Amodal completion as reflected by gaze durations

Transcription

1 Plomp et al. Occlusion and Fixation Page 1 Amodal completion as reflected by gaze durations Gijs Plomp, Chie Nakatani, Laboratory for Perceptual Dynamics, RIKEN BSI, Japan Valérie Bonnardel, University of Sunderland, Sunderland, UK Cees van Leeuwen 1 Laboratory for Perceptual Dynamics, RIKEN BSI, Japan University of Sunderland, Sunderland, UK 1 Corresponding author. Address: 2-1 Hirosawa, Wako-shi, Saitama Japan. ceesvl@brain.riken.go.jp. Fax +81 (0) , Tel. +81 (0)

2 Plomp et al. Occlusion and Fixation Page 2 Abstract In two experiments amodal completion of partly occluded shapes was investigated by recording eye movements in a directed visual search task. Participants searched arrays of shapes in a prescribed order for target figures that could partly be occluded. Longer gaze durations were found on occlusion patterns than on truncated control patterns for targets but not for non-targets. This effect of occlusion was restricted to a subset of the stimuli. A second experiment tested whether this restriction resulted from structural properties of the stimuli or their familiarity. Occlusion patterns in this experiment were ambiguous with respect to structure, allowing both local and global completions. One of the completions was always less familiar than the other. The results showed longer gazes only for the less familiar completions, irrespective of whether they were local or global.

3 Plomp et al. Occlusion and Fixation Page 3 1. Introduction The phenomenon of amodal completion (Michotte, Thinès and Crabbé, 1964) occurs when we perceive a partly hidden object as whole and complete. We set out to study this phenomenon using eye movement recordings, introducing this technique to study the role of high-level processing in the completion of two-dimensional occluded shapes. Amodal completion is as mundane as it is surprising. Three-dimensional depth cues, such as binocular disparity, facilitate the completion of partly occluded objects (Bruno, Domini and Bertamini, 1997). But completion is also readily achieved in absence of binocular depth information, as, for instance, in pictorial stimuli. From amongst the great variety of pictorial stimuli, contour images have most frequently been chosen for the study of amodal completion (Kanizsa and Gerbino, 1982; Pessoa, Thompson and Noë, 1998; Tse, 1999; van Lier, 2001). Their completed form can, in principle, be derived either from the local or the global characteristics of the unoccluded parts. Local completions are ones based on the extrapolation of stimulus features at the locus of the occluding edge (Figure 1a); global completions are based on enhancement of symmetry of the completed figure (Figure 1b). Local features provide an elegant explanation of several completion phenomena (Kanizsa and Gerbino 1982; Kellman and Shipley, 1991) but at times only the global structure of the occluded figure can explain the derived completion (Sekuler, Palmer and Flynn, 1994; van Lier, Leeuwenberg and van der Helm, 1995) Figure 1 about here

4 Plomp et al. Occlusion and Fixation Page In accord with the omnipresence of partial occlusion, a variety of experimental findings indicate that completion is a fast and mandatory process. Presentation times of around 200 ms are long enough to generate a functionally complete percept of a partly occluded figure (Sekuler and Palmer, 1992). The apparent speed seems to suggest that early visual processes can account for completion. Estimates of completion time are for an important part obtained with the primedmatching paradigm. In this paradigm a partly occluded figure primes a response to its completed equivalent. For instance, an occluded circle facilitates the response to a complete circle; this is then taken as an indication that the first is amodally completed into a circle. The minimal presentation time needed for such an effect to arise is understood as the time it takes for completion to finish. A problem with these estimates of completion time is that even uncompleted parts of contour images can prime the representation of the whole (Stins and van Leeuwen, 1993). Completion time estimates, moreover, are not invariant and range between 75 to 200 ms, depending on the experimental task as well as on how large a proportion of the shape is occluded (Murray, Sekuler and Bennet, 2001; Guttman, Sekuler and Kellman, 2003; Shore and Enns, 1997). In terms of our physiology, a difference between 75 ms and 200 ms of processing time is substantial and equating amodal completion with early visual processing on these grounds may seem premature. Visual search paradigms (He and Nakayama, 1992; Rauschenberger and Yantis, 2001; Rensink and Enns, 1998) have provided another line of argument that amodal completion is a process of relatively low-level. In Rauschenberger and Yantis

5 Plomp et al. Occlusion and Fixation Page 5 experiments truncated shapes sometimes appeared adjacent to a square, suggesting that the latter occluded the former. When the truncated shape was a search target, the adjacent square delayed target detection. This result may suggest that the figures were involuntarily completed. However, with this task it cannot be excluded that the truncated target shape and the adjacent square were merely grouped as one shape and thus made the detection of the truncated part more difficult. Such functional filling-in is not necessarily the same as a complete representation of a partly occluded figure (Rensink and Enns, 1998). A measure of completion times that does not rely on manual responses may characterize the underlying processes more accurately. It is likely that completion processes continue during response preparation. These later processes may be at least as relevant as the early ones, as they are likely to involve the complete representation of the partly occluded figure. Such later stages of completion may explain the influence of higher-order processes. When a figure is presented and subsequently occluded, the representation of the occluded region depends on the figure seen beforehand (Joseph and Nakayama, 1999; Zemel, Behrmann, Mozer and Bavelier, 2002). Completion, therefore, besides by local and global properties of the stimulus, is also influenced by high-level processes that are sensitive to the individual history of prior stimulation. To study these processes in amodal completion one should ensure, as best as possible, full completion of the occluded figure. For this reason we used a visual search task in which the search targets were completed figures. For instance, a partially occluded circle was a target of circle detection and appeared together with similar looking non-targets

6 Plomp et al. Occlusion and Fixation Page 6 that could not be completed. In such displays amodal completion is likely to be part of the detection strategy. We prefer to measure the process of amodal completion on-line. Such a measure could be provided by eye-movement recording techniques in the form of fixation durations. Besides for comparing occluded and unoccluded targets, fixation durations can also be used to compare non-targets in a display. If, for instance, occlusion effects occur for targets but not for non-targets, we might infer that these completion processes do not occur prior to target selection. Eye movement studies have contributed greatly to the understanding of various cognitive processes such as text comprehension, object identification and scene perception (Nakatani & Pollatsek, in press, Underwood, 1998; Rayner, 1998). Indices of eye movements can be used as measures of stimulus properties as well as cognitive factors (Kowler, 1990; Liversedge and Findlay, 2000). In particular, gaze duration reflects ongoing high-level processing of the stimulus (Henderson, 1993; Just and Carpenter, 1978; Sanders and van Duren, 1997). Gaze duration is the sum of consecutive fixation durations on a figure. Amodal completion is a quick and mandatory process that is nonetheless influenced by high-level factors. As a measure of ongoing activity with sensitivity to high-level factors, gaze durations may be appropriate to study amodal completion. To our knowledge, eye movement indices have only once been reported in relation to partly occluded figures. Vishwanath, Kowler and Feldman (2000) measured landing positions of the eye on occluded figures and concluded that a completed representation is not available to the system guiding these saccades. This result is, in fact, quite compatible with the possibility that gaze durations reflect late processes in

7 Plomp et al. Occlusion and Fixation Page 7 completion. The question we set out with is twofold. Firstly, can completion time itself be measured by gaze durations and secondly, what can potential differences in gazes tell us about the processes involved in amodal completion. 2. Experiment 1 In Experiment 1 participants searched for targets that could be either completely visible or partly occluded. Search targets appeared amongst multiple instances of nontargets. Both targets and non-targets could appear in plain view or partly occluded. Truncated figures were present in the displays as a control for complexity effects as well as to discourage search strategies based on visible features alone. While participants searched the display, their eye movements were measured. We propose that completion of an occluded figure is the result of more elaborate processing than for a comparable truncated one. When this difference is reflected in longer gaze durations for occlusion patterns than for truncated ones we refer to this as an occlusion effect. An occlusion effect for both targets and non-targets would suggest that these processes are mandatory and independent of target selection Method Participants scanned 9-item displays in search for target figures. The displays contained simple and composite figures. The simple figures were either whole or truncated figures. Composite figures were combinations of two figures and could be either mosaic or occlusion patterns. The mosaic patterns consisted of a square and a

8 Plomp et al. Occlusion and Fixation Page 8 truncated shape presented aside one another. Occlusion patterns consisted of the same two shapes conjoined, suggesting that the square was an occluder. The stimuli of Experiment 1 are displayed in Figure 2. All stimuli occurred as targets as well as non-targets in 9-item displays throughout the experiment. To obtain fixation times for targets as well as non-targets, the displays were scanned in a pre-specified order Participants Ten participants (5 male) with ages ranging between 20 and 26 received a small payment for their participation. One participant had taken part in a related eye movement experiment, but all of them were unfamiliar with the stimuli in the present experiment. Informed consent was obtained from all of them Apparatus Eye movements were registered continuously by an SMI Eyelink system with two headmounted cameras. Data were recorded at a sampling rate of 250 Hz. The eye movement data and the button presses were stored on a computer. A second computer presented the stimuli on a 21-inch CRT screen. Viewing distance from the monitor was 90 cm. The search array of 9 figures spanned 20 degrees of visual angle horizontally and 17.5 degrees vertically. A response pad with four buttons was used.

9 Plomp et al. Occlusion and Fixation Page Stimuli and design The stimuli consisted of two classes of figures, a circle and a hexagon class. Each class contained two simple figures and two composite figures. The simple figures were a whole figure and a truncated counterpart. The composite figures were an occlusion pattern and a mosaic pattern. Both composite patterns were similar in terms of complexity, yet one could be amodally completed and the other not. The size of the occluded region for the occluded circle was approximately 25 %, that of the occluded hexagon 21 % Figure 2 about here Figures from both classes were arranged into nine-item displays on an invisible threeby-three square grid upon a gray background. A display contained between 1 and 5 targets. A single stimulus occupied approximately 2.5 degrees of visual angle. All figures of the two stimulus classes appeared in four possible orientations that were 90-degree rotations of each other and were chosen at random. An example of a search display is shown in Figure 3. When one simple figure was a target (e.g. the whole circle), the other from that class did not occur in the display (in this case the truncated circle). This was to avoid confusion over the target figure. We distinguish four ways in which displays were composed, depending on the selection of two simple figures, one from each stimulus class. The four possible choices constitute four alternative display types that appeared with equal frequency in the experiment. The pool of possible stimuli to appear in a display type consisted of the two selected simple

10 Plomp et al. Occlusion and Fixation Page 10 figures and the composite figures from each class. Figures from the two classes could appear in four different proportions in a display: 3:6, 4:5, 5:4, and 6:3. Within a given ratio there were again seven possible variations of how many times a particular figure occurred in the display. Seven is the amount of different combinations that can be created from three stimuli under the conditions that at least two of them appear in the display and no single composition is repeated. Thus, four (proportions) x seven (variations) displays were created. Within these 28 displays each of the stimuli from a class appeared an equal number of times while the display compositions were maximally different from each other. A series of 28 displays was created for each type of display composition. This resulted in a grand total of (28 x 4) = 112 unique experimental displays. Half of the displays within a series of 28 were assigned to a circle task the other half to a hexagon task. This was done such that display compositions were balanced between the two tasks Figure 3 about here Procedure The experiment had a total of 112 trials and was randomly split into two sessions of 56 trials each. Each session took approximately 40 minutes and a refreshment break in which the headset was taken off was scheduled between the sessions. Trials were presented in a random order that was determined at the beginning of the session. The order of the two sessions was counterbalanced over participants.

11 Plomp et al. Occlusion and Fixation Page 11 The experiment was conducted in a dimly lit room with the participant seated in a comfortable, supportive chair in front of the monitor. Participants were informed about the general principles of the eye-tracking device before receiving the instructions for the experiment. The instruction was to memorize the target figure and count the instances of it in the subsequent display. It was emphasized that some figures could be partly hidden behind other figures and that some targets might lie very close to other figures. When a whole figure was the target, the corresponding occlusion pattern was a target as well. Likewise, when the target was a truncated shape, the corresponding mosaic pattern was a target as well. The displays were searched in a fixed order. First the top row was searched from left to right, then the middle row from right to left and then the last row again from left to right. The importance of refraining from head movements during the experiment was stressed. Participants were encouraged to take small breaks between trials to blink or relax if necessary. Two practice sessions of 8 trials each were completed before the start of the experiment. The first one was done without the headset and served to get accustomed to the task and the different targets. The second one was completed with the headset mounted and calibrated in order to specifically practice the way of scanning through the displays. When the participant understood the task and the scanning order, the experiment was started. If this was not the case, the relevant practice session was repeated. Trials were self-paced and started off with a screen that showed the search target for the subsequent display in each of its four possible orientations (For the circle target four

12 Plomp et al. Occlusion and Fixation Page 12 identical circles were shown). The four instances of the target figure were presented offcenter on the horizontal and vertical axis of the screen. After pressing the upper button on the response pad a fixation point appeared for 500 ms in the center of the screen. This point then moved to the upper left part of the screen, to the center of the area where the first figure of the search display would be located. The display appeared as soon as the eyes fixated on that position. Participants pressed a button after scanning through the display and then a new screen prompted for the number of targets. With every press on the right button the number on the screen could be increased; the left button could be used to decrease the amount again. By pressing the top button participants entered their response. Feedback was subsequently given in the form of a smiling icon or a frowning one. The icon remained on the screen until the participant started the next trial by pressing the upper button. The headset was calibrated at the beginning of each session and subsequently whenever deemed necessary by the experimenter. Viewing was binocular and the positions of both eyes were recorded throughout the trials. Drift correction was performed every ten trials Results The data of one participant was discarded from analysis since part of it was missing due to an error in recording. The error rate was 1.69%; the data of the erroneous trials were discarded. Nine regions of 150 x 150 pixels (approximately 4.5 degrees) were defined around the centers of where the stimuli were positioned. Fixations inside a region were

13 Plomp et al. Occlusion and Fixation Page 13 considered fixations on the figure presented in that region. Fixations that fell outside any region as well as fixations on a region that had been fixated earlier, i.e. re-fixations, were discarded from analysis. Together, fixations that fell outside any region and re-fixations constituted 7.6% of all fixations. When there was a blink between successive fixations on the same region, all fixations on that region were discarded. The cutoff value for all fixations used in the analysis was set at 933 ms, 2 standard deviations above the mean; fixations longer than this were removed. For each participant the data from one eye were used for the analysis. The right eye was chosen by default, except for one subject for whom the right eye recordings showed a big tremor. Gaze durations were calculated as the sum of subsequent fixations on a region. The mean gaze durations per condition were computed to the nearest millisecond for each participant. In the means for non-target figures only fixations on those non-target figures that were independent of the target choice were used for analysis. This meant that composite distracters from the same stimulus class as the search target were not analyzed. This was done to satisfy assumptions of independency in the analysis. The exclusion had no effect on the results. A repeated measures analysis of variance (ANOVA) was performed with the factors Complexity (simple, composite), Category (whole, truncated), Target (target, non-target) and Figure class (circle, hexagon). The mean values and standard errors of this analysis are shown in Figure Figure 4 about here

14 Plomp et al. Occlusion and Fixation Page Targets yielded longer gaze durations than non-targets, F(1,8) = 17.96, p < 0.01, MsErr = There was an effect of Complexity where composite figures got longer gazes than simple figures, F(1,8) = 57.72, p < 0.001, MsErr = The effect of Figure class was significant, F(1,8) = 34.09, p < 0.001, MsErr = 462, with the hexagon class drawing longer gaze durations than the circle class. The effect of Figure class interacted with Category, F(1,8) = 9.64, p = 0.015, MsErr = 924, such that whole figures from the hexagon class yielded longer gaze durations than whole figures of the circle class while both classes received equally long gaze durations on the truncated figures. In addition, figure class interacted with Target, F(1,8) = 6.09, p = 0.039, MsErr = 685, showing that gazes on targeted hexagon figures were longer than those on targeted circle figures, whereas there was no such difference for non-targets. Three significant three-way interactions were obtained. The first was an interaction between the factors Target, Complexity and Category, F(1,8) = 41.53, p < 0.001, MsErr = 335. This interaction showed that simple and composite figures received similar gazes over the factor Category (whole/truncated) when they were non-targets, but not when they were targets. In the target condition the composite whole figures (i.e. the partly occluded figures) received longer gazes than the composite truncated figures. This effect of Category was absent for targeted simple figures. The second three-way interaction was between the factors Target, Category and Figure class, F(1,8) = 7.19, p = 0.028, MsErr = 700. This interaction was the result of the differences in gaze duration between targets of the two figure classes. These differences

15 Plomp et al. Occlusion and Fixation Page 15 were caused by the whole figures; gazes on these were longer for the hexagon class than for the circle class. The last three-way interaction, between the factors Figure class, Complexity and Category was marginally significant, F(1,8) = 4.26, p = 0.073, MsErr = 537. This interaction was due to the longer gaze durations on occluded hexagons than on occluded circles while there was no such difference between gazes on the two mosaic patterns of the figure classes. Furthermore, this difference over the factor Category was absent for the simple figures. From the last two interactions it becomes clear that the longer gaze durations on whole composite figures of the previous interaction are due to the occlusion pattern of the hexagon class. Only for this class did the partly occluded target get longer gaze durations than the corresponding mosaic pattern Discussion Error rates were low, suggesting that the experimental task posed no difficulties. Furthermore, the amount of re-fixations and fixations that fell outside the areas containing figures was small. Participants had no apparent difficulty in scanning the display in the prescribed direction. It is noteworthy that complexity effects were observed for targets as well as nontargets. The longer gazes on composite non-targets than on simple non-targets suggest that the processes involved in target selection are sensitive to the complexity of the figure. This complexity effect was independent of whether the composite pattern was an occlusion or a mosaic pattern.

16 Plomp et al. Occlusion and Fixation Page 16 Targets received longer gaze durations than non-targets and within targets the gazes differed over conditions. These differences reflect selection and post-selection processes. Overall, the longest gazes fell on the occlusion patterns but this effect was due to the occlusion effect in the hexagon class. It took longer to detect a partly occluded hexagon than a similar truncated shape next to a square. This effect did not occur for circles and this indicates that their processing was less extensive than that of occluded hexagons. A possibility that cannot be excluded on logical grounds is that the hexagon was completed, while the circle was not. But given the mandatory character of amodal completion, at least in its early stages, we may consider this unlikely and ad-hoc. Another possibility is that the completion of the hexagon proceeds more high-level processing than the circle. We will discuss two reasons why this might be the case. One possible reason why occluded hexagons required more high-level processing than occluded circles relates to the difference between local and global processes in completion. Interpolation of curvature is known to be an early perceptual process that starts out locally (Field, Hayes, and Hess, 1993; Guttman et al., 2003; Kovacs and Julesz, 1993). By assuming that the interpolated contour has minimal inflection a whole circle can easily be completed based on local interpolation alone (Takeichi, Nakazawa, Murakami and Shimojo, 1995; Takeichi, 1995). For the hexagon the completion process may similarly start out locally as the interpolation of the two partially occluded lines. But at least one extra feature needs to be determined: the hidden angle between the two lines. Because the local inducers are small and are not continuous behind the occluder the angle may best be determined in accordance with the global properties of the figure. Processing the hidden part of the overall symmetry may involve high-level processes. The degree to

17 Plomp et al. Occlusion and Fixation Page 17 which global stimulus properties are involved may thus account for the difference in completion times observed between the occluded circle and hexagon. A different reason why the hexagon is more difficult to complete than the circle is related to the observation that the latter is a more familiar figure than the former. Given the role of past experience in completion (Joseph and Nakayama, 1999; Zemel et al., 2002) we could ascribe the difference in gaze durations to familiarity resulting from earlier exposure. Familiarity may have reduced the involvement of high-level processing for the circle to the extent that an occlusion effect on gaze duration could no longer be observed. On this account, the hexagon is not sufficiently familiar to achieve equally fast and effortless completion. Familiarity effects in occlusion would suggest that completion is influenced by other factors besides stimulus properties. Local or global stimulus properties as well as familiarity could, in principle, be the reason why some completion processes take noticeable time. Because the circle and the hexagon differ in stimulus properties as well as in familiarity the present experiment does not enable us to test between the two alternative hypotheses. Experiment 2 will address this by varying stimulus properties and familiarity independently. 3. Experiment 2 In Experiment 2 the critical search targets were ambiguously occluded figures. These are partly occluded figures that have two distinct, predominant, alternative completions. Both are believed to be generated by the visual system spontaneously and in parallel for such figures (van Lier, 2001; van Lier et al., 1995). With ambiguous occlusion the same

18 Plomp et al. Occlusion and Fixation Page 18 occluded figure can be a target for two different search targets. In that case differences in gaze duration over targets can only be attributed to differences in the completion process. In the ambiguously occluded figures of the present experiment, one interpretation is always based on the good continuation of lines at the point of occlusion (the local completion), the other on an optimization of the amount of symmetry axes (the global completion). This feature allows for testing whether local and global stimulus characteristics are responsible for different completion effects on gaze duration. Another aspect of these stimuli is that one of the alternative completions is more familiar than the other. This allows for testing the role of familiarity in completion as measured by gaze duration. In the present experiment the local-global and the familiarless familiar dimensions are independent factors. This makes it possible to test the globality against the familiarity explanation of the different effects of occlusion patterns on gaze duration in Experiment Method Participants Fourteen participants (5 males) with ages ranging from 20 to 29 took part in the experiment in return for a small payment. Half of them had previously participated in eye movement research and were familiar with the experimental procedure, but not with the stimuli. Informed consent was obtained.

19 Plomp et al. Occlusion and Fixation Page Apparatus This was identical to Experiment Stimuli and design The stimuli consisted of two figure classes of five figures each. These contained two composite figures and three simple figures. The composite figures were a mosaic pattern and an occlusion pattern. The occlusion patterns had two interpretations. For one figure class the local interpretation was the familiar one, for the other it was the global one. The simple figures consisted of the two interpretations of the occluded figure and a truncated figure. All stimuli of Experiment 2 are displayed in Figure 5. We will refer to the two stimulus classes as arrow class and star class respectively. An independent survey showed that these two were preferred as the most familiar interpretation within their respective classes. In this survey the arrow interpretation was deemed more familiar in 85% of the cases and the star interpretation in all cases. The arrow is an interpretation based on local stimulus properties whereas the star interpretation is based on global properties. Accordingly the four possible completions constitute a 2 x 2 factorial scheme in which local-global and familiar-less familiar are independently varied. For the arrow class the occluded region of the occlusion pattern was approximately 36 % for the local completion and 52% for the global completion. For the star class it was approximately 32% for the local and 23% for the global completion

20 Plomp et al. Occlusion and Fixation Page 20 Figure 5 about here The simple local, global, and truncated figures were possible search targets. When one of them was the target, neither of the other simple figures from the same class occurred in the display. A display could contain between 1 and 5 targets. Displays were constructed in a similar way as in Experiment 1 by selecting one simple figure and two composite figures from each class. Crossing the three possible search targets of each class of stimuli resulted in nine different types of displays. Over these display types each simple figure occurred as a target with each possible simple non-target of the other class and vice versa. For each type of display a series of 28 displays was created in the same way as for Experiment 1. This resulted in (9 x 28 =) 252 unique experimental displays. An example display is provided in Figure Figure 6 about here Procedure The 252 displays were split over four sessions that were in turn divided over two days. A single session took about 45 minutes to complete and a refreshment break in which the headset was taken off was scheduled in between the sessions. The order of the four sessions was different for each participant and pseudo counterbalanced. The trial order was randomized at the start of each session. The experimental task was similar to Experiment 1. In case a local or global simple figure was the target, the corresponding occlusion pattern was considered a target as well,

21 Plomp et al. Occlusion and Fixation Page 21 but the mosaic pattern from the same class was a non-target. When the simple truncated figure was the target, the corresponding mosaic pattern was a target because it contained the mosaic figure, but the occlusion pattern was a non-target. On the first day two practice sessions of nine trials were completed before the experiment. The first was done without the headset and the second one with the headset mounted to practice the scanning order. On the second day the second practice was repeated Results The data from two participants were excluded from analysis, one because part of it was missing and the other because of drowsiness of the participant. The error rate in the overall experiment was 4.46%. Erroneous trials were not further analyzed. Fixations that fell outside of regions as well as re-fixations were removed from the data and constituted 7.6 percent of all fixations in the experiment. The cutoff value for fixations was set at 927 ms, 2 standard deviations above the mean for all fixations. From the fixation data, mean gaze durations for the different conditions were computed for each participant. As in Experiment 1, the composite non-targets of the same class were not included in this calculation to satisfy assumptions of independence for the analyses. This selection did not influence the results. Two analyses were performed on the fixation data. The first was similar to Experiment 1 and focused on the differences between the target and non-target conditions. The second analysis was performed on gaze durations within the target condition alone and took into account the ambiguity of the occlusion patterns.

22 Plomp et al. Occlusion and Fixation Page 22 In the first analysis, gaze durations were analyzed with a repeated-measures ANOVA with the factors Target (target, non-target), Figure Class (arrow, star) and Figure type (the five figure types of each class). Means and standard errors of this analysis are depicted in Figure 7. Reported p-values are Greenhouse-Geisser corrected where appropriate. Targets received longer gaze durations than non-targets, F(1,11) = 96.54, p<0.01, MsErr = The effect of Figure type, F(4,44) = 42.23, p<0.01, MsErr = 1224, showed that composite figures received longer gaze durations than the simple figures. Figure type interacted with both Target, F(4,44) = 8.76, p<0.01, MsErr = 1536, and Figure class, F(4,44) = 8.78, p<0.01, MsErr = 796. The first interaction can be understood from the long gaze durations on the occlusion patterns in the target condition while for non-targets these were shorter and differed less from the other figures. The interaction of Figure type and Figure class showed the pattern of gazes over the five figure types to be different for the two figure classes. The simple figures of the star class differed more consistently among each other than those of the arrow class Figure 7 about here The second analysis concerned only the effects within the target condition and considered separately the gazes on the occluded figure when it was a local and when it was a global target. A repeated measures ANOVA with the factors Figure class (arrow, star), Complexity (simple, composite) and Category (local, global, truncated) was done on the mean gaze durations. The means and standard errors for this analysis are shown in Figure 8. The reported p-values of this analysis are Greenhouse-Geisser corrected.

23 Plomp et al. Occlusion and Fixation Page 23 Composite figures received longer gaze durations than simple figures, F(1,11) = 35.48, p < 0.001, MsErr = In addition, Complexity interacted significantly with Category, F(2,22) = 9.32, p < 0.01, MsErr = In this interaction, the longest gazes for simple figures fell on the truncated figures, whereas for composite figures the occlusion patterns got the longest gazes Figure 8 about here Figure class interacted with Category, F(2,22) = 9.94, p = 0.001, MsErr = This effect was due to the local interpretation yielding longer gazes than global ones for the star class, while the reverse was true for the arrow class. This resulted mostly from the long gazes on composite figures, as was indicated by the a three-way interaction between Figure class, Complexity and Category, F(2,22) = 4.57, p = 0.031, MsErr = Discussion The higher error rate suggests that Experiment 2 was more difficult than Experiment 1. The proportion of re-fixations and fixations falling outside the designated areas were identical in both experiments, indicating no extra difficulty in following the prescribed scanning order. Composite figures received longer gaze durations than simple figures. As in the previous experiment, this was the case for targets as well as non-targets and can be attributed to stimulus complexity. Also like in Experiment 1, gaze durations were longer for targets than for non-targets.

24 Plomp et al. Occlusion and Fixation Page 24 Occluded targets received longer gaze durations than mosaic pattern targets and there was no such effect for non-targets. This result reflects the aspects of completion that happen after target selection, like in Experiment 1. In addition, the alternative completions of the occlusion patterns were not made with equal ease. The occlusion pattern of the star class received the longest gazes for its local completion, whereas for the arrow class gazes were longest for the global completion. The occlusion effects corresponded systematically to the less familiar completions of the patterns irrespective of whether they were local or global; the gaze durations for the familiar completions did not differ from those of the mosaic patterns. 4. General Discussion In two experiments, we made a first attempt to use gaze durations in the study of amodal completion. The task aimed at inducing a completed representation of a partly occluded figure. We asked participants to count targets with the caveat that they could be partly hidden by other figures. Truncated non-targets were present in the search displays as a further manipulation to induce a complete representation. Detecting a target behind an occluder is more likely to induce completion than, for instance, passive viewing of an occlusion pattern. We assumed that gaze durations would reflect the high-level perceptual processes in this task. Consistent results were obtained over the two experiments. Composite figures attracted longer gazes than simple figures, and this was true for targets as well as nontargets. This effect of visual complexity happened for both targets and non-targets. This suggests that complexity plays a role during target selection in visual search.

25 Plomp et al. Occlusion and Fixation Page 25 In both experiments gaze duration showed effects of occlusion. It must be noted that the shortest gazes fell on those interpretations with the largest occluded regions. This is in apparent contrast with the systematic increase in completion time with more occlusion (Guttman, et al., 2003; Shore and Enns, 1997). We may attribute this discrepancy to the small differences in the sizes of the occluded regions and the predominance of other factors in our experiment. No effects of occlusion occurred for non-targets, suggesting that effects of occlusion on gaze duration arise after target selection. Perceivers fixate long enough on non-targets to identify them as such and then saccade to the next figure. This might still allow some completion of occluded non-targets. Completion is unlikely to be an all-or-none event; it is possible, for instance that a form of functional filling-in (Rensink and Enns, 1998) has occurred prior to the initiation of the saccade to the next item. These processes, however, must have occurred in parallel with the ones that led to the initiation of the saccade, or must have been fast enough not to delay it. Occlusion effects occurred only for a subset of the targets. We consider four possible explanations, the first two of which are methodological in nature. One reason may be that the mosaic patterns were inadequate as control stimuli. The mosaic patterns may be considered more complex than the occlusion patterns. Given that gazes were sensitive to the complexity of the stimuli this may account for the absence of a completion effect for familiar figures. Even so, the fact that completion effects were found for some completions is all the more striking. The other reason may lie in the influence of peripheral preview. During the scanning of the first figures in a display some information of the later ones was extracted extra-foveally (Henderson, Pollatsek and Rayner, 1987).

26 Plomp et al. Occlusion and Fixation Page 26 We know that occlusion information is unavailable to the saccadic system (Vishwanath et. al, 2000) and it may therefore be unlikely that the whole completion process can happen peripherally. Information from outside the attended area may however have set expectations that enable fast completion in a subset of the targets. We hope to address both these issues more extensively in subsequent investigations. In Experiment 1, an occlusion effect was obtained for hexagons but not for circles. This result suggested two possible explanations. The first one is based on stimulus properties and proposes that the completion of the hexagon takes longer because it requires more global processing. An alternative explanation goes beyond stimulus properties. This explanation posits that the circle is more familiar than the hexagon and that familiarity facilitates the completion process. These two explanations were contrasted in Experiment 2. The results showed that local and global completions were both rapidly made when they were familiar completions but that less familiar ones took longer to complete. The same logic as with the non-targets may explain this result. It may be that the completion of a familiar occluded target happened fast and in parallel with its selection as a target; fast enough to make gaze durations indistinguishable from those on an unoccluded control pattern. The familiarity of the completed figure appeared to be the relevant factor for completion time. This effect is in accordance with the interpretation of gaze duration effects as generally reflecting the higher-order, semantic aspects of processing. In our case, this could involve the time needed to verify an unfamiliar, unlikely completion. In a sense, these processes constitute the figural analog of word frequency effects on gaze

27 Plomp et al. Occlusion and Fixation Page 27 duration in sentence comprehension tasks (Inhoff and Rayner, 1986; Rayner and Duffy, 1986). The fixation indices in our experiments reflected the visual processing of a figure, the counting of targets, as well as the time it takes to initiate a new saccade. These processes run at least partly in parallel in ways the present experiments were unable to reveal. For this reason, little can be said about the absolute time needed for completion to finish on the basis of our data. However, the differences we find in gaze durations between conditions may be considered of importance. Completion effects occurred for less familiar targets and this suggests that a distinction could be made within the process of amodal completion. A distinction between functional filling-in (fast) and full, actual completion has already been made. Perhaps, we may also distinguish between completions that are anticipated (fast) and ones that are not (slow). The results bear on the question of to what extent amodal completion is an automatic or a high-level process. Completion seems automatic to a great extent. Earlier research has shown that the early stage is fast and mandatory and can result in a functional fillingin. For some figures, the later stage of reaching a complete representation of the partially occluded figure, appear to be fast enough not to have a noticeable effect on gaze duration. Other completions, however, require more extensive processing. In our experiments the properties of the stimulus could not account for these differences. It seems that familiarity with a figure can ensure a quick and mandatory completion when it appears partly occluded. We can only speculate about the precise nature of the processes that lead to longer gaze durations for the unfamiliar figures. In the case of the hexagon, we suggested that

28 Plomp et al. Occlusion and Fixation Page 28 the occluded symmetry takes time to complete, but Experiment 2 suggests that familiarity is the relevant factor. In the case of ambiguous occlusions, the more familiar completion will quickly be obtained. Perhaps this interferes with the unfamiliar target completion. This would be consistent with the notion that more than one completion is generated by the visual system (van Lier et al., 1995). The idea of familiarity as a factor in amodal completion is not a novel one (Shimaya, 1997; Shore and Enns, 1997). The notion makes intuitive sense and familiarity can demonstrably influence completion (e.g. Palmer, 1999 p. 289). Our experiments confirm this idea. Assigning a role to familiarity in amodal completion is not to say that it is the sole determinant of it. That it is certainly not. The prevalence of other factors can sometimes give rise to very unfamiliar interpretations (Kanizsa and Gerbino, 1982; Gerbino and Zabaï, 2003). Our results are in line with an account of amodal completion that stresses its sensitivity to spatial-temporal context (Rauschenberger, Peterson, Mosca and Bruno, 2004). They furthermore corroborate that amodal completion is anything but a homogeneous category of processes that takes approximately the same time to finish. Several factors are playing their part in what is clearly a complex process. We suggest that familiarity with the stimuli is one factor that can enhance the speed at which an occluded figure is completed. The role of familiarity in amodal completion illustrates how our visual system interacts with the world. It performs better at what is already familiar, yet its capacities for filling in the occluded extend to less familiar situations. It only takes a little longer.

29 Plomp et al. Occlusion and Fixation Page 29 Acknowledments The authors wish to thank Nicola Bruno and two anonymous reviewers for their helpful comments on an earlier version of this manuscript. 5. References Bruno N, Bertamini M, Domini F, 1997 Amodal completion of partly occluded surfaces: is there a mosaic stage? Journal of Experimental Psychology: Human Perception and Performance Gerbino W, Zabai C, 2003 The joint Acta Psychologica Gerbino W, Salmaso D, 1987 The effect of amodal completion on visual matching Acta Psychologica Guttman S E, Sekuler A B, Kellman P J (2003). "Temporal variations in visual completion: a reflection of spatial limits?" Journal of Experimental Psychology: Human Perception and Performance Field D J, Hayes A, Hess R F, 1993 Contour integration by the human visual system: evidence for a local association field Vision Research He Z J, Nakayama K, 1992 Surfaces versus features in visual search Nature Henderson J M, 1993 Eye movement control during visual object processing: Effects of initial fixation position on semantic constraint Canadian Journal of Experimental Psychology

30 Plomp et al. Occlusion and Fixation Page 30 Henderson J M, Pollatsek A, Rayner K, 1987 Effects of Foveal Priming and Extrafoveal Preview on Object Identification Journal of Experimental Psychology: Human Perception and Performance Inhoff A W, Rayner K, 1986 Parafoveal word processing during eye fixations in reading: Effects of word frequency Perception and Psychophysics Joseph J S, Nakayama K, 1999 Amodal representation depends on the object seen before partial occlusion Vision Research Just A M, Carpenter P A, 1976 Eye Fixations and Cognitive Processes Cognitive Psychology Kanizsa G, Gerbino W, 1982 Amodal completion: Seeing or thinking? in Organisation and Representation in Perception ed J Beck (Hillsdale New Jersey: Lawrence Erlbaum Associates) Kellman P J, Shipley T F, 1991 "A Theory of Visual Interpolation in Object Perception" Cognitive Psychology Kovacs I, Julesz B, 1993 A closed curve is much more than an incomplete one: effect of closure in figure-ground segmentation Proceedings of the National Academy of Sciences of the United States of America Kowler E (Ed.), 1990 Eye movements and their role in visual and cognitive processes (Amsterdam NL: North Holland/Elsevier) Liversedge S P, Findlay J M, 2000 Saccadic eye movements and cognition Trends in Cognitive Sciences

31 Plomp et al. Occlusion and Fixation Page 31 Michotte A, Thinès G, Crabbé G, 1964 Les Complements Amodaux des Structures Perceptives Studia Psychologica (Institute de Psychologie de l Université de Louvain) Murray R F, Sekuler A B, Bennet P J, 2001 Time course of amodal completion revealed by a shape discrimination task Psychonomic Bulletin & Review Nakatani C, Pollatsek A, in press An Eye movement Analysis of "Mental Rotation" of Simple Scenes Perception and Psychophysics Palmer S E, 1999 Vision science: photons to phenomenology, MIT Press, Cambridge, MA Pessoa L, Thompson E, Noë A, 1998 Finding out about filling-in: A guide to perceptual completion for visual science and the philosophy of perception Behavioral and Brain Sciences Rauschenberger R, Peterson M A, Mosca F, Bruno N, 2004 Amodal completion in visual search: Preemption or context effects? Psychological Science In Press. Rauschenberger R, Yantis S, 2001 Masking unveils pre-amodal completion representation in visual search Nature Rayner K, 1998 Eye movements in reading and information processing: 20 years of research Psychological Bulletin Rayner K, Duffy S A, 1986 Lexical complexity and fixation times in reading: Effects of word frequency, verb complexity, and lexical ambiguity Memory and Cognition Rensink R A, Enns J T, 1998 Early completion of occluded objects Vision Research

32 Plomp et al. Occlusion and Fixation Page 32 Sanders A F, van Duren L L (1998) Stimulus control of visual fixation duration in a single saccade paradigm Acta Psychologica Sekuler A B, Palmer S E, 1992 Perception of Partly Occluded Objects: A Microgenetic Analysis Journal of Experimental Psychology: General Sekuler A B, Palmer S E, Flynn C, 1994 Local and global processes in visual completion Psychological Science Shore D I, Enns J T, 1997 Shape completion time depends on the size of the occluded region Journal of Experimental Psychology: Human Perception and Performance Shimaya A (1997) Perception of complex line drawings Journal of Experimental Psychology: Human Perception and Performance Stins, J, van Leeuwen C, 1993 Context influence on the perception of figures as conditional upon perceptual organization strategies Perception & Psychophysics Takeichi H, 1995 The effect of curvature on visual interpolation Perception Takeichi H, Nakazawa H, Murakami H, Shimojo S, 1995 The theory of the curvatureconstraint line for amodal completion Perception Tse P U, 1999 Volume Completion Cognitive Psychology van Lier R, 2001 Visuo-cognitive disambiguation of occluded shapes Behavioral and Brain Sciences van Lier R J Leeuwenberg E L J, van der Helm P A, 1995 Multiple Completions Primed by Occlusion Patterns Perception

33 Plomp et al. Occlusion and Fixation Page 33 Vishwanath D, Kowler E, Feldman J, 2000 Saccadic localization of occluded targets Vision Research Zemel R S, Behrmann M, Mozer M C, Bavelier D, 2002 Experience-Dependent Perceptual Grouping and Object-Based Attention Journal of Experimental Psychology: Human Perception and Performance

34 Plomp et al. Occlusion and Fixation Page Figures Figure 1. Local completion based on the good continuation of lines at the point of occlusion (A) and completion based on global properties of the figure (B). Figure A after Kanizsa and Gerbino (1982). Figure 2. The eight stimuli used in experiment 1. Circle figures are shown in the left panel, hexagon ones in the right panel. Stimuli were of two categories, whole figures (top row) or truncated figures (bottom row) and had two levels of complexity; simple figures (left hand side of each panel) and composite figures (right hand side of each panel).

35 Plomp et al. Occlusion and Fixation Page 35 Figure 3. Example of a search display used in Experiment 1. Figure 4. Mean gaze durations and standard errors for targets (left panel) and non-targets (right panel) for the two figure classes of Experiment 1.

36 Plomp et al. Occlusion and Fixation Page 36 Figure 5. The two classes of stimuli of experiment 2. The arrow class (derived from van Lier et al., 1995) is pictured in the right panel, the star class in the left panel. Each class features three simple figures: a local, global and a truncated one. In addition, each class contains two composite figures, an occlusion pattern and a mosaic pattern. Figure 6. Example of a search display used in Experiment 2.

37 Plomp et al. Occlusion and Fixation Page 37 Figure 7. Mean gaze durations and standard errors of Experiment 2. The bars reflect simple local (L), global (G), truncated (T) and the composite occlusion (O) and truncated (T) figures for both figure classes. Targets are depicted in the left panel, non-targets in the right one. Figure 8. Mean gaze durations and standard errors for the target condition of Experiment 2