Regularity of symmetry verticality guides perceptual judgments of objects

Previous research indicated that most salient, real-world objects possess natural regularities that observers commonly assume in perceptual judgments of figural orientation and interpretation. Regularities include 3-dimensionality, bilateral symmetry, and the tendency for object tops to possess more salient information than bottoms. Thus, when observers interpret randomly shaped figures, they reliably impose volume, bilateral symmetry, and top and front orientation directions, even when figures are 2-dimensional and asymmetric. We confirmed generalizability for observers to assume these regularities with stimuli that vary in complexity, and we found evidence supporting another regularity, that of symmetry verticality (symmetry about a vertical axis). Findings support use of a family of perceptual heuristics corresponding to natural regularities that constrain stimulus indeterminacy and help guide judgment of object orientation and interpretation.     

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.     

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.     

The effect of vertical and horizontal symmetry on memory for tactile patterns in late blind individuals

Visual stimuli that exhibit vertical symmetry are easier to remember than stimuli symmetric along other axes, an advantage that extends to the haptic modality as well. Critically, the vertical symmetry memory advantage has not been found in early blind individuals, despite their overall superior memory, as compared with sighted individuals, and the presence of an overall advantage for identifying symmetric over asymmetric patterns. The absence of the vertical axis memory advantage in the early blind may depend on their total lack of visual experience or on the effect of prolonged visual deprivation. To disentangle this issue, in this study, we measured the ability of late blind individuals to remember tactile spatial patterns that were either vertically or horizontally symmetric or asymmetric. Late blind participants showed better memory performance for symmetric patterns. An additional advantage for the vertical axis of symmetry over the horizontal one was reported, but only for patterns presented in the frontal plane. In the horizontal plane, no difference was observed between vertical and horizontal symmetric patterns, due to the latter being recalled particularly well. These results are discussed in terms of the influence of the spatial reference frame adopted during exploration. Overall, our data suggest that prior visual experience is sufficient to drive the vertical symmetry memory advantage, at least when an external reference frame based on geocentric cues (i.e., gravity) is adopted.     

Complexity and goodness of dot patterns varying in symmetry

Summary Two experiments were performed to specify stimulus determinants of pattern complexity and pattern goodness. Dot patterns distributed in 3×3 and 4×4 matrices with a rectilinear frame were used in Experiment 1, and dot patterns in hexagonal frameworks with a circular frame were used in Experiment 2. The patterns were invariant for transformations of rotation or reflection, and formed symmetry groups of different orders, i.e., cyclic and dihedral groups. The complexity and goodness of the patterns depended upon such stimulus variables as follows: (1) complexity decreased with the order of symmetry groups with equal weights for cyclic and dihedral groups, whereas goodness increased with the order of both symmetry groups with different weights; (2) the simplicity and goodness of patterns with a vertical axis were greater than those with a horizontal axis and those with an oblique one; (3) the complexity of the patterns that had collinear elements with equal length was rated the simplest; (4) pattern goodness increased as a function of the number of dots and the concentrations of dot to rotation/reflection axis in 3×3 and 4 × 4 matrices. Thus, complexity and goodness of pattern differed with respect to these stimulus variables.     

The preference for symmetry in flower-naïve and not-so-naïve bumblebees

Truly flower-naïve bumblebees, with no prior rewarded experience for visits on any visual patterns outside the colony, were tested for their choice of bilaterally symmetric over asymmetric patterns in a radial-arm maze. No preference for symmetry was found. Prior training with rewarded black and white disks did, however, lead to a significant preference for symmetry. The preference was not specific to symmetry along the vertical axis: a preference for horizontal symmetry was found as well. The results challenge the notion that a preference for bilateral symmetry is unlearned. The preference for symmetry was the product of non-differential conditioning.     

Symmetry, gestalt and information theory

Two kinds of patterns were made up out of crosses. The first kind was symmetrical and the second contained a sub-pattern repeated in the same orientation. Subjects were requested to reproduce the stimuli after viewing them for 2 sec. It was found that there was no difference between the two kinds of stimuli when symmetry about the horizontal axis was involved but that when symmetry about the vertical axis occurred the symmetrical stimuli were reproduced more accurately than the repeated stimuli. Introduction of contrasting colours on the two portions of each pattern decreased the frequency of correct responses, whilst stressing the grid line subdividing the stimuli into two portions containing the same information had no significant effect.     

Effect of stimulus opening size in global dominance with orientation classification task

The aims of this study is to examine whether global dominance depends on the opening size of the stimulus with concentric hierarchical figures and orientation classification task and to determine the role of the salience of global opening and its coincidence with vertical symmetry axis of context. In the first experiment, participants had to indicate the opening direction of stimuli, which were open-left and open-right figures. Three openings were included: 10, 25 and 50% of the total circle perimeter. The results showed a local advantage with stimuli of 10%, absence of global or local advantage with stimuli of 25% and global advantage with stimuli of 50%. In the second experiment, stimuli with an opening of 50% were presented randomly in several positions in the visual field in order to avoid the coincidence of global opening with the vertical symmetry axis of context. The results showed an absence of global or local advantage. These findings indicate that global dominance with orientation classification task depends on stimulus characteristics such as opening size, and strategies used in visual recognition.     

Why do children confuse mirror-image obliques?

Thirty-five children aged from 4.17 to 6.58 years were given a delayed-matching task in which they had to choose on each trial which of two lines was the same as a previously displayed standard line. Their choices were no better than random when the lines differed in degree of slope but not in left-right orientation and were only marginally more accurate when the lines were left-right mirror images. Performance improved significantly when the lines differed both in degree of slope from the vertical and in left-right orientation and improved still further if at least one of the lines was horizontal or vertical. The results suggest that young children have extreme difficulty encoding in memory either the degree of slope or the left-right orientation of an oblique line.     

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.     

Detection of symmetry as a function of angular orientation.

Subjects decided as quickly as possible whether dot patterns were or were not symmetrical about a line. Their decision times were shorter when the line was verticle and increased as the angle between the line and the verticle increased. This orientation function was essentially the same whether or not the subjects knew in advance what the orientation of the line would be. When the subjects tilted their heads, the function shifted in the direction of the head tilt, indicating that it was tied more closely to retinal than to gravitational coordinates. These data can be interpreted to mean that people mentally rotate patterns to a vertical orientation before judging their symmetry. This in turn suggests that the "template" for detecting symmetry may itself be embedded symmetrically in the brain.     

Identification of symmetry: Effects of stimulus orientation and head position

It has been argued that the perceptual advantage of symmetry depends upon the essentially symmetrical properties of the visual system. According to this explanation, the ease of identification of symmetries about different axes of orientation should decrease with increasing distance from the vertical: Reaction times to vertical symmetry should be faster than those to diagonal symmetry, which in turn should be faster than those to horizontal symmetry. Previous research demonstrating this pattern of responding employed stimuli with linear axes. In the present study, the subjects viewed tachistoscopically presented symmetrical and asymmetrical dot patterns (which had no explicit axes) in one of three head positions: upright, 45 deg left, and 45 deg right. The subjects’ performance failed to support the structural explanation: Identification of symmetry is equivalently fast for vertical and horizontal; vertical and horizontal show strong advantages over obliques, and this general advantage follows retinal coordinates. Findings are discussed in light of alternative theories of symmetry processing.     

Invariant recognition of natural objects in the presence of shadows

Shadows are frequently present when we recognize natural objects, but it is unclear whether they help or hinder recognition. Shadows could improve recognition by providing information about illumination and 3-D surface shape, or impair recognition by introducing spurious contours that are confused with object boundaries. In three experiments, we explored the effect of shadows on recognition of natural objects. The stimuli were digitized photographs of fruits and vegetables displayed with or without shadows. In experiment 1, we evaluated the effects of shadows, color, and image resolution on naming latency and accuracy. Performance was not affected by the presence of shadows, even for gray-scale, blurry images, where shadows are difficult to identify. In experiment 2, we explored recognition of two-tone images of the same objects. In these images, shadow edges are difficult to distinguish from object and surface edges because all edges are defined by a luminance boundary. Shadows impaired performance, but only in the early trials. In experiment 3, we examined whether shadows have a stronger impact when exposure time is limited, allowing little time for processing shadows; no effect of shadows was found. These studies show that recognition of natural objects is highly invariant to the complex luminance patterns caused by shadows.     

Is there an assignment of top and bottom during symmetry perception?

We report data from a discrimination task in which participants had to decide whether a single-item display was either vertically symmetric or asymmetric. This decision was found to be easier when items with a top bottom polarity were placed in an orientation where the wide end was the base of the stimulus and the narrow end was the top. The difference in reaction times between this orientation and its inversion was about 10 ms. We suggest that top and bottom labels are assigned to stimuli during the detection of bilateral symmetry.     

Seeing versus imagining movement in depth

Subjects judged the quality of rigid motion between pairs of three-dimensional drawings that differed by a rotation in depth. The figures were aligned with, and rotated around, either the vertical axis or an axis that was oblique with respect to the XYZ co-ordinate system. Rated quality of motion decreased with increasing angular disparity between the figures and with decreasing stimulus duration, regardless of whether the figures were vertical or oblique. The same subjects then participated in a mental rotation task using the same stimuli and angular disparities. An effect of principal axis emerged, such that subjects took longer to make decisions about obliquely aligned stimuli than about vertically aligned stimuli, especially if they received the oblique stimuli first. These data imply that perceived versus imagined movement through the same trajectory involves different processes. Whereas the apparent motion system performs its computations relatively automatically, the processes involved in mental rotation are more strategic in nature.     

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 similarity of mirror images in infancy

Perception of mirror images by three-to four-month infants was studied in five experiments using habituation paradigms. In the first experiment, babies discriminated right profiles of two different faces but not the left and right profile of the same face. In the second, babies discriminated a 45° oblique from a vertical line, but not the oblique from its mirror image. In the third, babies discriminated oblique lines that differed by 50° and were not mirror images. In the final experiments. 90° rotations of a ?-shape were discriminated but not 180° rotations that formed lateral or vertical mirror images. These results demonstrated that although babies were able to discriminate differences in orientation (even among obliques) they tended to view mirror images, especially lateral mirror images, as equivalent stimuli. We propose that the perceptual equivalence of mirror images reflects an adaptive mode of visual processing; mirror images in nature are almost always aspects of the same object, and they usually need not be discriminated. The relations of the perceptual similarity of mirror images to the ontogeny of the object concept and to the development of reading are discussed.     

Floral guidance of learning a preference for symmetry by bumblebees

This study examines the mechanism underlying one way in which bumblebees are known to develop a preference for symmetric patterns: through prior non-differential reinforcement on simple patterns (black discs and white discs). In three experiments, bees were given a choice among symmetric and asymmetric black-and-white non-rewarding patterns presented at the ends of corridors in a radial maze. Experimental groups had prior rewarded non-discrimination training on white patterns and black patterns, while control groups had no pre-test experience outside the colony. No preference for symmetry was obtained for any of the control groups. Prior training with circular patterns highlighting a horizontal axis of symmetry led to a specific subsequent preference for horizontal over vertical symmetry, while training with a vertical axis abolished this effect. Circles highlighting both axes created a general avoidance of asymmetry in favour of symmetric patterns with vertical, horizontal or both axes of symmetry. Training with plain circles, but not with deformed circles, led to a preference for symmetry: there was no evidence that the preference emerged just by virtue of having attention drawn away from irrelevant pattern differences. Our results point to a preference for symmetry developing gradually through first learning to extract an axis of symmetry from simple patterns and subsequently recognizing that axis in new patterns. They highlight the importance of continued learning through non-differential reinforcement by skilled foragers. Floral guides can function not only to guide pollinators to the source of reward but also to highlight an axis of symmetry for use in subsequent floral encounters.     

Effects of pattern orientation and number of symmetry axes on the detection of mirror symmetry in dot and solid patterns

It has been postulated that as the number of axes of symmetry in a pattern increases, so pattern 'goodness' increases. Recently, a distinction was made between two different theoretical accounts of regularity or 'goodness' in relation to patterns with mirror symmetry: the 'transformational' and the 'holographic' models. It was argued that the former predicts a 'goodness' ordering of four > three > two > one whereas the latter predicts four > two > three > one, where '>' means greater regularity or goodness. In three experiments, we have tested these predictions. In experiment 1, we measured percentage correct and reaction time to dot patterns which had one, two, three, or four axes of symmetry and were flashed for 150 ms. Experiment 2 was identical except that patterns were presented for 2000 ms. In experiment 3, dot patterns were replaced by solid shapes which also had one, two, three, or four axes of symmetry. Although it was found that stimuli with four axes clearly allowed superior performance to that of stimuli with one axis, results obtained with stimuli with two and three axes were almost identical and in between those obtained with one and four axes. The data thus support the suggestion that extra axes add 'goodness' to symmetrical patterns but not in a monotonic fashion.