Vision Research 47 (2007) 145156 www.elsevier.com/locate/visres
Visual learning by cue-dependent and cue-invariant mechanisms
Volodymyr Ivanchenko, Robert A. Jacobs
Department of Brain and Cognitive Sciences, Center for Visual Science, University of Rochester, Rochester, NY 14627, USA Received 15 December 2005; received in revised form 13 September 2006
Abstract We examined learning at multiple levels of the visual system. Subjects were trained and tested on a same/dierent slant judgment task or a same/dierent curvature judgment task using simulated planar surfaces or curved surfaces dened by either stereo or monocular (texture and motion) cues. Taken as a whole, the results of four experiments are consistent with the hypothesis that learning takes place at both cue-dependent and cue-invariant levels, and that learning at these levels can have dierent generalization properties. If so, then cue-invariant mechanisms may mediate the transfer of learning from familiar cue conditions to novel cue conditions, thereby allowing perceptual learning to be robust and ecient. We claim that learning takes place at multiple levels of the visual system, and that a comprehensive understanding of visual perception requires a good understanding of learning at each of these levels. 2006 Elsevier Ltd. All rights reserved.
Keywords: Visual learning; Cue-invariance
1. Introduction Despite decades of research, perceptual learning is a poorly understood phenomenon. Perhaps the most important lesson that research has taught us is that our current theories and experiments are too simple and too narrowly focused. It is likely that perceptual learning takes place at multiple levels of the human perceptual system, and that a comprehensive understanding of perception will require a good understanding of learning at each of these levels. Unfortunately, the study of perceptual learning at multiple levels is nearly unexplored in the scientic literature (see Ahissar & Hochstein, 1997, 2002, for a notable exception). This lack of understanding of learning at multiple levels is, we believe, a major reason why the literature on perceptual learning often contains seemingly confusing (and contradictory) results. This article reports the results of experiments investigating learning at two levels of the visual system, namely the
levels of visual cue-dependent and visual cue-invariant mechanisms (e.g., shape-from-visual-texture or shapefrom-visual-motion mechanisms versus a mechanism for perceiving shape that is independent of the visual cue used to dene the shape).1 Within the vision sciences, the study of visual cue-invariant mechanisms is relatively unusual. These mechanisms ought to be of fundamental interest to scientists because visual perception of natural environments must integrate information provided by multiple cues. In this sense, these mechanisms can be regarded as among the highest level mechanisms of our visual systems.
Corresponding author. Fax: +442 9216. E-mail addresses: vivanchenko@bcs.rochester.edu (V. Ivanchenko), robbie@bcs.rochester.edu (R.A. Jacobs). 0042-6989/$ - see front matter 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.visres.2006.09.028
1 We hypothesize that visual cue-invariant mechanisms are constructed from cue-dependent mechanisms. For example, a cue-invariant mechanism for representing visual shape might receive inputs from both a mechanism that represents shape-from-visual texture and a mechanism that represents shape-from-visual-motion (and, perhaps, inputs from several other cue-dependent mechanisms for representing shape). If this mechanisms output at any moment in time does not depend on which mechanism provided an input, then its output would be cue-invariant. To our knowledge, the vision sciences literature does not contain any studies directly evaluating this hypothesis.
V. Ivanchenko, R.A. Jacobs / Vision Research 47 (2007) 145156
Do visual cue-invariant mechanisms exist? Recent psychophysical data suggests that the human visual system may contain neural mechanisms that represent object shape or depth independent from the visual cue(s) specifying the shape or depth. For example, Poom and Borjesson (1999) reported that prolonged viewing of an adaptation surface caused a test surface to appear to slant in the direction opposite to that of the adaptation surface regardless of whether the two surfaces were dened by the same cue (either motion parallax or binocular disparity) or dierent cues. Other behavioral studies suggesting visual cue-invariant mechanisms are Bradshaw and Rogers (1996) and Domini et al. (2001). Related data have been found in neuroscientic studies using monkeys. For example, Sakata et al. (1999) showed that some visually responsive neurons in the macaque anterior intraparietal area encode surface tilt regardless of whether the tilt is specied by disparity alone, monocular cues alone, or both. Other neuroscientic studies indicating visual cue-invariant mechanisms in monkeys are Sary, Vogels, and Orban (1993), Sereno, Trinath, Augath, and Logothetis (2002), Tsutsui, Sakata, Naganuma, and Taira (2002). Brain-imaging studies using human observers have reported similar data. Grill-Spector, Kushnir, Edelman, Itzchak, and Malach (1998) found that a region located on the lateral aspect of the occipital lobe was preferentially activated during a visual object recognition task relative to control conditions irrespective of whether the object shape was dened by luminance, motion, or texture cues. Kourtzi and Kanwisher (2000) reported overlapping activations in the lateral and ventral occipital cortex for objects depicted by dierent visual formats (grayscale images and line drawings), and a reduced response when objects were repeated, independent of whether they recurred in the same or a different format.2 Other relevant brain-imaging studies using human observers are reported in Kourtzi, Betts, Sarkhei, and Welchman (2005) Welchman, Deubelius, Conrad, Bu ltho, and Kourtzi (2005). Although the studies cited above suggest the existence of visual cue-invariant mechanisms, they did not examine the nature of these mechanisms in a detailed way and, importantly for our purposes, they did not examine the role of these mechanisms in perceptual learning. To date, we are aware of only one study on cue-invariant mechanisms and perceptual learning. Rivest, Boutet, and Intrilligator (1996) trained dierent sets of observers to visually discrim2 It is interesting to note that cue-invariance may take place across sensory modalities, not just within the visual modality. Brain-imaging studies with humans have provided evidence for neural mechanisms which are modality-invariant. Amedi, Malach, Hendler, Peled, and Zohary (2001) found preferential activation in the lateral occipital complex when observers viewed objects and also when they grasped the same objects. Pietrini et al. (2004) found that visual and tactile recognition of man-made objects evoked category-related patterns of responses in a ventral extrastriate visual area in the inferior temporal gyrus that were correlated across sensory modality.

inate the orientations of color-dened bars, of luminancedened bars, or of motion-dened bars. A similar improvement from pre-test to post-test was found regardless of whether the bars seen after training were dened by the same or by a dierent cue as the cue seen during training. The authors concluded that training changed the sensitivity of cells that represent visual orientation in a cue-invariant manner. This article studies the hypothesis that cue-invariant mechanisms mediate the transfer of learning from familiar cue conditions to novel cue conditions, thereby allowing perceptual learning to be robust and ecient. For example, if an observer learns to make more accurate depth-from-visual-texture judgments, then it would be advantageous to the observer to generalize this gained knowledge so that it can be used when estimating depth from cues other than texture, such as when making depth-from-visual-motion judgments. An important goal of the reported experiments is to evaluate this hypothesis. A secondary goal is to compare the generalization properties of visual cue-dependent versus cue-invariant mechanisms. We hypothesize that the lower level cue-dependent mechanisms tend to use local representations that lead to stimulus-specic learning (i.e., learning eects are limited to the specic stimulus conditions used during training), whereas the higher level cue-invariant mechanisms tend to use global representations that lead to stimulus-general learning (i.e., learning eects generalize to novel stimulus conditions). To our knowledge, there are currently no studies comparing the properties of cue-dependent versus cue-invariant mechanisms. The results of four experiments are reported. In the rst experiment, subjects were trained to judge the 3D orientations of planar surfaces slanted in depth when surfaces were dened by a training cue and when slants were centered near a training slant. Subjects were tested on the same task when surfaces were dened by either the training cue or a novel cue, and when slants were centered either near the training slant or near a novel slant. Because subjects showed improved performance when tested both with the training cue and with the novel cue, the results suggest that training produced modications to both cue-dependent and cue-invariant mechanisms. Furthermore, these two sets of mechanisms seem to have dierent propertiescue-dependent mechanisms of visual slant are slant-specic whereas cue-invariant mechanisms are not. Experiment 2 was similar to Experiment 1, but it required subjects to judge the slants of cylinders. As in Experiment 1, its results suggest that training produced modications to both cue-dependent and cue-invariant mechanisms, thereby producing transfer of learning from training to novel cue conditions. In addition, this experiment found that both sets of mechanisms either ignored or generalized over an irrelevant shape attribute. Experiment 3 required subjects to judge the curvature-in-depth of cylinders. The results again demonstrate learning by both cue-dependent and cue-invariant mechanisms. Experiment 4 found that learning

was task-specictraining on the curvature judgment task did not produce improved performance on the slant judgment task. This result indicates that learning was not due to adaptations of cognitive factors, and that observers do not have one set of mechanisms for judging visual depth but rather have dierent mechanisms for judging curvature-in-depth and slant-in-depth. Taken as a whole, the experiments support the hypothesis that cue-invariant mechanisms mediate the transfer of learning from familiar cue conditions to novel cue conditions, thereby allowing perceptual learning to be robust and ecient. 2. Experiment 1 To motivate Experiment 1, consider an observer viewing a planar surface slanted in depth. Suppose the observer is trained to discriminate the slants of surfaces dened by a stereo cue when the slants are near 45 from vertical (the top of the surface is closer to the observer than the bottom), and the observer improves at this task over time due to training. The observer is then tested with surfaces dened by either the training cue (stereo) or by a novel cue (e.g., visual texture) using slants that are either near the training slant (45) or far from the training slant (e.g., 45). In regard to generalization, at least four possibilities exist: (i) learning does not generalize to any novel stimulus conditions. Because learning did not transfer across cues in this case, this outcome suggests that learning did not inuence cue-invariant mechanisms. Furthermore, because training with the training cue and training slant did not lead to improved performance with the training cue and a novel slant, learning must have inuenced representations that can be characterized as slant-local. Slant-local representations would occur in a population of mechanisms in which each individual mechanism represents a specic (or small range) of slants, and dierent mechanisms represent dierent slants (e.g., consider a neural network that uses a localist representation of surface slant). In the case considered here, training might have inuenced an individual mechanism that represents stereo-dened surfaces slanted at about 45, and not inuenced other mechanisms such as cue-invariant mechanisms or a mechanism that represents stereo-dened surfaces slanted at 45. Hence there was no transfer of learning when discriminating surfaces dened by a novel cue, or surfaces dened by the training cue but at a novel slant; (ii) transfer of learning occurs when surfaces are dened by a novel visual cue but only when the surfaces are near the training slant (45). The outcome in this case suggests the existence of both visual cue-dependent and cue-invariant representations for surface slant and, moreover, that both these representations are slantlocal;

same or dierent. The two stereo pairs were chosen so that either they both depicted planar surfaces slanted at 45, or one pair depicted a surface slanted at 41 and the other depicted a surface slanted at 49. After judging whether the surface slants were the same or different, subjects received auditory feedback indicating whether their response was correct. Next, subjects performed 240 test trials designed to evaluate whether they could perform the slant judgment task on the basis of the sets of dots present in individual images from stereo pairs. On each trial, subjects viewed (monocularly) an individual image from a stereo pair of images and then viewed a second individual image from a dierent stereo pair. For example, the left and right sides of Fig. 1 illustrate individual images from stereo pairs depicting surfaces with slants of 41 and 49, respectively. After viewing the two individual images, subjects judged whether the depicted surface slants were the same or different. Auditory feedback was not provided. The results are shown in Fig. 2. The height of a bar in this gure
indicates a subjects performance on the test trials in terms of percent correct (the error bars indicate 95% condence intervals based on 9000 simulated bootstrap trials; Efron & Tibshirani, 1994). Chance performance is 50% correct. The performances of 7 of 8 subjects did not dier signicantly from chance performance. Consequently, we conclude that the set of dots in an individual left-eye or right-eye image from a stereo pair did not provide a useful texture cue to surface slant. (ii) Texture and motion: Stimuli were monocular views of a planar surface densely covered with a homogeneous texture consisting of square patches. Fig. 3 illustrates a display of a planar surface dened by a texture cue. Each texture element subtended 0.82 of visual angle when a surface was frontoparallel. The placement of texture elements was randomized in each display (average density of 0.33 texels/deg2). A motion cue to surface slant was added to each display by rotating a surface back and forth around a vertical axis that passed through the center of the surface. The range of rotation was 15, and the speed of rotation was 30 per second. Stimuli were presented on a standard CRT monitor using a resolution of pixels and a 100 Hz refresh

Control experiment

0.8 0.7 Percen t co rrect 0.6 0.5 0.4 0.3 0.2 0.Subject pk sg djk ek mk nm am m dd

combination of cue and center slant. On Days 2 and 3, they performed 4 training blocks. The center slant was 45 for all training trials. Training trials used the stereo cue for half the experimental subjects, and the monocular cues for the remaining experimental subjects. Recall that subjects received feedback regarding the correctness of their responses on training trials. On Day 4, experimental subjects performed 1 training block followed by 4 post-test blocks (which were identical to pre-test blocks). In contrast to experimental subjects, control subjects did not receive trainingthey performed 4 practice and 4 pre-test blocks on Day 1, and 4 post-test blocks on Day 2. 2.1.3. Subjects Sixteen undergraduate students at the University of Rochester served as experimental subjects and eight students served as control subjects. All subjects were nave to the goals of the experiment, and all had normal or corrected-to-normal vision. 2.2. Results The results are illustrated in Fig. 4. The graphs on the top and bottom plot the data for the experimental and control subjects, respectively. We rst consider the top graph.

Experimental Subjects

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2.500 2.000 1.500

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mono 45

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Fig. 4. (Top) The results for the experimental subjects in Experiment 1. The horizontal axis indicates the test condition. For example cue: same, slant: same means that subjects were tested using the same cue and center slant as were used during training. The vertical axis plots Dd 0 which is a subjects d 0 on post-test trials minus this value on pre-test trials averaged over all subjects. Error bars give the standard errors of the means. The two asterisks (**) above a bar mean that the value indicated by the bar is signicantly greater than zero at the p <.01 level based on a two-tailed ttest; (Bottom) the results for the control subjects. The horizontal axis indicates the test condition, and the vertical axis plots Dd 0.
The vertical axis plots experimental subjects average improvement in performance in units of Dd 0 which is the value of a subjects d 0 on post-test trials minus this value on pre-test trials averaged over all subjects. Error bars give the standard errors of the means. The horizontal axis indicates the experimental condition. For example, condition cue: same, slant: same is the set of pre- and post-test trials that used the same cue and center slant as were used during a subjects training trials. Condition cue: same, slant: di is the set of test trials that used the same cue as was used during a subjects training trials but a dierent (novel) center slant. The graph on the bottom has a similar format, but is not identical because control subjects did not receive training trials. In this case, condition stereo, 45 is the set of test trials that used the stereo cue and the 45 center slant, whereas condition stereo, 45 is the set of test trials that used the stereo cue and the 45 center slant. Several observations can be made. First, the experimental subjects showed large learning eects when evaluated

Experimental Subjects: cues same, slant different
3.2.d' 1.0.an mr sp nt mk ea jb jw ct ch vp md mfc sm es exl subjects pretest posttest
with the same cue and center slant as used during training (top graph of Fig. 4, condition cue: same, slant: same). Second, these subjects also showed moderate-sized learning eects when evaluated with novel cues and/or novel slants. In all conditions, Dd 0 values are signicantly greater than zero (based on two-tailed t-tests with a p <.01 signicance level). Moreover, it appears that roughly equal amounts of transfer of learning were found to novel cues as to novel slants. In contrast, control subjects never showed improvements from pre- to post-test (bottom graph in Fig. 4). This result was expected as control subjects never received training. A more detailed view of experimental subjects data is given in Fig. 5. The rst set of eight subjects in each graph were trained with planar surfaces dened by the monocular cues, whereas the second set of eight subjects were trained with surfaces dened by the stereo cue. For each subject, there are two bars showing a subjects performances (in units of d 0 ) on the pre-test and post-test trials. For the sake of brevity, this data is only provided for the test trials that used the same cue as a subjects training trials but a novel slant (top graph of Fig. 5), and for the test trials that used a novel cue and a novel slant (bottom graph). 2.3. Discussion Based on this data, we can conclude the following. First, training produced modications to experimental subjects cue-dependent representations of visual slant (e.g., slantfrom-stereo, slant-from-texture, slant-from-motion) as evidenced by the large amounts of learning with a subjects training cue and training slant (condition cue: same, slant: same). Second, and importantly for our purposes, training also produced modications to subjects representations of visual slant which are visual cue-invariant, as demonstrated by subjects cue-invariant generalizations (conditions cue: di, slant: same and cue: di, slant: di). Above we hypothesized that cue-invariant mechanisms mediate the transfer of learning from familiar cue conditions to novel cue conditions, thereby allowing perceptual learning to be robust and ecient. The results of Experiment 1 support this hypothesis. In regard to the issue of whether the modied slant representations are slant-local versus slant-global, these data indicate that the cue-dependent representations are best characterized as slant-local because learning eects with the training slant were much larger than learning eects with the novel slant.3 The cue-invariant representations, in contrast, are best characterized as slant-global because subjects showed as much transfer of learning to a novel cue and novel slant as to a novel cue but familiar slant. That is, these data indicate that cue-dependent and cue-in3 For the sake of simplicity, we assume that only cue-dependent mechanisms are involved in the tests with the training cue and only cueinvariant mechanisms are involved in the tests with a novel cue. Whether this simplifying assumption is correct is a topic of future research.

for each combination of cue (stereo or monocular) and center slant (45 or 45). On Days 2 and 3, subjects performed 4 training blocks using the curved surface dened by a stereo cue and a center slant of 45. On Day 4, they performed 1 training block followed by 4 post-test blocks (which were identical to pre-test blocks). 3.1.3. Subjects Eight undergraduate students at the University of Rochester served as experimental subjects. All subjects were nave to the goals of the experiment, and all had nor mal or corrected-to-normal vision. 3.2. Results The results are shown in the graph in Fig. 6. The horizontal axis indicates the experimental condition, and the vertical axis plots the subjects average improvement in performance in units of Dd 0. Error bars give the standard errors of the means. The four leftmost bars show the average performance improvement in the four test conditions (post-test d 0 minus pre-test d 0 ), whereas the rightmost bar shows the improvement during training (d 0 on last training block on Day 3 minus d 0 on rst training block on Day 2). Subjects showed signicant improvement on the slant judgment task during training with curved surfaces and a center slant of 45 (p =.015; rightmost bar of Fig. 6). In addition, they showed signicant improvement from preto post-test in three of four test conditions with planar surfaces (p <.05 based on a two-tailed t-test; the improvement in the remaining conditiontest trials using planar surfaces dened by the monocular cues and a center slant of 45is not statistically signicant). 3.3. Discussion Training with curved surfaces was eective as evidenced by the improvement in performance on the slant judgment task from the start to the end of training. In addition, train1 0.8

0.6 0.4 0.2 0

test stereo 45 deg. planar test stereo -45 deg. planar test mono 45 deg. planar test mono -45 deg. planar
training stereo 45 deg. curved
Fig. 6. The rst four bars show subjects performance improvements in the test conditions of Experiment 2, whereas the rightmost bar shows subjects improvements during training. The horizontal axis indicates the test or training condition, and the vertical axis plots the improvement in units of Dd 0. Error bars give the standard errors of the means. An asterisk (*) above a bar means that the value indicated by the bar is signicantly greater than zero at the p <.05 level based on a two-tailed t-test.

ing produced modications to cue-dependent mechanisms as evidenced by the improved performance on test trials using the training (stereo) cue, as well as to cue-invariant mechanisms as evidenced by the improved performance in one test condition with a novel (monocular) cue and the nearly signicant improvement in the other test condition with a novel cue. These results are consistent with the results of Experiment 1 in the sense that both experiments show visual learning by both cue-dependent and cue-invariant mechanisms. The results also show learning eects of similar sizes in all cases, thereby indicating that both cue-dependent and cue-invariant representations of visual slant are best characterized as shape-global. We rst consider the cue-dependent representation. To evaluate whether it is shape-local or shape-global, it is necessary to compare conditions that used the same cue, but dierent shapes. Compare the performance improvement during training (stereo cue, curved surface; see rightmost bar of Fig. 6) with the improvements in the rst and second test conditions (stereo cue, planar surface; see rst and second bars of Fig. 6). If the former improvement is larger than the latter improvements, we would conclude that subjects cue-dependent representations of visual slant are shape-local because a larger improvement is found with the training shape than with a novel shape. However, the data do not show that the former improvement is larger. Instead, the data show that these two improvements are about the same size, meaning that subjects showed complete transfer of learning from displays of curved surfaces to displays of planar surfaces. This result suggests that training produced modications of subjects cue-dependent mechanisms that applied equally to all shapes, consistent with a shape-global representation. In regard to whether subjects cue-invariant representations of visual slant are best characterized as shape-local or shape-global, it is necessary to compare conditions that used both dierent cues and dierent shapes. Compare the performance improvements during training (stereo cue, curved surface; see rightmost bar of Fig. 6) and during the third and fourth test conditions (monocular cues, planar surface; see third and fourth bars of Fig. 6). These performance improvements are about the same size, meaning that subjects showed complete transfer of learning between displays of curved surfaces dened by a stereo cue to displays of planar surfaces dened by the monocular cues. We conclude that training produced modications of subjects cue-invariant mechanisms that applied equally to all shapes and, thus, the cue-invariant representations are also best characterized as shape-global. Experiment 2 produced results which might be regarded as inconsistent with those of Experiment 1 in two ways. First, in the introductory section of this article, we hypothesized that lower level cue-dependent mechanisms tend to use local representations that lead to stimulus-specic learning (i.e., learning eects are limited to the specic stimulus conditions used during training), whereas the

higher level cue-invariant mechanisms tend to use global representations that lead to stimulus-general learning (i.e., learning eects generalize to novel stimulus conditions). Experiment 1 found evidence supporting this hypothesissubjects cue-dependent representations of visual slant were slant-local whereas their cue-invariant representations were slant-global. However, Experiment 2 did notsubjects cue-dependent representations of visual slant were shape-global, not shape-local. A possible explanation is that the stimuli used during training in Experiment 2 contained an attribute (shape) which was irrelevant and possibly dicult to interpret for the purpose of performing the experimental task (slant judgment task). It may be that subjects cue-dependent mechanisms either ignored the irrelevant shape information or, perhaps equivalently, generalized across the irrelevant shape dimensions (thereby producing complete transfer of learning from curved to planar surfaces) because shape was an irrelevant attribute. Future research will need to explore this possibility. Second, Experiment 1 found that subjects cue-dependent mechanisms showed greater performance improvement with the training slant than with a novel slant (rst and second bars of the top graph of Fig. 4), whereas Experiment 2 found that subjects cue-dependent mechanisms showed equal performance improvement with training and novel slants (rst and second bars of Fig. 6). A possible explanation is that Experiment 2 not only used a novel slant, but also a novel shape. Observers cue-dependent mechanisms may generalize dierently to novel slants than to conjunctions of novel slants and novel (irrelevant) shapes. Again, future research will need to study this issue. 4. Experiment 3 An important goal of this research project was to evaluate the hypothesis that cue-invariant mechanisms mediate the transfer of learning from familiar cue conditions to novel cue conditions. Experiments 1 and 2 evaluated subjects performances in familiar and novel cue conditions on a slant judgment task. The results of these experiments provide compelling evidence supporting this hypothesis. Experiment 3 is a control experiment designed to make sure that the results reported above are not due to the use of a particular type of task (i.e., a slant judgment task) but, rather, that the basic ndings can be replicated with at least one other perceptual task. This experiment used a curvature judgment task. 4.1. Methods 4.1.1. Apparatus and stimuli Stimuli simulated perspective views of curved surfaces. These surfaces were vertically oriented elliptical cylinders. All cylinders had the same width, though dierent cylinders had dierent object depths. Cylinders were dened by either a stereo or texture cue. When dened by a stereo cue, displays were identical to those used in Experiment 2.

When dened by a texture cue, an isotropic texture consisting of red circles was mapped to the green surface of a cylinder. The gradient of texture element foreshortening, size, and density provided a useful cue to a cylinders shape. Fig. 7 illustrates a display of a cylinder dened by a texture cue. As was the case in Experiment 2, displays of cylinders contained red borders at the top and bottom rendered at the monitor depth. These borders occluded the top and bottom edges of a cylinder, thereby eliminating contour cues to a cylinders shape. The visible portion of a cylinder subtended 11.9 of visual angle in the horizontal direction and 15.4 in the vertical direction. 4.1.2. Procedure Subjects performed a two-alternative forced-choice same/dierent curvature judgment task. On each trial, subjects were presented with a successive pair of cylinders, and judged whether the cylinders had the same or dierent curvature. (Note that this is identical to judging whether the cylinders had the same or dierent shape, or the same or dierent object depth.) Cylinders were displayed for 1000 ms, and inter-stimulus and inter-trial intervals were 700 ms. Both experimental and control subjects participated in this experiment. Experimental subjects performed practice, pre-test, training, and post-test blocks of trials over 4 days. On Day 1, they performed 2 practice blocks, one block used the stereo cue and the other block used the texture cue. When cylinders had the same curvature, the depthto-width ratio of their horizontal cross-sections was 1.0 (the cylinders were equally deep as wide). When their curvatures were dierent, one cylinder had a depth-to-width ratio of 0.5 (the cylinders width was twice its depth) and the other had a ratio of 1.5 (the cylinders depth was 1.5 times its width). Practice blocks were followed by 2 pre-test blocks. All test trials used cylinders dened by the texture cue. When cylinders had the same curvature, the depthto-width ratio of their horizontal cross-sections was 1.0.
Fig. 7. Illustration of a display of a cylinder dened by a texture cue.
When their curvatures were dierent, one cylinder had a depth-to-width ratio of 0.8 and the other had a ratio of 1.2. On Days 2 and 3, subjects performed 6 blocks of training trials. Training trials used cylinders dened by the stereo cue. They used the same depth-to-width ratios as test trials. On Day 4, subjects performed 2 training blocks followed by 2 post-test blocks. Post-test blocks were identical to pre-test blocks. In contrast to experimental subjects, control subjects did not receive trainingthey performed 2 practice and 2 pre-test blocks on Day 1, and 2 post-test blocks on Day 2. 4.1.3. Subjects Six undergraduate students at the University of Rochester served as experimental subjects, and six students served as control subjects. All subjects were nave to the goals of the experiment, and all had normal or corrected-to-normal vision. 4.2. Results and discussion The results are shown in Fig. 8. For each subject, the two bars show a subjects performances (in units of d 0 ) on pre-test and post-test trials. Control subjects performances on post-test trials did not dier signicantly from their performances on pre-test trials (bottom graph of Fig. 8). This was expected as control subjects did not receive training. Experimental subjects, in contrast, showed signicantly better performance on post-test trials than

0.-0.5

training

stereo test

mono test
Fig. 9. Results for Experiment 4. The rst (leftmost) bar shows subjects average performance improvement during training in units of Dd 0 (d 0 on the last training block of Day 3 minus d 0 on the rst training block of Day 2). The remaining bars show subjects average performance improvements on the post-test versus pre-test trials when planar surfaces were dened by the stereo cue or the monocular cues, respectively. Error bars give the standard errors of the means. The two asterisks (**) above a bar mean that the value indicated by the bar is signicantly greater than zero at the p <.01 level based on a two-tailed t-test.
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strate learning by cue-invariant mechanisms. Experiment 4 found that learning was task-specictraining on the curvature judgment task did not produce improved performance on the slant judgment task. This result indicates that learning was not due to adaptations of cognitive factors; it also shows that observers do not have one set of mechanisms for judging visual depth but rather have dierent mechanisms for judging curvature-in-depth and slant-in-depth. Taken as a whole, the experiments support the hypothesis that cue-invariant mechanisms mediate the transfer of learning from familiar cue conditions to novel cue conditions, thereby allowing perceptual learning to be robust and ecient. Our results suggest that visual learning takes place at multiple levels of the human visual system, and that a comprehensive understanding of visual perception will require a good understanding of learning at each of these levels. Unfortunately, the study of visual learning at multiple levels is nearly unexplored in the scientic literature. This lack of understanding of learning at multiple levels is, we believe, a major reason why the literature on visual learning often contains seemingly confusing (and contradictory) results. Our work represents an early step toward an examination of learning at multiple levels of the visual system. We hope that the study of visual learning at multiple levels becomes a common practice in the eld. Acknowledgments We thank two anonymous reviewers for their helpful comments on an earlier version of this manuscript. We also thank D. Knill for many interesting conversations on these issues, and I. Csapo for his contribution to Experiment 3. This work was supported by NIH research grant RO1EY13149. References
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