Coordinate frame for symmetry detection and object recognition

Can subjects voluntarily set an internal coordinate frame in such a way as to facilitate the detection of symmetry about an arbitrary axis? If so, is this internal coordinate frame the same as that involved in determining perceived top and bottom in object recognition and shape perception? Subjects were required to determine whether dot patterns were symmetric. Cuing the subjects in advance about the orientation of the axis of symmetry produced a substantial speedup in performance (Experiments 1 and 3) and an increase in accuracy with brief displays (Experiment 2). The effects appeared roughly additive, with an overall advantage for vertical symmetry; thus, the vertical axis effect is not due to a tendency to prepare for the vertical axis. The cuing advantage was found to depend upon the subject's knowing in advance the spatial location as well as orientation of the frame of reference (Experiment 4). The fifth experiment provided evidence that the frame of reference responsible for these effects is the same as the one that determines shape perception: Subjects viewed displays containing a letter (at an unpredictable orientation) and a dot pattern, rapidly naming the letter and then determining whether the dots were symmetric about a prespecified axis. When the top-bottom axis of the letter was oriented the same way as the axis of symmetry for the dots, symmetry judgments were significantly more accurate. Thus, the results suggest a single frame of reference for both types of judgment. The General Discussion proposes a theory of how visual symmetry may be computed, which might account for these phenomena and also characterize their relation to "mental rotation" effects.     

The differential effects of simultaneous and successive cueing on the detection of bilateral symmetry in dot patterns.

Corballis and Roldan (1975) obtained speeded judgements of whether dot patterns were bilaterally symmetrical about, or translated across, a line. Reaction times (RTs) were ordered V (vertical) > D (diagonal) > H (horizontal) where ">" means faster than. Similar results occurred with blocked axis orientations, suggesting subjects cannot prepare by rotating a mental frame of reference. Blocking trials may have been ineffective because blocking cannot provide incremental benefits over those already provided by axis lines. Four experiments show that the usual axis orientation ordering of V > H > D is markedly attentuated by simultaneous but not successive axis lines. Also, axis cue lines and axis blocking are not equivalent treatments. Instead, unblocked line cues require finite processing time whereas, under blocking, subjects can prepare for the expected orientation. There was no suggestion anywhere of the V > D > H axis ordering that Corballis and Roldan reported. Successive axis line cues may only direct attention to the orientation being cued, but simultaneous line cues may change the stimulus itself, thus providing an additional means of visual processing that facilitates symmetry detection at non-vertical axis orientations.     

What’s up in mental rotation?

We report two experiments on the influence of head tilt on mental rotation. In Experiment I, subjects decided whether dot patterns were or were not repeated about a line. Their reaction times (RTs) were consistent with the interpretation that they mentally rotated the patterns so that the line was subjectively vertical before making their decisions. When the subjects tilted their heads, the RT functions shifted in the direction of the tilt, indicating that the subjective vertical lay closer to the retinal than to the gravitational vertical. In Experiment II, subjects decided whether singly presented alphanumeric characters in various orientations were standard or backward (mirror-reversed). Again, analysis of their RTs suggested mental rotation to the standard upright, but the function was unaffected by head tilt; in this case, the subjects operated in subjective gravitational rather than retinal coordinates. The choice of retinal or gravitational coordinates may depend on whether the stimuli are interpreted egocentrically or as part of the external world.     

Mental transformations in the identification of left and right hands.

Subjects determined as rapidly as possible whether each line drawing portrayed a left or a right hand when the drawings were presented in any of four versions (palm or back of either hand) and in any of six orientations in the picture plane. Reaction time varied systematically with orientation and, in the absence of advance information, was over 400 msec longer for the fingers-down orientation. However, when subjects were instructed to imagine a specified (palm or back) view of a specified (left or right) hand in a specified orientation, reaction times to test hands that were consistent with these instructions were short (about 500 msec), independent of orientation, and unacompanied by errors. It is proposed that subjects determine whether a visually presented hand is left or right by moving a mental "phantom" of one of their own hands into the portrayed position and by then comparing its imagined appearance against the appearance of the externally presented hand.     

Imagining and naming rotated natural objects

The present experiment examined whether subjects can form and store imagined objects in various orientations. Subjects in a training phase named line drawings of natural objects shown at six orientations, named objects shown upright, or imagined upright objects at six orientations. Time to imagine an upright object at another orientation increased the farther the designated orientation was from the upright, with faster image formation times at 180° than at 120°. Similar systematic patterns of effects of orientation on identification time were found for rotated objects. During the test phase, all subjects named the previously experienced objects as well as new objects, at six orientations. The orientation effect for old objects seen previously in a variety of orientations was much reduced relative to the orientation effect for new objects. In contrast, substantial effects of orientation on naming time were observed for old objects for subjects who had previously seen the objects upright only or upright but imagined at different orientations. The results suggest that the attenuation of initially large effects of orientation with practice cannot be due to imagining and forming representations of objects at a number of orientations.     

THREE-DIMENSIONAL BILATERAL SYMMETRY BIAS IN JUDGMENTS OF FIGURAL IDENTITY AND ORIENTATION

Abstract— The two experiments reported explored a bias toward symmetry in judging identity and orientation of indeterminate two-dimensional shapes. Subjects viewed symmetric and asymmetric filled, random polygons and described, "what each figure looks like" and its orientation. Viewers almost universally interpreted the shapes as silhouettes of bilaterally symmetric three-dimensional (3-D) objects. This assumption of 3-D symmetry tended to constrain perceived vantage of the identified objects such that symmetric shapes were interpreted as straight-on views, and asymmetric shapes as profile or oblique views. Because most salient objects in the world are bilaterally symmetric, these findings are consistent with the view that assuming 3-D symmetry can be a robust heuristic for constraining orientation when identifying objects from indeterminate patterns.     

Perceptual use of nonaccidental properties.

Under the assumption of a general viewpoint, particular image properties, such as cotermination, straightness, and parallelism, can be used to infer, more or less reliably, the corresponding characteristics in the world. In this paper, the literature about these nonaccidental properties (NAPs) is reviewed to trace its historical roots, to list the properties that function as NAPs, and to discuss the psychological evidence for their detection and use. Against this background, four experiments are reviewed and four are fully described that were designed to test the perceptual use of skewed symmetry (SS), which results from orthographic projection of planar bilateral or mirror symmetry (BS). Despite the large symmetry advantage obtained in all experiments, SS is only perceived as BS-in-depth in cases of closed polygons or dot patterns with higher-order types of symmetry. In all random dot patterns and in some symmetric patterns with low "Gestalt", subjects relied on more local groupings which are qualitatively affine invariant, such as clusters based on proximity or curvilinearity. Based on previous approaches in the literature and these new findings, I suggest some distinctions between different ways of using NAPs, which might foster further research.     

Concept formation and categorization of complex,asymmetric, and impossible figures

Impossible figures are striking examples of inconsistencies between global and local perceptual structures, in which the overall spatial configuration of the depicted image does not yield a coherent three-dimensional object. In order to investigate whether structural “impossibility” is an important perceptual property of depicted objects, we used a category formation task in which subjects were asked to divide pictures of shapes into groups that seemed most natural to them. Category formation is usually unidimensional, such that sorting is dominated by a single perceptual property, so this task can serve as a measure of which dimensions are most salient. In Experiment 1, subjects received sets of 12 line drawings consisting of six possible and six impossible objects. Very few subjects grouped the figures by impossibility on the first try, and only half did so after multiple attempts at sorting. In Experiment 2, we investigated other global properties of figures: symmetry and complexity. Subjects readily sorted objects by complexity, but seldom by symmetry. In Experiment 3, subjects were asked to draw each of the figures before sorting them, which had only a minimal effect on categorization. Finally, in Experiment 4, subjects were explicitly instructed to divide the shapes by symmetry or impossibility. Performance on this task was perfect for symmetry, but not for impossibility. Although global properties of figures seem extremely important to our perception, the results suggest that some of these cues are not immediately obvious or salient for most observers.     

Detection of bilateral symmetry in complex biological images

The recognition of bilateral symmetry in simple dot patterns is reliably influenced by orientation. Performance is best when the axis of symmetry is vertical. We conducted two experiments to determine whether stimulus orientation also affects detection of the low levels of naturally occurring asymmetry in complex biological images. University students judged whether colour images displayed on a computer monitor possessed perfect bilateral symmetry. Stimuli were generated from high-resolution plan-view images of crabs and insects. In experiment 1, the asymmetric stimuli were the original animals, displayed on a standard black background. Symmetrical versions of each natural image were generated by sectioning the shape at the midline, copying and reflecting one side and then fusing the two halves together. To facilitate comparison of results with those obtained in earlier studies, we also presented dot patterns based upon both the slightly asymmetric and perfectly symmetrical natural images. Experiment 2 was designed to assess whether symmetry detection was dependent upon the markings and patterns on the body and appendages of the animals. The natural images were converted to silhouettes and tested against matched dot patterns. In both studies, images were presented in a random sequence with the axis of symmetry vertical, horizontal, oblique left, and oblique right. Performance with the biological images was consistently better than with the dot patterns. Abolishing fine detail did not appreciably reduce this effect. A pronounced vertical advantage was apparent with all stimuli, demonstrating that this phenomenon is robust despite considerable variation in image complexity. The implications of orientation effects for perception of natural structures are discussed.     

The effect of apparent movement on mental rotation

Eleven subjects were timed as they judged whether a small bar perpendicular to one side of a clockhand would point left or right if the hand was pointing upward (i.e., at the "12 o'clock" position). The clockhand was shown in two successive orientations 30 degrees apart, so that it was perceived to jump from one to the other in either a clockwise or a counterclockwise direction. Reaction times were consistent with the interpretation that the subjects "mentally rotated" the clockhand from its perceived orientation back to the upright before making their decisions. The direction of the jump influenced perceived orientation but did not influence either the direction or rate of mental rotation itself.     

Specialised higher-level mechanisms for facial-symmetry perception: evidence from orientation-tuning functions

Bilateral symmetry is important in many perceptual analyses from low-level figure-ground segmentation to higher-level face and object perception. Despite the success of low-level, image-based symmetry-detection models, these may not provide a complete account of symmetry perception. Better symmetry detection and stronger preferences for symmetry in upright faces than comparable patterns (e.g. inverted faces) that do not engage specialised face-coding mechanisms suggest a contribution of higher-level mechanisms to symmetry perception. We replicated better symmetry detection and stronger symmetry preferences for upright than inverted faces in experiment 1, and examined their orientation tuning in more detail in experiment 2. Decreasing performance as faces are mis-oriented away from the canonical upright orientation is the signature of specialised face-processing mechanisms, which are engaged less effectively as faces are mis-oriented. Lower-level symmetry-detection mechanisms, which operate better with vertical than horizontal, and horizontal than oblique, axes of symmetry would produce a W-shaped orientation-tuning function. Identical orientation-tuning functions were obtained for symmetry detection and preferences. Both declined with increasing mis-orientation over the 0 degrees-135 degrees range, consistent with a contribution from specialised face-coding mechanisms. Both increased from 135 degrees to 180 degrees, consistent with reliance on lower-level image-based mechanisms for severely misoriented faces. Taken together, the results implicate specialised, higher-level mechanisms in the detection of, and preference for, facial symmetry.     

Three-space inference from two-space stimulation.

Oblique contours sloping at 30 degrees with respect to the horizontal were presented alone, in combination to form chevrons, or with a vertical line to form arrowhead or Y patterns; they were projected onto a screen in the frontal parallel plane and viewed from positions that gave viewing angles of 90 degrees (normal to the screen's surface), 53 degrees, or 34 degrees. The perceived orientation of the contours, as assessed by a movable arm that the subjects set to be parallel to the obliques, changed monotonically as a function of viewing angle. The change was as great for single obliques as for combinations of obliques within the chevron, arrowhead, and Y patterns. The results of Experiment 1 were extended in Experiment 2, in which obliques at 30 degrees and 50 degrees with respect to the horizontal were presented singly or in combination as chevron patterns. It is argued that the results of both experiments indicate that single two-space oblique lines are immediately interpreted as lying in three-space and that the changes in perceived orientation are a consequence of this perceptual inference.     

Orientational Effects and Component Processes in Symmetry Detection

In previous research on symmetry detection, factors contributing to orientational effects (axis and virtual lines connecting symmetrically positioned dots) and component processes (axis selection and pointwise evaluation) have always been confounded. The reason is the restriction to bilateral symmetry (BS), with pointwise correspondences being orthogonal to the axis of symmetry. In our experiments, subjects had to discriminate random dot patterns from symmetries defined by combining 12 axis orientations (every 15°) with seven reflection angles (0°, yielding BS, and three clockwise and counterclockwise 15° steps, yielding skewed symmetry, SS). In Experiment 1, with completely randomized trial order, a significant interaction between axis and skewing angle was obtained, indicating that classically observed orientational effects are restricted to BS and that the orientation of the pointwise correspondences is important. These basic findings were replicated in three subsequent experiments, which differed in that they used blocks containing patterns with the same axis (Experiment 2), virtual lines orientation (Experiment 3), or their combination (Experiment 4). Based on a comparison between the results obtained by these manipulations, we suggest a possible reason for the failure of preattentive symmetry detection in the case of dot patterns with SS.     

Two-dimensional symmetric form discrimination: Fast learning,but notthat fast

Several authors have characterized a striking phenomenon of perceptual learning in visual discrimination tasks. This learning process is selective for the stimulus characteristics and location in the visual field. Since the human visual system exploits symmetry for object recognition we were interested in exploring how it learns to use preattentive symmetry cues for discriminating simple, meaningless, forms. In this study, similar to previous studies of perceptual learning, we asked whether the effects of practice acquired in the discrimination of pairs of shape with a specific orientation of the symmetry axis would transfer to the discrimination of shapes with different orientation of symmetry axis, or to shapes presented in different areas of the visual field. We found that there was no learning transfer between forms with very different axes of symmetry (90° apart). Interestingly, however, we found a transfer of learning effect to horizontally oriented symmetry axis from a condition with an axis of symmetry differing by 45°. Also it appears that some subjects took a longer time to learn than the typical fast learning paradigm would predict. Data showed that when observers practice discrimination of meaningless symmetric forms, consistent improvement in the performance occurs. This improvement is lasting over days, and it tends to be specific for the area of the visual field trained. We will discuss results from some of the observers whose learning was not fast, but who actually improved with more practice and with large time intervals (1 day) between training sessions.     

Temporal characteristics of line orientation identification

The hypothesis that identification of line orientation is based on different mechanisms--a detector mechanism at large orientation differences and a computational one at small orientation differences--was tested in three experiments. The first two experiments compared reaction time and time of complete temporal summation (tc) in two tasks, line detection and line orientation identification. Identification at orientation differences 15 degrees or more was similar to detection in several respects, suggesting that it was accomplished according to the principle of "labeled lines." In agreement with the initial hypothesis, identification at differences smaller than 15 degrees had a slower time course and could not be explained by the "labeled lines" principle. Experiment 3 explored the orientation acuity as a function of exposure duration and stimulus energy. Energy could not completely substitute for time in providing high orientation acuity, a result suggesting the involvement of neurophysiological mechanisms of large time constants.     

Interactions among emergent relations during equivalence class formation

The interactions among symmetry, transitivity, and equivalence tests during the formation of 3-member equivalence classes were studied with 14 college students. After training AB and BC, a test with BA, CB, AC, and CA was conducted concurrently. Failure led to serial testing with probes for CA equivalence, BA symmetry, CA equivalence, CB symmetry, CA equivalence, AC transitivity, and CA equivalence. For five subjects, equivalence tests were passed immediately once BA and CB symmetry as well as AC transitivity had been induced. Thus, symmetry and transitivity were precursors for successful performance on equivalence tests. The conjoint function of symmetry and transitivity was assessed with the equivalence probes. As the equivalence probes were passed immediately, the presence of symmetry alone and transitivity alone were sufficient for their conjoint function without additional intervention. For different subjects, transitivity alone and symmetry were induced either directly with BA, CB, or AC probes or indirectly with equivalence probes. Equivalence probes can also induce various combinations of symmetry and transitivity. Thus, different subjects formed classes in various patterns at different rates.     

The Goldmeier effect in adults and children: environmental, retinal, and phenomenal influences on judgments of visual symmetry

Adults judge that patterns symmetrical about the vertical axis are more similar to standard patterns symmetrical about both major orthogonal axes than are patterns which are symmetrical only about the horizontal axis (the Goldmeier effect). Thus, symmetry about the vertical axis is more salient for adults than symmetry about the horizontal axis. Two experiments are reported in which subjects from three age groups (preschool, 8 years old, and adult) were given Goldmeier problems under different conditions. In experiment 1 three head-tilt conditions were used (0 degrees, 45 degrees, 90 degrees); in experiment 2 there were four conditions defined by head orientation (0 degrees, 90 degrees) and phenomenal instructions (top of figure at 0 degrees or at 90 degrees). In both experiments, increasing head tilt from 0 degrees decreased the consistency with which the environmentally vertical pattern was chosen. Noncorrespondence between the three spatial frameworks (environmental, retinal, and phenomenal) failed to produce biases in favor of either retinal-egocentric or phenomenal systems. For rotated adult subjects in experiment 2, 0 degrees phenomenal instructions strengthened an environmental bias, and 90 degrees phenomenal instructions shifted responses toward a retinal bias. These findings provide strong refutation of explanations for symmetry perception that are based solely upon the anatomical symmetry of the visual system. The data also fail to support arguments for environmental or phenomenal frameworks as singular influences. The results are best explained in terms of failure of constancy mechanisms to coordinate environmental and retinal information as a function of degree of head rotation and stimulus complexity.     

光栅朝向分辨学习中存在关于45°对角线对称的镜像迁

采用光栅朝向分辨任务来探讨视知觉学习中是否存在关于45°对角线对称的镜像迁移现象。训练被试分辨15°或75°朝向3或5天,每天约1小时,训练前后测量15°、75°、45°朝向的分辨阈值。通过训练,训练朝向（15°或75°）的阈值下降,该学习效应没有迁移至45°朝向,但基本迁移到关于45°对称的朝向（75°或15°）上。这提示,视知觉学习可能发生在中间视皮层,该皮层同时具有一定的朝向特异性和关于45°对角线对称的镜像迁移性     

Feature analysis and the role of similarity in preattentive vision.

Texture arrays of line elements at various orientations were used to study three phenomena of preattentive vision. Subjects were asked (1) to discriminate texture areas and to distinguish their form (experiments on texture segmentation); (2) to detect salient or vertical line elements (experiments on pop-out); and (3) to identify configurations of similar or or dissimilar targets (experiments on grouping). Within the patterns, line orientation was systematically varied to distinguish the effect of differences between areas from the effect of similarity within areas. In all of the experiments, performance was found to depend on local orientation contrast at texture borders rather than on the analysis of line orientation itself. Texture areas were correctly identified only when the orientation contrast at the border well exceeded the overall variation of line orientation in the pattern. Similarly, only target elements with high local orientation contrast were detected fast and "in parallel". Targets with an orientation contrast lower than background variation required serial search. Preattentive grouping was found to depend on saliency, as defined by local orientation contrast, but not on the similarity of line elements. In addition to local orientation contrast, which played an important role in all of the visual phenomena studied, influences from the alignment of line elements with the outline of a figure were also seen.