Journal of Vision (2010) 10(1):11, 1–13 http://journalofvision.org/10/1/11/ 1

The Müller-Lyer illusion: Investigation of a center of gravity effect on the amplitudes of

Institute of Physiology, Christian-Albrechts-Universität, R. Gilster Kiel, Germany

Institute of Physiology, Christian-Albrechts-Universität, J. P. Kuhtz-Buschbeck Kiel, Germany

Previous research has compared the effects of visual illusions on perception with their effects on action to investigate if the action system and the perceptual system use different or common codes. Appropriate conclusions based on this comparison rely on effects that reflect the internal parameter estimates of the action and of the perceptual system. We investigated an additional factor that can possibly change the amplitudes of saccades along the Müller-Lyer illusion, the center of gravity effect. It refers to the finding that the endpoints of saccades can be diverted from the target point in the direction of the center of gravity of a stimulus configuration. We measured the perceptual (adjustment method) and the action effects (amplitudes of saccades) of the illusion. In addition, we let subjects carry out saccades along Müller-Lyer figures and a neutral figure that appeared to have the same size (but differed in actual sizes). The amplitudes of saccades differed for these figures. This was interpreted as evidence for a center of gravity effect. Its quantification allowed a correction of the action effect, which was then remarkably similar to the perceptual effect. Our results are in agreement with the notion of a common internal representation for perception and action. Keywords: Müller-Lyer, illusion, perception, action, separate coding, common coding, dorsal stream, ventral stream, center of gravity Citation: Gilster, R., & Kuhtz-Buschbeck, J. P. (2010). The Müller-Lyer illusion: Investigation of a center of gravity effect on the amplitudes of saccades. Journal of Vision, 10(1):11, 1–13, http://journalofvision.org/10/1/11/, doi:10.1167/10.1.11.

Obviously, appropriate conclusions are only valid if the Introduction effects of visual illusions on perception and action reflect the internal parameter estimates (of e.g. size, form, weight Center of gravity effect (COGE) etc.) used by the perceptual and the motor systems. If other factors increase or decrease the perception and/or action effect, fair comparisons cannot be made, unless The internal codes of the perceptual system and the these factors are controlled or corrected for. Gilster, action system are of considerable interest for current Kuhtz-Buschbeck, Wiesner, and Ferstl (2006) investigated research in psychology and neuroscience. The separate the maximum grip aperture (MGA) when the central disc coding approach (Milner & Goodale, 1995)isbasedon of an Ebbinghaus illusion was grasped. By measuring the the assumption that visually guided movements and MGAs for the illusory conditions (small and large flankers rely on different processes that can be surrounded the central disc that was grasped) and for a tied to the so-called dorsal and ventral stream. The neutral condition as well (no surrounding flankers), it was common coding approach (Franz, Fahle, Bu¨lthoff, & shown that the MGA was largest for the neutral condition, Gegenfurtner, 2001) assumes that a common internal although the perceived size lay in between the illusory representation for perception and visuomotor control conditions. It seems that the action system treated the exists. The effect of visual illusions on perception has flankers as obstacles despite the fact that they were two- been compared with their effect on action. Differences dimensional. This unspecific reduction effect decreases between these effects have been interpreted as evidence in the difference in the MGA between the illusory conditions, favor of the separate coding approach (Aglioti, DeSouza, i.e. the action effect was reduced. Hence, it is questionable &Goodale,1995;Dewar&Carey,2006;Ganel,Tanzer,& if a fair comparison between perception and action can be Goodale, 2008; Haffenden & Goodale, 1998; Westwood, accomplished for the Ebbinghaus illusion. Heath, & Roy, 2000) whereas similar effects support the Another unspecific effect, namely the center of gravity common coding model (de Grave, Biegstraaten, Smeets, & effect (COGE), could affect eye movements that occur Brenner, 2005; Franz, Gegenfurtner, Bu¨lthoff, & Fahle, during the inspection of visual illusions. According to 2000; Franz et al., 2001; Pavani, Boscagli, Benvenuti, Findlay (1982), the COGE can be “loosely described by Rabuffetti, & Farne`, 1999). saying [that] the is directed to the center of gravity

doi: 10.1167/10.1.11 Received April 20, 2009; published January 21, 2010 ISSN 1534-7362 * ARVO

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Two previous studies used the Brentano version of the Mu¨ller-Lyer illusion (Figure 1b) to investigate possible influences of a COGE. McCarley, Kramer, and DiGirolamo (2003) analyzed the amplitudes of saccades according to a median split for movement latency, since COGEs are known to be larger for short-latency saccades in compar- ison to long-latency saccades (Coe¨ffe´ & O’Regan, 1987; Ottes, van Gisbergen, & Eggermont, 1985). However, an effect of the movement latency could not be found. Interestingly, they found larger amplitudes for wings-out figures in comparison to wings-in figures despite the fact that the perceived sizes were equal (i.e. their actual sizes were different). The authors suggested that this difference might be due to an imperfect adjustment of shaft lengths because it had been carried out in a pre-test by two sub- jects only. Yet, it seems also plausible that the difference might be due to a COGE, since it is in accordance with the Figure 1. a) The Müller-Lyer illusion and a neutral figure. In the expectations for such an effect. standard version of the Müller-Lyer illusion, the shaft (horizontal de Grave, Smeets et al. (2006) used vertically oriented line) of the wings-out figure (top) appears to be larger than the Brentano figures (Figure 1b) and let subjects carry out shaft of the wings-in figure (middle), although their actual sizes saccades towards the middle vertex of the shaft. The eye are the same. The perceived size of a so-called neutral figure movements started from the top or bottom vertex of the (bottom) lies somewhere between the illusory figures. The green Brentano illusion (i.e. vertical saccades, along the shaft) dots mark the starting points of saccades. The target point of the and from outside the figure (i.e. horizontal saccades, saccade is the right vertex. According to the assumptions about perpendicular to the shaft). The deviation of saccade the COGE, the endpoints of the saccades may be pulled towards endpoints from the middle vertex was measured for both the COG of the respective figure (red dots). The COG is assumed the vertical and horizontal saccades. For the vertical to lie in the center of the arrowhead. b) The Brentano version of saccades, the authors found effects that were similar to the Müller-Lyer illusion. The COG (red dot) is shown for the region the perceptual judgements, whereas the horizontal of the middle vertex. The green dots mark the starting points of saccades did not deviate in a vertical direction. This saccades towards the middle vertex (blue dot) in the study of de absence of a vertical error of the horizontal saccades was Grave, Smeets, and Brenner (2006). interpreted as evidence against a COGE. However, this interpretation is only valid if it is assumed that the influence of the COG on the amplitudes (i.e. increase or [COG] of the stimulus configuration” (p. 1033). Hence the decrease of the amplitude) of saccades is directly com- COGE is not specific for visual illusions, but will exert its parable to the influence on the direction of saccades (i.e. influence in any configuration where the target of a saccade deviation of the saccade from the principal direction that is surrounded by distracting nontargets (He & Kowler, connects the starting point and the target point). Clearly, 1989). Such an unspecific influence will also distort the their results ruled out the possibility that the COG action effect of visual illusions on saccades, because it affects the direction of saccades in the Brentano illusion. does not reflect the size estimation that is used by the Yet, a small or nonexistent influence on direction does motor system to plan the movement. Figure 1 illustrates not necessarily rule out the possibility that the ampli- the situation for the Mu¨ller-Lyer illusion and a neutral tudes of saccades are influenced by the COG. After all, figure. Saccades start from one end of the shaft (green the amplitude and the direction of the saccade differ with dots) and are directed towards its other end. If a COGE respect to the contributions of the involved eye muscles. exists, these saccades will be diverted in the direction of A change in amplitude indicates a change of contrac- the COG (Findlay, 1982), which is assumed to lie in the tions of the same eye muscles, whereas a deviation in center of the arrowheads (Figure 1a; red dots). This direction indicates a change of the muscular activation location of the COG is in line with the related study of de pattern. Grave, Smeets, and Brenner (2006),whousedthe In our view, it remains an open question if the absence Brentano version of the illusion (Figure 1b). If a COGE of a COGE on direction rules out a possible influence on exists for the Mu¨ller-Lyer illusion, the saccades along the the amplitudes of saccades. To this end, we conducted shaft of the wings-out figure will therefore be larger than perceptual and action measures using the Mu¨ller-Lyer the saccades along the wings-in figure, because their illusion. In Experiment 1 (Perceptual adjustments) we endpoints are pulled towards the center of the arrowheads. measured the perceptual effect and obtained sizes for In the present study, we aim to find evidence for such a perceptually adjusted figures (i.e. the actual sizes of the COGE and to quantify its influence. Mu¨ller-Lyer figures and the neutral figure were adjusted,

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so that the perceived sizes became equal). In Experiment 2 (Saccades) we let subjects carry out saccades along the Mu¨ller-Lyer figures and along the neutral figure. By using the same actual sizes for these figures, we calculated the action effect and compared it with the perceptual effect. In addition, we also investigated saccades along the percep- tually adjusted figures, which had been obtained in Experiment 1. If the amplitudes of saccades do not differ between perceptually adjusted illusory and neutral figures, then this would speak against the COGE. If however, the amplitudes of saccades for perceptually adjusted illusory figures deviate from the neutral figure, then this would be evidence for the COGE. The quantification of such an effect can ensure that comparisons between perceptual and action effects are conducted under fair circumstances.

Experiment 1: Perceptual Figure 2. Illustration of the adjustment task. One match figure and one target figure were presented in each trial. Nine different adjustments adjustments (each repeated eight times) for each target size (4 cm and 6 cm) were carried out by the subjects. The type of “ ” The aim of Experiment 1 was to determine the size of comparison is indicated on the right. The comparisons with * are the perceptual effect and to obtain sizes for perceptually used for the computation of the perceptual effects (see also Figure 3). fi @ adjusted figures (different actual sizes that appear to be of SCA = same con guration adjustment; = adjusted to. the same size) that are used in Experiment 2 in order to investigate the COGE. to the indirect comparisons. They argued that motor tasks We used the adjustment task (Franz, 2003; Franz et al., are much more comparable to the indirect comparisons 2000) for the perceptual measures. The subject actively because only one illusory figure is attended to during these varies figure sizes in order to make the figures equivalent tasks. in perceived size (by changing figure sizes on a computer Note that we also investigated adjustments where the screen). Subjects were presented with two figures and MF and the TF had the same configuration (same con- were asked to perceptually adjust the size of one of the figuration adjustment = SCA). We did this for two figures (the match figure = MF) to the size of the second reasons: First, comparisons between perceptual and action figure (the target figure = TF). The configurations used for effects are only appropriate if the slopes of the functions both the MF and the TF were the wings-out, the wings-in, that relate the actual size of the object with the size of the and the neutral figure. Essentially, this resulted in nine perceptual and the motor measures are the same (Franz, different adjustments for each size of the target figure 2003; Franz et al., 2000). If the slopes differ, one can (4 cm and 6 cm, Figure 2). divide the perceptual and action effects by the slope that From these adjustments, the perceptual effect can be characterizes the respective method of measurement and obtained in two ways (Franz et al., 2000) depending of the thereby correct for these differences. Depending on the type of comparison (indicated on the right in Figure 2). In comparison under consideration, the SCA can be used to the direct comparison, subjects adjust one illusory config- determine the slope in order to correct the perceptual uration (e.g. the wings-in figure) to the other nonidentical effect (see Figure 3 in the Results section). Second, the illusory configuration (e.g. the wings-out figure). In the SCA is needed to correct for possible “offsets” of the indirect comparison, the neutral figure is adjusted to each adjustments. This is important for the direct comparisons of the illusory figures. Both comparisons can also be carried because offsets inherent in a comparison are not accounted out in the reversed direction (reversed direct and indirect for (Figure 3a). In contrast, possible offsets in the indirect comparisons in Figure 2). The perceptual effects were comparisons are counterbalanced and thus corrected computed only for the direct and indirect comparisons indirectly (Figure 3b). (marked with asterisks in Figure 2). For methodical details on how the effects are computed, see Figure 3 and the descriptionintheResults section. Former research Method indicates that the perceptual effects obtained by direct and indirect comparisons may differ. Franz et al. (2000) Subjects used the Ebbinghaus illusion and measured larger Subjects were nine adults from the University of Kiel. perceptual effects for the direct comparison in contrast Because of technical problems in Experiment 2, one of the

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subjects was excluded from the analysis. From the remaining for the direct and indirect comparison (see the Appendix A eight subjects, six were naive to the purpose of the experi- for a tabular account of results). In principle, the analysis ment and were recruited from the Department of Psychology. is the same for the two comparisons. First, the size of the They participated in order to earn credit points as part of a MF (which is perceptually adjusted to the TF) for the study fulfillment. Two of the subjects were the authors. All comparison under consideration is plotted against the size subjects had normal or corrected to normal vision. of the TF (e.g. the adjustment of the wings-in figure to the wings-out figure in the direct comparison, see Figure 3a). Apparatus Second, the appropriate SCA (same configuration adjust- ment) for the figure that serves as a target is plotted in Stimuli were presented on a computer screen (17W, 1024 order to determine the slope (d/p) for correction purposes 768 pixels, 85 Hz). The viewing distance of 55 cm was and to detect possible offsets of the adjustments. D fixed. Adjustments of the match figure were made using (respectively d1 and d2 in the indirect comparison) is the “+” and the “j” keys on a keyboard. One press on defined as the difference between the comparison under either key resulted in an increase or decrease of 1 mm. consideration and the SCA at the average size of the TF. The adjustment was accepted by pressing the “*” key. Following Bruno and Franz (2009), the perceptual effect is then determined as: Stimuli The stimuli consisted of two figures (match figure (MF)  and target figure (TF)) presented side by side. The shafts % ¼ d 100 were oriented horizontally with their midpoints placed six slope average size of TF centimeters to the right (respectively to the left) emanat- p ing from the center of the screen. The size of the TF was ¼ 100: ð1Þ either 4 cm or 6 cm. The size of the MF at the beginning average size of TF of a trial was chosen randomly between 2 cm and 9 cm. The colors of the figures were red for the TF and green for the MF for four subjects and vice versa for the remaining The slopes for the two SCAs are close to 1.0, meaning subjects. The background color was gray. The wings for that there is almost no difference between d and p the illusory figure configurations were angled at 30- for (respectively between d1 +d2 and p1 +p2 in the indirect - comparison). However, we found a slight offset of 0.11 T the wings-in figure and 150 for the wings-out figure rela- T tive to the shaft. The angle for the neutral figure was 90-. 0.02 cm (mean SEM) for the SCA of the wings-out figure [t(7) = 4.92, P = 0.002, two-tailed, Figure 3a]. The The length of the wings was one third of the length of the T shaft. The thickness of the shafts was 1 mm. offset (0.07 0.03 cm) of the SCA for the wings-in figure (Figure 3b bottom) was marginally significant [t(7) = Procedure 2.30, P = 0.055, two-tailed]. Note that without the SCA, the difference d in the direct comparison (Figure 3a) Each subject performed two blocks of 72 adjustments would be computed as the difference between the (nine match figures two target sizes eight repetitions) matched size of the wings-in figure and the dashed line, in random order (Figure 2). For each condition, the TF resulting in an overestimation of d and p and thus in turn was presented four times on the right side and four times to a larger perceptual effect. For the indirect comparison on the left side. In total, the eight subjects carried out (Figure 3b), offsets are compensated for indirectly because 1152 adjustments. In each trial, a TF and a MF were over- and underestimations are counterbalanced. Also presented. Subjects were instructed to adjust the MF to the note that we used only the conditions marked with an TF (indicated by the color of the figures) until the lengths asterisk in Figure 2 for the computation of the direct and of the two shafts appeared to be equal. The adjustment indirect comparison. The conditions that were left out was carried out using the keyboard. By pressing the “*” represent the “reversed direct and indirect comparisons”. key, the subject confirmed the adjustment. The next trial Since the perceptual effects of these reversed compar- started immediately after. No time limit was given for the isons were quite similar to the effects computed here, we adjustments. Trials were excluded from further analysis if decided to omit the presentation of these effects. Never- the adjustments exceeded T three standard deviations of theless, all adjustments shown in Figure 2 are used in the respective condition. This resulted in a loss of 0.8% of Experiment 2. all trials. T-tests were used in order to compare the perceptual effects (Figure 4). Remember that Franz et al. (2000) found that the perceptual effect for the direct comparison Results was larger than the effect for the indirect comparison. However, we found no evidence for an enhanced Results of Experiment 1 are shown in Figure 3. The perceptual effect for the direct comparison [t(7) = figure illustrates how the perceptual effects are determined j0.57, P = 0.59].

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Figure 3. Perceptual effects obtained with the direct (a) and indirect (b) comparison (see Figure 2).

Discussion Mu¨ller-Lyer illusion. Hence, the present result shows that direct comparisons do not always yield larger perceptual In Experiment 1, we measured perceptual effects and effects than indirect comparisons. obtained sizes for perceptually adjusted figures that are used in Experiment 2. The perceptual effects were obtained with the direct and the indirect comparisons. Experiment 2: Saccades We found no evidence for differences between the sizes of the perceptual effects determined with these methods. This result is in contrast to the findings of Franz et al. The aim of Experiment 2 was to investigate the center (2000), who investigated the Ebbinghaus illusion. In of gravity effect (COGE) with respect to amplitudes of their study, the direct method yielded a perceptual effect saccades. Since the conclusions about the internal format that was 50% larger than the indirect method. It was argued of the action and perceptual system (separate coding vs. (see also Franz & Gegenfurtner, 2008) that this difference common coding) rely on fair comparisons of perceptual between the perceptual effects is caused by an interaction and action effects (i.e. the effects should be due to the of the surrounding circles in the direct comparisons. internal size estimate in the action and perception system), Evidently, such an enhancing effect is not present in the possible factors that change these effects, like the COGE,

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Apparatus Stimuli were presented on the same monitor as in Experiment 1. Eye movements were recorded with an eye tracker (iView X Hi-Speed, SMI Berlin) with a temporal resolution of 240 Hz and a spatial resolution of 0.25-.If an exceeded the velocity of 75-/s and if the single peak velocity was reached in the range of 20% to 80% of the distance between start point and endpoint, it was classified as a saccade. The distance from the eye to the midpoint of the screen was 55 cm (as in Experiment 1). A chin rest was used to control for the viewing distance.

Stimuli The MFs were presented horizontally with their left end Figure 4. Perceptual effects (Experiment 1, blue bars) and action or their right end of the shaft placed on the center of the effects (see Experiment 2, red bars). Error bars depict T SEM screen. The sizes of the MFs corresponded to the adjusted (contains between-subject variability). AE = Action effect; AEno- sizes in Experiment 1. In cases where the MF config- COGE = Action effect without the center of gravity effect. uration (the SCA figure) was identical to the correspond- ing TF, the size of the SCA figure was either 4 cm or need to be controlled for (de Grave, Smeets et al., 2006). 6 cm. The color of the MF was either red or green Therefore, we let subjects carry out saccades along the (according to the color in Experiment 1 for the subject). Mu¨ller-Lyer figures and a neutral figure, which were of The background color was gray. Stimuli were otherwise the same actual sizes. We calculated the action effect (AE) identical to Experiment 1. and compared it with the perceptual effect (Experiment 1). In addition, saccades were carried out along perceptually Procedure adjusted figures. If the saccades are scaled according to Each subject performed three blocks of 72 saccades the perceived equal sizes of the figures, they will always have about the same amplitude. If however, the ampli- (nine MFs two TF sizes twelve repetitions) in tudes of saccades differ for perceptually adjusted figures random order. For each condition, the MF was presented in the direction of the center of gravity (e.g. larger six times on the left (i.e. the right end of the shaft was amplitudes for wings-out figures in comparison to wings- positioned in the center of the screen) and six times on the in figures), then this would indeed indicate the existence right. In total, the eight subjects performed 1728 saccades. of a COGE. Each trial started with the presentation of a fixation cross In Experiment 2 we will again use the terms target in the center of the screen. After three seconds, the cross figure (TF) and match(ed) figure (MF). They refer to the disappeared and a MF was presented for two seconds, conditions in Experiment 1. MFs are size adjusted figures, resulting in the fixation of the right end or the left end of whose adjustments have been carried out to TFs with fixed the horizontal shaft. Subjects were instructed to carry out sizes (i.e. length of shaft) of either 4 cm or 6 cm (Figure 2). a saccade to the other end of the horizontal shaft right The three MFs that are of the same configuration as the after the appearance of the figure. A gray screen followed TFs (e.g. wings-out MF and wings-out TF) are called SCA for three seconds. The next trial started immediately after. figures. The shaft lengths of the SCA figures were always 4 cm or 6 cm. The aims of Experiment 2 can be achieved by letting Results subjects carry out saccades to the MFs (nine MFs two Data analysis TF sizes). By comparing the amplitudes of saccades for the SCA figures, the action effect can be computed. The We were interested in the amplitudes of the primary COGE is investigated by comparing the amplitudes of saccades. Secondary (corrective) saccades were not saccades for each “triplet” of MFs that belongs to a TF. analyzed. Several reasons could lead to the exclusion of a trial: The saccade was carried out too early (G50 ms after stimulus presentation), too late (91000 ms), or not at Method all. Furthermore, trials were discarded if the subject blinked during the execution of the movement or if the Subjects amplitudes deviated T 1 cm from the mean value of the The same eight subjects from Experiment 1 participated condition under consideration. Overall, this resulted in in Experiment 2. 84.3% valid trials. In order to compare the perceptual

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measures with the action measures, we calculated the “covered distances on the screen” (in cm) as the amplitudes of saccades. The action effects were computed analogous to the perceptual effects in Experiment 1, i.e. we took into account the neutral figure as well. Hitherto, only a few studies did this (Bernardis, Knox, & Bruno, 2005; de Grave, Franz, & Gegenfurtner, 2006; Knox & Bruno, 2007). In these studies, effects were computed using the formula [(difference between illusory figures)/ neutral] 100. In the study conducted by Bernardis et al. (2005), the comparison between the perceptual and the action effect based on this measure was justified by the fact that the authors found similar slopes for the verbal estimations (perceptual measure) and for the amplitudes of saccades (action effect). Hence, there was no need to correct for the slopes. In the other two studies, only action effects were obtained. If corrections have been carried out in other studies (due to different slopes for the perceptual and the action measures), the slope was calculated as the average of the slopes obtained from the illusory figures (Franz, 2003; Franz et al., 2000). This procedure impli- citly assumes that the slope for the neutral figure is equal to the mean of slopes for the illusory figures. By actually measuring the slope for the neutral figure, one should be able to see if this assumption is justified.

The action effect The action effect can be determined by comparing the amplitudes of saccades for the three configurations that are of the same actual size (i.e. for the SCA figures; Figure 5a). For illustrative purposes, results for the saccades that were carried out from right to left were mirror-reversed and collapsed on the saccades that were Figure 5. Mean amplitudes of saccades for the SCA figures. carried out from left to right. a) The figure shows the endpoints of saccades (saccades from The mean amplitudes of the saccades for the SCA right to left were mirror-reversed and collapsed on the saccades figures are plotted against their actual sizes (Figure 5b). that were carried out from left to right) for the three SCA figures Applying the formula of Bruno and Franz (2009), the that had the same actual size (average shaft length = 5 cm). The action effect is then calculated as: corresponding mean amplitudes of saccades are shown on the right (T SEM). The differences between the endpoints of saccades d1 þ d2 fi fi % ¼ 100 for the illusory gures to the neutral gure are denoted as d1 and slope average size of SCA figure d2. b) The action effect (AE). The mean amplitudes of saccades m þ m for the SCA figures are plotted against their actual sizes. The ¼ 1 2 100: average size of SCA figure action effect is computed according to Bruno and Franz (2009): Action effect = AE = [d1 + d2 / (slope average size of SCA ð2Þ figure)] 100 = [m1 + m2 / 5] 100 = 27.34 T 3.77%.

The action effect amounts to 27.34 T 3.77%. Note that the slope for the neutral figure is not justified [t(7) = 2.38, the slope for the neutral figure is different from the arith- P = 0.049, two-tailed]. Hence, by correcting the action metic mean of the slopes that characterize saccades along effect with the slope obtained from the neutral figure the two illusory figures. While the slope for the wings-out (which serves as a reference for the illusory figures), the figure was 1.16 T 0.03, the slope for the wings-in figure effect slightly increases. It should also be mentioned that amounted to 0.87 T 0.03, which was almost identical to the (primary) saccades along the neutral figure undershot the slope of the neutral figure (0.90 T 0.03). Thus, the the actual figure size, as can be appreciated in Figures 5a implicit assumption (Franz, 2003; Franz et al., 2000) that and 5b. Such undershoots are well known (Becker & the mean slope of the illusory figures (1.02 T 0.02) equals Fuchs, 1969; Troost, Weber, & Daroff, 1974) and cannot

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Figure 6. Mean amplitudes of the saccades along the MFs (shown on white background) in comparison with the mean actual sizes of these MFs (yellow background). For each TF (wings-out, wings-in, neutral) with the size of 4 cm or 6 cm, the saccades (saccade triplet, white background) and the actual sizes of the three corresponding MFs (adjusted sizes triplet, yellow background) are shown (see Tables A1 and A2). The saccades were carried out along the MFs that had the actual sizes shown in the yellow vertical bars. Note that although the sizes of the MFs in each adjusted sizes triplet were different, they were perceived to be of equal size (see Experiment 1). While the actual sizes show the largest values for the wings-in, medium values for the neutral, and smallest values for the wings-out figure in each adjusted sizes triplet, this sequence is reversed for the saccade triplets. This reversed sequence is evidence of the center of gravity effect (COGE). Dashed figures indicate saccades along the SCA figures (i.e. the actual sizes of these figures were either 4 cm or 6 cm, see also Figure 5). Error bars depict T SEM. MF = matched figure; TF = target figure.

be interpreted in terms of imprecise measures. In addition, triplet are largest for the wings-out figure, medium-sized secondary saccades (not shown here) that were carried out for the neutral figure, and smallest for the wings-in figure. by the subjects in order to compensate for deviations from This sequence is in accordance with the expected direction the endpoint of the shaft, confirmed this interpretation. for the COGE. In order to quantify this effect, we pooled the data shown in Figure 6 over the size and configuration of the TF and therefore reduced the six saccade triplets to The center of gravity effect (COGE) an average saccade triplet and the six adjusted sizes Figure 6 shows mean amplitudes of saccades in com- triplets to an average adjusted sizes triplet (Figure 7). The parison with the mean actual sizes of the MFs (matched figure shows the relation between the average saccade figures) for all tested conditions. The MFs are ordered triplet and the average adjusted sizes triplet. according to the TF (target figure) they belong to (either The endpoint of saccades for the neutral figure serves as 4 cm or 6 cm), resulting in six saccade triplets (white a reference point for the saccades carried out to the illusory background) and in six adjusted sizes triplets (yellow conditions. Remember that this figure is neutral (in a literal background). Note that the MFs in the adjusted sizes sense) because the COG is located on the end of the shaft triplets were of different actual sizes (i.e. shaft lengths (see Figure 1a). The undershoot of saccades for the neutral differed) but were perceived to be of equal size. The figure is typical (Becker & Fuchs, 1969; Troost et al., amplitudes of saccades along the MFs and the actual sizes 1974). Since the illusory figures and the neutral figure are of the MFs are listed in Table A1 and in Table A2. perceived to be of equal size, one would expect no dif- The center of gravity effect (COGE) can be investigated ferences for the endpoints of saccades from the reference by comparing the amplitudes of saccades for the saccade point (i.e. the green cross in Figure 7) if the COGE did not triplets. If the saccades are scaled to the perceived size exist. However, the saccades along the wings-out figure of the figures, which is equal, one would expect equal were larger compared to the neutral figure [t(7) = 2.82, P = amplitudes of the saccades in each triplet as well. However, 0.013, one-tailed] by about 5.0%. Also, the saccades for as can be gleaned from Figure 6, the amplitudes of the the wings-in figure were smaller than the neutral figure saccades differ in a systematic way for each saccade [t(7) = 1.98, P = 0.044, one-tailed] by about 4.2%. triplet. Generally speaking, the saccades for each saccade Together, this indicates the existence of the COGE.

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Comparison of perceptual and action effects Since the action effects (AE and AEnoCOGE) are obtained using the neutral figure as a reference for correction purposes, an obvious choice for fair compar- isons is the perceptual effect obtained from the indirect comparisons, which also relies on a neutral figure as a reference for correction purposes. The perceptual effect was significantly smaller than the AE [t(7) = 2.90, P = 0.023, two-tailed]. In contrast, the action effect that was corrected for the center of gravity effect (AEnoCOGE) did not differ from the perceptual effect [t(7) = 0.224, P = 0.83, two-tailed].

Discussion

In Experiment 2, we measured action effects for the amplitudes of saccades using the Mu¨ller-Lyer illusion. We Figure 7. Illustration of the center of gravity effect (COGE). The showed that the action effect (AE) was considerably larger amplitudes of the saccades and the actual sizes of the MFs than the perceptual effect. This “dissociation” between (matched figures) are pooled over the configuration (wings-in, perception and action is in contrast to the assumptions of wings-out, neutral) and the size of the TF (target figure), resulting the separate coding approach (Milner & Goodale, 1995) in an average adjusted sizes triplet (shaft lengths are indicated) that postulates stronger perceptual effects and weaker and in an average saccade triplet (amplitudes of saccades are action effects. However, the large AE was in part due to a shown on the right; endpoints of saccades are indicated with COGE, i.e. the saccades were pulled towards the center of colored crosses in the figure). For illustrative purposes, saccades gravity (COG) of the respective illusory figure. Therefore, carried out from right to left were mirror-reversed and collapsed on a fair comparison between perceptual and action effects the saccades that were carried out from left to right. The deviation (i.e. effects are only due to the internal size estimates in of the orange cross to the right (+5.0%) and the deviation of the the perceptual and action system) can only be assured if blue cross to the left (j4.2%) from the reference point (green the additional COGE is eliminated from the AE. By cross) add up to the center of gravity effect (COGE).

The action effect corrected for the center of gravity effect The existence of a COGE has implications for the com- parison between perceptual and action effects. Clearly, the action effect that was determined earlier (Figure 5) includes the COGE. Consequently, for a fair comparison between perceptual and action effects, the part of the action effect that is caused by the COGE should be eliminated. Since the amplitudes of the saccades for the wings-out figures are enlarged by 5.0% due to the COGE, a reduction by this amount should yield the true action effect (i.e. the action effect that is caused only by the visual illusion). The same argument applies for the wings-in figure, resulting in an increase of 4.2%. Figure 8 shows how the action effect (without the COGE) is determined. The measured values for the mean amplitudes of the saccades are increased by 4.2% for the wings-in Figure 8. The action effect without the center of gravity effect figure, decreased by 5.0% for the wings-out figure and (AEnoCOGE). The mean amplitudes of the saccades were unchanged for the neutral figure. Therefore, the action increased by 4.2% for the wings-in figure and decreased by effect without the center of gravity effect (AEnoCOGE) 5.0% for the wings-out figure to correct for the COGE. The values decreases to 17.29 T 1.78%. The AE (27.34%) and the for the neutral figure were unchanged. The AEnoCOGE is then AEnoCOGE (17.29%) differ significantly [t(7) = 4.21, P = computed as: [d1 + d2 / (slope average size of SCA figure)] 0.02, one-tailed, see Figure 4]. 100 = [m1 + m2 / 5] 100 = 17.29 T 1.78%.

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quantifying the COGE, we were able to correct the action respect to perceived size nor with respect to the slope of effect and determine an action effect without the center of the function that relates the actual figure size with the size gravity effect (AEnoCOGE). The AEnoCOGE was almost of the dependent measure. Hence, it is necessary to identical in size to the perceptual effect, i.e. although the measure not only the motor responses for the illusory action effect was corrected (and therefore decreased in figures but for the neutral figure as well (Figure 5b). size), the action effect was not smaller than the perceptual The action effect (AE) was considerably larger than the effect. This result is in accordance with the common perceptual effects. However, it could be shown that the coding approach (Franz et al., 2001). amplitudes of saccades were influenced by a center of gravity effect (COGE). A fair comparison between percep- tion and action (with the aim to test the assumptions of the separate and common coding approaches) should account General discussion for the influence of factors that constitute a bias for the respective effects. Certainly, the tendency of saccades to be pulled towards the center of gravity of a stimulus config- In this study, we investigated the center of gravity effect uration (Findlay, 1982; He & Kowler, 1989) is such a (COGE) on saccades in the Mu¨ller-Lyer illusion. To this factor. The quantification of the COGE allowed for the end, we not only measured the perceptual effect and the computation of a corrected action effect (AEnoCOGE). action effect, but we let subjects also carry out saccades This action effect did not differ from the perceptual effect. along perceptually adjusted Mu¨ller-Lyer figures (same The COGE found in the present study appears to be at perceived size; different actual sizes). odds with previous research on the Brentano version of Regarding the perceptual measures, we followed Franz the Mu¨ller-Lyer illusion. de Grave, Smeets et al. (2006) et al. (2001) and distinguished the direct (wings-in figure did not report an indication of a COGE. While the is adjusted to the wings-out figure) and the indirect amplitudes of the saccades along the shafts of the Brentano comparison (the neutral figure is adjusted to the wings-in figure (oriented vertically) were similar to the perceptual as well as to the wings-out figure). The perceptual effects effect, the horizontal saccades (perpendicular to the shaft) obtained with these two methods did not differ signifi- from outside the figure to the midpoints of the Brentano cantly. By contrast, Franz et al. (2000) found a consid- figure did not show deviations in the direction of the erably larger perceptual effect for the direct method in expected COGE. Three reasons may explain the differ- comparison to an indirect method. Various reasons may ence between the study of de Grave, Smeets et al. (2006) explain this discrepancy. First, while Franz et al. (2000) and our study: First, de Grave and colleagues excluded used the Ebbinghaus illusion, we investigated the Mu¨ller- that a COGE changed the direction of saccades that Lyer illusion. It was argued (Franz & Gegenfurtner, 2008) started from outside the Brentano illusion (see Figure 1b, that the difference between the direct and indirect methods green dot) and aimed at the middle vertex of the figure may be due to an enhancing effect, i.e. by an interaction of (Figure 1b, blue dot), while we investigated influences of the surrounding circles of the Ebbinghaus illusion in the a COGE on the amplitude of saccades that were carried direct comparisons. This explanation might not be true for out along the shaft of Mu¨ller-Lyer figures. It is possible the Mu¨ller-Lyer illusion. Therefore, direct comparisons that saccades along the shaft of a visual illusion are may not per se yield larger perceptual effects than indirect influenced more by a COGE than saccades that are carried comparisons. out perpendicular to the shaft. Isodirectional influences With respect to fair comparisons between perceptual enlarge or diminish the amplitude of saccades without and action effects, it needs to be established that the slopes changing their direction. Orthogonal influences alter the of the functions that relate the actual size of the figure direction of saccades and therefore involve other neuro- with the size of the perceptual measure (adjustments) and physiological mechanisms (change of the muscular acti- the motor measures (amplitudes of saccades) are the same; vation pattern, recruitment of other external eye muscles). otherwise corrections are necessary (Bruno & Franz, Concerning the (vertical) saccades along the shaft of the 2009). Since the basic idea for the use of visual illusions Brentano illusion, de Grave and colleagues could not is that an illusory size change has the same effect as a differentiate between effects of the perceived size and a physical size change of a neutral figure, it seems possible additional COGE. By analyzing saccades along mandatory to determine the slopes of the functions for perceptually adjusted figures (perceived sizes were equal), the neutral figure. While the perceptual measures yielded our Experiment 2 aimed to disentangle this issue. Second, slopes close to 1.0, the action measures resulted in a slope in the study of de Grave, Franz et al. (2006) the target for the neutral figure of 0.9. This value was different from point was indicated with a small dot in each trial (Figure 1b, the average slope for the two illusory figures (È1.0). This blue dot). The presentation of the target point super- is not overly surprising given the fact that the neutral imposed on the middle vertex of the Brentano illusion figure is defined only as “not biased in perceived size due might have reduced or even eliminated a possible to wings”. Thus, the neutral figure is neither considered influence of the COG on the direction of the saccade. lying exactly in the middle of the illusory figures with Third, de Grave and colleagues did not vary the size of the

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Brentano illusion. Therefore, they could not measure the Bernardis et al. (2005) was larger (22.3 T 2.2%) than the slopes of the functions that relate the dependent variable effect that we obtained in the present study (17.7 T 1.8%). with the actual sizes of the figures. Hence, it remains open Interestingly, the verbal estimation task as employed by if the perceptual and action effects would have differed if Bernardis et al. (2005) was carried out with short a correction by the slopes had been carried out. presentation times (200 ms) of the illusory figures, McCarley et al. (2003) analyzed the amplitudes of comparable to the presentation time in their eye move- saccades post-hoc according to the movement latency ment task. This resulted in perceptual and action effects (median split), based on the assumption that COGEs are that did not differ statistically. It is conceivable that the larger for short-latency saccades compared to long-latency perceptual effect can be enhanced when presentation times saccades (Coe¨ffe´ & O’Regan, 1987; Ottes et al., 1985). are short. An obvious possibility to test this would be to Since the authors found no effect for movement latency, a vary the presentation times of the stimuli for the COGE was ruled out. However, given the fact that perceptual measures as well as for the motor responses. movement latency was not varied systematically, the The usual range of perceptual effects has been reported differences between the conditions for each type of by Bruno and Franz (2009). In their review on 15 studies saccade (reflexive or voluntary) after the median split that investigated grasping at the Mu¨ller-Lyer illusion, the can be assumed to be rather small (the authors gave no mean perceptual effect was 10.7% (range from 5% to information on differences between saccade latencies after 18.8%). All studies were conducted with the “classical” the median split). Hence, it remains unclear if the Mu¨ller-Lyer illusion, i.e. the stimuli consisted of (separate) differences in movement latency between the groups after wings-in and wings-out figures that contained a shaft. the median split were large enough so that COGEs could Moreover, all reported effects were corrected for the be expected to show up. Nonetheless, in the very same slope. However, in another review (Bruno, Bernardis, & study, the authors found that amplitudes of voluntary Gentilucci, 2008) on 11 studies that investigated pointing saccades along perceptually adjusted wings-in and wings- at the “Mu¨ller-Lyer family” (including the “classical” out figures differed in the expected direction of the COGE. Mu¨ller-Lyer illusion, the “no shaft” Mu¨ller-Lyer illusion, This finding is in line with the results in our study. the Brentano illusion, the Dumbbell illusion, the Judd With respect to the assumptions about the COGE as illusion and the Kanisza’s compression illusion), the spelled out in this study, some further points need to be mean perceptual effect amounted to 22.4% (range from addressed. Here, we followed McCarley et al. (2003)as 4% to 36.7%). In addition to the fact that the stimuli well as de Grave, Smeets et al. (2006), who treated the were quite inhomogeneous, the effects were (in most COGE as an effect on saccades only, i.e. only the action cases) not corrected for the slopes. These striking system but not the perceptual system is influenced. We differences of the perceptual effects may indicate that treated the effect of the illusion on saccades and the effect they are quite variable if the stimulus conditions change of the COG as two separate additive effects. However, it is and/or if the effects are not corrected for the slopes. possible that these two effects cannot be disentangled that And yet, it should be kept in mind that the variability of easily. A prominent interpretation of the Mu¨ller-Lyer perceptual effects does not per se pose a problem to the illusion stems from Gregory (1966). He tried to explain general idea to compare perceptual and action effects. the illusion with the (so called false) attempt of the visual While the separate coding approach always predicts a system for size constancy. It was assumed that the wings- dissociation between perception and action (i.e. the in figure is near to the observer, like the protruding corner action effects are smaller than the perceptual effects), the of a building, while the wings-out figure is supposed to be common coding approach predicts associations between further away. This idea is questionable, since the dumbbell perception and action (i.e. no differences between effects). illusion (which is supposedly a variation of the Mu¨ller-Lyer These predictions are, so to speak, not dependent on the figure) cannot be explained in the same way. According to “strength” of the illusion but only on the internal size another interpretation of Ginsburg (1986), the illusion may estimate (that may vary in accordance with the “strength” be caused by spatial filtering mechanisms, leading to size of the illusion) in the perceptual and in action system. distortions in the filtered images that are similar to the However, if additional factors (that may arise due to perceived sizes. This filtering theory resembles the assump- different stimulus conditions) influence the size of an effect, tions for the COGE on saccades. Yet, so far no consensus like the COGE, the interpretation of comparisons between has been found with respect to the causation of the illusion. perceptual and actions effects is impeded. The study of Bernardis et al. (2005) may provide an In the present study, an attempt was made to measure interesting hint concerning the size of perceptual effects. such an additional factor on saccades, the so called center of The authors found no difference between the perceptual gravity effect (COGE). The results indicate that the COGE effect (obtained with verbal estimations) and the action should be taken into account when dealing with the effect (obtained with saccades) using a modified Mu¨ller- “classical” Mu¨ller-Lyer illusion. This has been demonstrated Lyer illusion (only wings, no shafts), i.e. the perceptual for action effects that were obtained with the amplitudes of and the action effect were similar even without correcting saccades. To conclude, our results are in accordance with the for the COGE. The perceptual effect in the study of common coding approach (Franz et al., 2001).

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TF MF MF size for 4 cm TF MF size for 5 cm TF MF size for 6 cm TF

9VG9VG 4.08 (0.03) 5.11 (0.02) 6.15 (0.03) GV9 4.84 (0.11) 5.97 (0.09) 7.10 (0.11) ªVª 4.49 (0.10) 5.58 (0.09) 6.67 (0.08) GV99VG 3.56 (0.06) 4.33 (0.05) 5.09 (0.07) GV9 4.05 (0.03) 5.07 (0.03) 6.08 (0.04) ªVª 3.69 (0.07) 4.63 (0.08) 5.57 (0.11) ªVª 9VG 3.86 (0.07) 4.69 (0.10) 5.51 (0.13) GV9 4.58 (0.11) 5.48 (0.09) 6.38 (0.09) ªVª 4.03 (0.03) 4.99 (0.03)5.94 (0.03) Table A1. Mean sizes (in cm) of the match figures (MF) after perceptual adjustment to the target figures (TF). MF sizes (SEM in parentheses) are shown for the two TF sizes used in Experiment 1 (4 cm and 6 cm) and for the average size of the TF (5 cm). Gray cells indicate sizes for the SCA figures. In Experiment 2, the subjects carried out saccades along the MF with shaft lengths equivalent to the sizes shown here for the 4 cm TF and for the 6 cm TF. Shaft lengths of 4 cm or 6 cm were used for the SCA figures.

TF MF MF saccades for 4 cm TF MF saccades for 5 cm TF MF saccades for 6 cm TF

9VG9VG 4.22 (0.09) 5.38 (0.10) 6.54 (0.11) GV9 3.99 (0.06) 4.98 (0.08) 5.97 (0.14) ªVª 4.28 (0.10) 5.26 (0.08) 6.24 (0.09) GV99VG 3.78 (0.06) 4.64 (0.07) 5.50 (0.10) GV9 3.31 (0.09) 4.17 (0.10) 5.04 (0.12) ªVª 3.39 (0.09) 4.35 (0.07) 5.30 (0.08) ªVª 9VG 4.17 (0.08) 5.05 (0.09) 5.93 (0.13) GV9 3.81 (0.12) 4.58 (0.10) 5.35 (0.11) ªVª 3.85 (0.04) 4.75 (0.06) 5.64 (0.87)

Table A2. Mean amplitudes of saccades (in cm) along the matched figures (MF). MF saccades (SEM in parentheses) are shown for the two TF sizes (4 cm and 6 cm) and for the average size of the TF (5 cm). Gray cells indicate the amplitudes of saccades for the SCA figures (see the red points in Figure 5b and the dashed figures in Figure 6).

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