confusing left with right), committing in mean 1.91% These qualities may give pie and marking menus the chance to es-
errors, which made up about 20% of the total errors. For the eight tablish as a standard in gaze control.
slices menu, perceiving and remembering coordinates like “SW-
SW - S - W” can be assumed to be more difﬁcult than the numbers References
like “8 - 8 - 6 - 10” used with six and twelve slices.
Performance with two depth layers was found to be signiﬁcantly C ALLAHAN , J., H OPKINS , D., W EISER , M., AND S HNEIDER -
faster than with more layers. One explanation may be, that par- MAN , B. 1988. An empirical comparison of pie vs. linear menus.
ticipants were able to mark the selection path completely ahead. In CHI ’88: Proceedings of the SIGCHI conference on Human
This strategy was harder to follow with more than two depth layers. factors in computing systems, ACM, New York, NY, USA, 95–
Even though, the performance achieved with three and four depth 100.
layers was acceptable and showed no additional costs presenting H UCKAUF, A., AND U RBINA , M. H. 2008. Gazing with peyes:
more depth layers. Therefore, to allocate more items in a pie menu, towards a universal input for various applications. In ETRA ’08:
our data suggest increasing the number of depth layers. Proceedings of the 2008 symposium on Eye tracking research &
The results show that for gaze control, slice width is more important applications, ACM, New York, NY, USA, 51–54.
than menu depth. This is in contrast to the data provided by Kurten- H UCKAUF, A., AND U RBINA , M. H. 2008. On object selection
bach and Buxton  who found no limitation for the number in gaze controlled environments. In Journal of Eye Movement
of slices per menu, but for the number of depth levels. We assume Research, vol. 2 of 4, 1–7.
that the difference in number of slices is mainly due to the lower
accuracy of gaze tracking, as well as to the difﬁculty of performing I STANCE , H., BATES , R., H YRSKYKARI , A., AND V ICKERS , S.
selective actions with a perceptual organ [Zhai et al. 1999]. 2008. Snap clutch, a moded approach to solving the midas touch
problem. In ETRA ’08: Proceedings of the 2008 symposium
Of course, the number of layers is restricted by the screen size. on Eye tracking research & applications, ACM, New York, NY,
Therefore, it may not be inﬁnite. An alternative method of present- USA, 221–228.
ing more layers might be arranging forthcoming pie menus either
directly overlaying the former one, or centred on the current ﬁx- K URTENBACH , G., AND B UXTON , W. 1993. The limits of expert
ation position. Both of these alternatives, however, have a severe performance using hierarchic marking menus. In CHI ’93: Pro-
disadvantage inherent: Whereas the ﬁrst solution would require ad- ceedings of the SIGCHI conference on Human factors in com-
ditional saccades back to the starting point, destroying the naviga- puting systems, ACM Press, New York, NY, USA, 482–487.
tion metaphor adopted for hierarchical menus, the second solution ¨ ¨
M AJARANTA , P., M AC K ENZIE , S., AULA , A., AND R AIH A , K.-
would reduce the capability of marking ahead, since each menu J. 2006. Effects of feedback and dwell time on eye typing speed
would change in position on the screen each time it appears, which and accuracy. Univers. Access Inf. Soc. 5, 2, 199–208.
may interfere with the path learning process seen in this experiment.
U RBINA , M. H., AND H UCKAUF, A. 2007. Dwell-time free eye
Subjects showed a signiﬁcant learning effect using pie menus. Even typing approaches. In Proceedings of the 3rd Conference on
after 128 selections, they continued improving signiﬁcantly their Communication by Gaze Interaction (COGAIN 2007), 65–70.
IST, with a constant and relatively low error rate. Experienced
users have been expected to be capable of marking ahead a com- Z HAI , S., M ORIMOTO , C., AND I HDE , S. 1999. Manual and gaze
plete path (or gesture). This could be conﬁrmed for our observers: input cascaded (magic) pointing. In CHI ’99: Proceedings of
After already 96 trials with a menu designed with four slices and the SIGCHI conference on Human factors in computing systems,
two layers, the accuracy of performance without any visual cue did ACM Press, New York, NY, USA, 246–253.
not differ from performance within the ﬁrst 32 trials. Even if there
was a lower selection speed for these blind trials, the hypothesis Z HAI , S. 2008. On the ease and efﬁciency of human-computer
of marking ahead trajectories can be conﬁrmed also for pie menus interfaces. In ETRA ’08: Proceedings of the 2008 symposium
operated by gaze. on Eye tracking research & applications, ACM, New York, NY,
The selection methods differed in accuracy, but not in IST: Selec-