Perception, 1978, volume 7, pages 575-581

Eye movements during the viewing of Necker cubes

Stephen R Ellis, Lawrence Stark Department of Physiological Optics, University of California, Berkeley, California 94720, USA Received 30 January 1978, in revised form 26 May 1978

Abstract. Eye movements were recorded while subjects viewed a Kopfermann-like series of Necker cubes and signaled perceptual reversals. At the instant of reversal, subjects tend to fixate the vicinity of the externally appearing corner. These fixations at the instant of reversal tend to have longer duration than those immediately before or after. The longer fixation times associated with perceptual reversal probably reflect the time required to construct the alternate three-dimensional interpretation of the cube. After construction of this new model, the subject then fixates the vicinity of the newly interpreted externally appearing corner. 1 Introduction A variety of objective studies of the spontaneous reversals of perspective of ambiguous figures have been conducted (Vicholkovska 1906; Kopfermann 1930; Washburn et al 1931; Carlson 1953; Cohen 1959; Orbach et al 1963a, 1963b; Orbach and Zucker 1964). Often a central question was whether idiosyncratic eye movements were a cause or an effect of the reversals (Sisson 1935; Boring 1942; Pheiffer et al 1956; Magnussen 1970). In general these studies have favored the latter but we believe the question may remain open because of the correlational nature of much of the evidence. Alternatively, the spatial and temporal pattern of the eye movements made during the viewing of the Necker cube (Necker 1832) may be analyzed to try to infer the information processing underlying the reversals. Since the spatial interpretation of the cube has been shown to be influenced by central cognitive factors (Bradley and Petry 1977) and since analysis of eye movements has recently been shown to be useful for the experimental analysis of scenic information processing (Monty and Senders 1976), the present study was conducted to use eye scanning data to investigate the underlying cognitive process used to generate the three-dimensional interpretation of the cube. The most complete study to date of eye movements made during viewing of the Necker cube was conducted by Glen (1940), who made detailed analyses of the temporal relationship between eye movements and estimated instants of perceptual reversal. However, probably owing to the awkward photographic form in which his data were collected, his results are basically frequency histograms of the occurrence of eye movement irrespective of the spatial positions and durations of the fixations. Despite older claims that direction of gaze does not always indicate the locus of visual attention (Llewellyn-Thomas 1968; Kaufman and Richards 1969), fixation position and duration have been successfully used by Carpenter and Just (1976) and Abrams and Zuber (1972) to identify periods during the viewing of pictorial stimuli, in which the complexity of internal information processing increases (also see Tinker 1950). Accordingly, the present investigation was conducted to collect the spatial and temporal information absent from Glen's report by analyzing the loci and duration of fixations during perceived reversals of the cubes. As in the above studies, these data may provide clues to the time course and structure of the information processing during perceptual interpretation of the two-dimensional interpretations of the cube.

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2 Experimental Six subjects naive with respect to the purposes of the experiment, three experimental and three control, viewed a CRT-displayed, randomly ordered, Kopfermann-like (Kopfermann 1930) series of six two-dimensional cubes (see upper part of figure 3) while their horizontal and vertical eye movements were monitored by means of the infrared scleral reflectance technique (Stark and Sandberg 1961; Stark et al 1962). The subject's head movement was restrained by a headrest and bite bar and he was in a darkened room. The line width was 0-5 min with a green color and luminance of approximately 4-4 millilamberts against a background of 0-02 millilambert as measured with a SEI spot photometer at the 68 cm viewing distance. Total vertical and horizontal extent of the cube was 12 deg. Each subject was given about 2 min practice viewing the cubes and signalling the apparent reversals of orientation with a three-position toggle switch (ARCO Electric DPDT momentary contact). Leaving the switch in the middle 'off position signified for experimental subjects that no depth was seen in the figure while maintenance in either 'on' position signalled continued appearance of the cube in one of the two common three-dimensional orientations. The orientations were defined in terms of the appearance of the cube vertex locations A and B in the upper part of figure 3. During the experiment, each cube was presented for 25 s and the presentation was preceded and followed by 25 s calibration periods. Occasionally, a time-out was required to adjust the spectaclemounted eye monitor. The subject's switch signals and eye position data were recorded with 50 ms sample interval onto a disk by ONLINE6 system programs developed by Frederick Hsu, Christian Freska, and the authors for data acquisition and processing with the PDP-8/I computer systems at the University of California at Berkeley Optometry School. All subjects viewed twenty-five calibration dots presented sequentially, 1 s per dot, in a 5 x 5 , 1 2 deg x 12 deg square array that was presented before and after the viewing of each cube. The fixation positions recorded during these calibrations provided checks on the stationarity of the eye position signal as well as information for automatic gain adjustment, linearization, and removal of cross talk between the horizontal and vertical channels. Each of the control subjects was given similar practice but in their case the switch signals were in response to verbal commands. During their viewing of the cube, the schedule of these commands was chosen to correspond to the temporal pattern of reversals from a previously run experimental subject with whom the control was paired. This procedure dissociates the control subjects' experiences of perceptual reverses from their switch-signalling patterns while matching their temporal patterns of signalling to those of the experimental subjects. Furthermore, this procedure controls for the effects of operations of the switch. After data collection and computer processing to adjust gain, linearize, and remove cross talk, the eye position data were analyzed into a sequence of fixations by a method derived from Anliker's (1976) position-variance methods with a sliding time window of 200 ms. A listing of the spatial and temporal parameters of the sequence of fixations with respect to the onset and offset times of switch signals was prepared in conjunction with a plot of the fixation positions. These data were used to determine the fixation position at the instant during which each cube was perceived to organize into a particular orientation. These fixations will be called organization fixations. Human factors literature suggests that the reaction time of a switch response with a toggle switch used in such an essentially two-choice situation is approximately 400 ms (McCormick 1976). In preliminary pilot experiments this value was assumed as the subjects' reaction time in order to identify the organization fixation associated

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Eye movements during the viewing of Necker cubes

with each reversal of a cube. It was discovered that considerable leeway existed for this assumption since estimated reaction times between 325 and 475 ms identified the same fixation about 90% of the time. Thus, further subject-specific reactiontime experiments seemed unnecessary, especially since in the case of Necker cube reversal it is not clear what the correct experiment is. Glen (1940) attempted to determine this type of reaction time by timing subjects' responses to briefly lit threedimensional cubes actually in different orientations. But it is not clear how this situation compares to the signalling of illusory shifts in position since other factors such as accommodation, vergence, and possible differences in information processing probably affect the result. In any case, Glen's overall average reaction time of 490 ms compares well with our estimate since the other factors would be likely to introduce delays, increasing his estimate. 3 Results Reversals of the cube occurred at intervals of from 3 to 5 s, coming more frequently when the subjects viewed cubes in the middle of the Kopfermann series. Figure 1 shows the mean fixation durations for the organization fixation and temporally flanking fixations for experimental and control subjects collapsed across type of cube. All three experimental subjects show a clearly marked increase in fixation duration at the instant of the cube's reversal. Separate one-way analyses of variance on each of these subjects confirm the impression of longer organization fixations (GDF—F4jl28 = S-31; p < 0-001; SRE— ^4,193 = 6-96; p< 0-001; RLR—F4>124 = 4 - 8 1 ; p < 0 - 0 1 ) . Similar analyses on the comparable control subjects do not show statistically reliable deviations (TAB— ^4,130 = 0-94; p> 0-05; KTJ—F4,195 = 1 -72; p > 0-05; HIJ—F 4jl29 = 2-18; p > 0-05). The difference between the experimental and the control subjects is also seen in a ratio between the duration of the organization fixation and the average of the temporally flanking fixations shown in figure 1. The values of this ratio for the experimental subjects (2-05, 1 -66, 1 -55) are significantly larger than the corresponding ratios for the arbitrary organization fixations of the control group (1 -34, 1 -34, 1 -28; t4 = 2 -85; p < 0-05). Thus, the two groups' values do not overlap and the longer fixation durations can not be attributed to manual operation of the switch.

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Figure 1. The mean fixation duration is plotted centered at the organization fixation (OF) for each experimental subject and at the arbitrary organization fixation (AOF) for each control subject. The mean duration for the two antecedent and subsequent fixations temporallyflankingthe organization fixations are shown. Error bars represent ± one standard error.

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Figure 2 shows two illustrative plots of the sequence of fixations during the experimental condition while subjects were viewing two different cubes. The organization fixations are circled. Though the organization fixations for each of the alternative spatial orientations seem separated from each other along the long axis of the projected cube's outline, they do not seem as precisely associated with the vertices of the ambiguous internal and external corners as might have been suspected from Necker's original report. The Kopfermann-like series used as stimuli are shown in figure 3, which also shows an illustrative summary of the location of organization fixations for an experimental and a paired control subject for the entire series of cubes. The distribution of fixations for the experimental subject (figure 3, left) shows our experimental finding that the organization fixations for the different orientations of the cube are separated into two groups along the long axis of the projected cube. In free viewing, the observer's direction of gaze is attracted to those extended areas of the cube interpreted as external corners. It is, however, clear that these fixations do not cluster tightly around the vertices of the ambiguous internal/external corners for, if they did, the fixations should arrange themselves in numerical order reflecting the shift of these ambiguous corners in the series of cubes used (see upper part of figure 3). The subject's scanning behavior may be described as shifting back and forth between the temporally changing external-appearing corners. The simple alternate scanning along the main diagonal of the cube precludes use of the scanning information to make a detailed analysis of the constructive process used to determine the three-dimensional interpretation of the cube. The longer fixations associated with reversals, however, imply an increase of internal information processing at the instant of reversal, presumably the instant at which each particular three-dimensional interpretation is constructed. Since this construction occurs when an ambiguous internal/external corner is fixated, one may surmise that the construction operations depend upon the spatial interpretation of this 'Y'-shaped feature. One possibility is that the spatial interpretation of this ambiguous feature is first assigned

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Figure 2. Computer-plotted eye movement sequences illustrating the order of fixations subjects make while reporting spontaneous reversals are shown for a subject's scans on two different cubes. The four different-size numbers indicating the fixation positions also indicate the duration of each fixation. They represent, in proportion to their size, fixations of four different categories: 750 ms. The open circles mark organization fixations corresponding to perceptual shifting of the upper-right ambiguous corner from external to internal. The divided circles indicate the same shift, for the lower-left ambiguous corner.

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and propagated so that the spatial interpretations of the other elements of the cube are made to be consistent with this initial decision. The longer organization fixations are consistent with the report of Orbach et al (1963a) that viewing Necker cubes illuminated by flickering light can interfere with reversals of the cubes provided short periods of illumination are interspersed with relatively longer dark periods, producing an asymmetric duty cycle such as 200 ms1200 ms. The brief on-period presumably does not allow time for the interpretive processes to proceed to reversal while the relatively long off-period prevents up-dating of the process. This uninterrupted time postulated by Orbach et al (1963a, 1963b) as necessary for reversal is probably provided by the relatively longer organization fixations we have experimentally found. Indeed, forced scanning back and forth between the ambiguous corners also interferes with, but does not prevent, the occurrence of perceptual reversals (Glen 1940). Conversely, movement of the cube itself, which can interfere with longer fixations, also has been shown to reduce the reversal rate (Orbach and Zucker 1964). In fact, we have further observed that rapid, directed scanning of a randomly moving marker on a two-dimensional projection of a large cube subtending at least 20 deg can interfere with the perception of any threedimensional shape.

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Eye movements during the viewing of Necker cubes.

Perception, 1978, volume 7, pages 575-581 Eye movements during the viewing of Necker cubes Stephen R Ellis, Lawrence Stark Department of Physiologic...
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