Reference frames in mental rotation

Four experiments are reported that investigate whether images or reference frames are transformed during a mental rotation task. In all experiments a display of four identical letters (P1) was presented at either +90 degrees or -90 degrees from upright, and subjects had to decide whether the letters were normal or mirror-image reflections. A single letter (P2) was then presented 100 ms later in a variable orientation with the same task instructions. Reaction times to P2 were assessed to determine whether an image of P2 was rotated to upright or whether an internal reference frame was rotated into congruence with P2 from the orientation of P1. The results as a whole suggest that transformations of P2 can be initiated either relative to upright or relative to the orientation of P1. They further indicate that the probability of using each reference orientation can be changed by procedural variations. The findings are most parsimoniously interpreted as suggesting that mental rotation involves the transformation of reference frames rather than the transformation of template-like representations.     

Out with the old? The role of selective attention in retaining targets in partial report

In the partial-report task, subjects are asked to report only a portion of the items presented. Selective attention chooses which objects to represent in short-term memory (STM) on the basis of their relevance. Because STM is limited in capacity, one must sometimes choose which objects are removed from memory in light of new relevant information. We tested the hypothesis that the choices among newly presented information and old information in STM involve the same process—that both are acts of selective attention. We tested this hypothesis using a two-display partial-report procedure. In this procedure, subjects had to select and retain relevant letters (targets) from two sequentially presented displays. If selection in perception and retention in STM are the same process, then irrelevant letters (distractors) in the second display, which demanded attention because of their similarity to the targets, should have decreased target report from the first display. This effect was not obtained in any of four experiments. Thus, choosing objects to keep in STM is not the same process as choosing new objects to bring into STM.     

Development of three-dimensional form perception

In three experiments with infants and one with adults we explored the generality, limitations, and informational bases of early form perception. In the infant studies we used a habituation-of-looking-time procedure and the method of Kellman (1984), in which responses to three-dimensional (3-D) form were isolated by habituating 16-week-old subjects to a single object in two different axes of rotation in depth, and testing afterward for dishabituation to the same object and to a different object in a novel axis of rotation. In Experiment 1, continuous optical transformations given by moving 16-week-old observers around a stationary 3-D object specified 3-D form to infants. In Experiment 2 we found no evidence of 3-D form perception from multiple, stationary, binocular views of objects by 16- and 24-week-olds. Experiment 3A indicated that perspective transformations of the bounding contours of an object, apart from surface information, can specify form at 16 weeks. Experiment 3B provided a methodological check, showing that adult subjects could neither perceive 3-D forms from the static views of the objects in Experiment 3A nor match views of either object across different rotations by proximal stimulus similarities. The results identify continuous perspective transformations, given by object or observer movement, as the informational bases of early 3-D form perception. Detecting form in stationary views appears to be a later developmental acquisition.     

Reaction time to letter name or letter case

Subjects were shown two letters from the set BDGbdg. In one condition, subjects were required to decide whether or not the letters had the same name. In the other condition, subjects decided whether or not the two letters were presented in the same case. Reaction times were always faster when the two letters on a given trial were physically identical. However, there was no difference in the speed of a name match or a case match when the two letters were not physically identical. Since subjects could have based a case match on the presence or absence of a single feature — a protruding vertical line — it was concluded that subjects are not able to selectively attend to a single visual feature in order to identify a letter. Rather, a subject analyzes several features in parallel in order to arrive at a simultaneous decision about a letter's name or case.     

Representation of Object Orientation in Children: Evidence from Mirror-Image Confusions

Although many cognitive functions require information about the orientations of objects, little is known about representation or processing of object orientation. Mirror-image confusion provides a potential clue. This phenomenon is typically characterized as a tendency to confuse images related by left-right reflection (reflection across an extrinsic vertical axis). However, in most previous studies the stimuli were inadequate for identifying a specific mirror-image (or other) relationship as the cause of the observed confusions. Using stimuli constructed to resolve this problem, Gregory and McCloskey (2010) found that adults' errors were primarily reflections across an object axis, and not left-right reflections. The present study demonstrates that young children's orientation errors include both object-axis reflections and left-right reflections. We argue that children and adults represent object orientation in the same coordinate-system format (McCloskey, 2009), with orientation errors resulting from difficulty encoding or retaining one (adults) or two (children) specific components of the posited representations.     

Representation of object orientation in children: Evidence from mirror-image confusions

Although many cognitive functions require information about the orientations of objects, little is known about representation or processing of object orientation. Mirror-image confusion provides a potential clue. This phenomenon is typically characterized as a tendency to confuse images related by left–right reflection (reflection across an extrinsic vertical axis). However, in most previous studies the stimuli were inadequate for identifying a specific mirror-image (or other) relationship as the cause of the observed confusions. Using stimuli constructed to resolve this problem, Gregory and McCloskey (2010) found that adults’ errors were primarily reflections across an object axis, and not left–right reflections. The present study demonstrates that young children's orientation errors include both object–axis reflections and left–right reflections. We argue that children and adults represent object orientation in the same coordinate-system format (McCloskey, 2009), with orientation errors resulting from difficulty encoding or retaining one (adults) or two (children) specific components of the posited representations.     

Viewpoint-dependent recognition of scenes

Three experiments investigated scene recognition across viewpoint changes, involving same/different judgements on scenes consisting of three objects on a desktop. On same trials, the comparison scene appeared either from the same viewpoint as the standard scene or from a different viewpoint with the desktop rotated about one or more axes. Different trials were created either by interchanging the locations of two or three of the objects (location change condition), or by rotating either one or all three of the objects around their vertical axes (orientation change condition). Response times and errors increased as a function of the angular distance between the standard and comparison views, but this effect was bigger for rotations around the vertical axis than for those about the line of sight or horizontal axis. Furthermore, the time to detect location changes was less than that to detect orientation changes, and this difference increased with increasing angular disparity between the standard and comparison scenes. Rotation times estimated in a double-axis rotation were no longer than other rotations in depth, indicating that alignment was not necessarily simpler around a "natural" axis of rotation. These results are consistent with the hypothesis that scenes, like many objects, may be represented in a viewpoint dependent manner and recognized by aligning standard and comparison views, but that the alignment of scenes is not a holistic process.     

Characteristic views and the visual inspection of simple faceted and smooth objects: 'tetrahedra and potatoes'

The way in which human subjects distribute their time when attempting to learn the surface appearance of objects placed on a stand free to rotate about its vertical axis was investigated. Experiments were undertaken to establish whether observers concentrate their time on particular views and, if so, to determine the image characteristics of the preferred views. For tetrahedra, subjects concentrated on views which presented a face or an edge centred on the line of sight. Both of these views were symmetric about the vertical axis. For potatoes as examples of opaque smooth objects, subjects concentrated on four views in which the object's principal (long) axis was oriented side-on or end-on to their line of sight. For such views the horizontal width (and surface area) of the object's image had maximum and minimum values. Preferred views were not systematically related to views defined as stable from the appearance of surface boundaries or 'singularities'.     

Interaction between perceived and imagined rotation

In Experiment 1, subjects performed a mental-rotation task in which they were timed as they decided whether rotated letters were normal or backwards. Between presentations of the letters, they watched a rotating textured disk that induced an aftereffect of rotary movement on the letters. The function relating reaction times to orientation was influenced asymmetrically by the aftereffect, suggesting that perceived movement interacts with imagined movement. Experiment 2 showed that the aftereffect produced a negligible influence on perceived orientation, suggesting that the influence of the aftereffect on mental rotation was not caused by changes in the perceived orientations of the letters. Detailed analysis of the mental-rotation functions suggested that the aftereffect may sometimes have induced subjects to rotate letters through the larger rather than the smaller angle back to the upright where the aftereffect was in the appropriate direction.     

身体部位心理旋转的认知与神经机制

除了经典的对于抽象几何图形或字母的心理旋转任务,还有一类心理旋转以手、脚等身体部位图片作为反应刺激。在身体部位心理旋转中,被试一般想象的是自身身体旋转,想象过程受当前身体姿势与身体生理局限性的影响。而在客体心理旋转中,被试往往将刺激作为外在的客体进行想象旋转。两类心理旋转任务都被发现存在顶叶区域的激活,但运动相关皮层的激活更多地在身体部位心理旋转任务中被发现。关于儿童身体部位心理旋转与实际运动的联系紧密性的讨论尚未得到一致的结论,未来研究需要继续探讨随着年龄增长,身体部位心理旋转受生理局限性的影响是增强还是减弱。身体图片加工的自动性,身体部位心理旋转的可塑性也是未来研究可以深入探讨的问题。对于身体部位心理旋转的深入了解也有助于这一任务在临床诊断治疗、运动员与飞行员训练和选拔中的应用。     

An eye movement analysis of "mental rotation" of simple scenes

Participants saw a standard scene of three objects on a desktop and then judged whether a comparison scene was either the same, except for the viewpoint of the scene, or different, when one or more of the objects either exchanged places or were rotated around their center. As in Nakatani, Pollatsek, and Johnson (2002), judgment times were longer when the rotation angles of the comparison scene increased, and the size of the rotation effect varied for different axes and was larger for same judgments than for different judgments. A second experiment, which included trials without the desktop, indicated that removing the desktop frame of reference mainly affected the y-axis rotation conditions (the axis going vertically through the desktop plane). In addition, eye movement analyses indicated that the process was far more than a simple analogue rotation of the standard scene. The total response latency was divided into three components: the initial eye movement latency, the first-pass time, and the second-pass time. The only indication of a rotation effect in the time to execute the first two components was for z-axis (plane of sight) rotations. Thus, for x- and y-axis rotations, rotation effects occurred only in the probability of there being a second pass and the time to execute it. The data are inconsistent either with an initial rotation of the memory representation of the standard scene to the orientation of the comparison scene or with a holistic alignment of the comparison scene prior to comparing it with the memory representation of the standard scene. Indeed, the eye movement analysis suggests that little of the increased response time for rotated comparison scenes is due to something like a time-consuming analogue process but is, instead, due to more comparisons on individual objects being made (possibly more double checking).     

Aiming error under transformed spatial mappings suggests a structure for visual-motor maps

Transformed spatial mappings were used to perturb normal visual-motor processes and reveal the structure of internal spatial representations used by the motor control system. In a 2-D discrete aiming task performed under rotated visual-motor mappings, the pattern of spatial movement error was the same for all Ss: peak error between 90 degrees and 135 degrees of rotation and low error for 180 degrees rotation. A two-component spatial representation, based on oriented bidirectional movement axes plus direction of travel along such axes, is hypothesized. Observed reversals of movement direction under rotations greater than 90 degrees are consistent with the hypothesized structure. Aiming error under reflections, unlike rotations, depended on direction of movement relative to the axis of reflection (see Cunningham & Pavel, in press). Reaction time and movement time effects were observed, but a speed-accuracy tradeoff was found only for rotations for which the direction-reversal strategy could be used. Finally, adaptation to rotation operates at all target locations equally but does not alter the relative difficulty of different rotations. Structural properties of the representation are invariant under learning.     

Transformation processes upon the visual code

Seven experiments investigated whether orientation-dependent latency functions for the visual code resemble those observed in studies of mental rotations of visual images. The subjects were required to perform “same-different” classifications of two simultaneously presented letters. The dependent variables considered were reaction time IRT and accuracy. Experiments 1, 2, 4, 5, and 6 showed that subjects could correctly classify two different letters on the basis of the visual code without preceding transformations. Experiments 1, 2, and 7 showed orientationdependent effects for “same“ responses. It appeared, however, that orientation functions for the visual cede were clearly different from those previously observed for visual images. In addition, the findings of Experiments 4, 5, and 6 indicated that a frame that jointly rotated with the disoriented letters could eliminate the orientation-dependent effects for “same” responses. Experiment 7 showed that the results of Experiments 4, 5, and 6 must be attributed to the structural characteristics of the frame and not to a directional cue. The results of Experiment 3 seemed to demonstrate that transformations did not occur when the subjects used the phonetic code to classify the letters. Overall, the results of the seven experiments were considered to provide a demonstration of the importance of the distinction between the operations on visual images and those on the visual code.     

Effect of orientation on visual and vibrotactile letter identification

The effect of stimulus orientation of letters presented either visually or vibrotactually was examined to obtain basic information on sensory substitution using the tactile sense. The reaction time (RT) to identify the letters F and R presented in normal or mirror-image form at four orientations each was measured. In addition, conditions of 0 degree and 270 degrees of head rotation from vertical and arm rotation from the midline axis were employed. Data from 5 trained subjects showed that vibrotactile RTs were always longer than visual RTs. Stimulus rotation away from normal orientation increased visual RTs significantly but not vibrotactile RTs. Visual orientation effect then seemed to be determined by the body-coordinate system but not the vibrotactile orientation. Although further studies are warranted, from the results of this experiment, any convenient and constant stimulus orientation could be used with a wearable vibrotactile display system to exploit passive touch.     

Effects of distance between objects and distance from the vertical axis on shape identity judgments

In three experiments, we independently manipulated the angular disparity between objects to be compared and the angular distance between the central axis of the objects and the vertical axis in a mental rotation paradigm. There was a linear increase in reaction times that was attributable to both factors. This result held whether the objects were rotated (with respect to each other and to the upright) within the frontal-parallel plane (Experiment 1) or in depth (Experiment 2), although the effects of both factors were greater for objects rotated in depth than for objects rotated within the frontal-parallel plane (Experiment 3). In addition, the factors interacted when the subjects had to search for matching ends of the figures (Experiments 1 and 2), but they were additive when the ends that matched were evident (Experiment 3). These data may be interpreted to mean that subjects normalize or reference an object with respect to the vertical upright as well as compute the rotational transformations used to determine shape identity.     

Modality-specific coding in matching letters

Auditory and visual similarity was manipulated in a same-different reaction-time task to investigate the use of modality-specific codes in same-different judgments for pairs of letters. Experiment 1 showed that letters presented simultaneously in the auditory and visual modalities were matched on the auditory dimension. In Experiment 2, the letters were presented sequentially, and the modality of the second letter was randomly varied. Subjects matched the pairs on the modality dimension of the second letter even though the modality could not be reliably predicted. In Experiment 3, subjects judged adjacent pairs of letters presented for 50 msec, and in one condition they also named the letters. Matches were made on visual codes in both conditions. In general, the results indicate that when subjects are instructed to determine if two letters are the same, the letters will be matched on a modality-specific code in a way that will minimize the information processing necessary to complete the match.     

Mental rotation with egocentric and object-based transformations

Two experiments were conducted to address methodological issues with past studies investigating the influence of egocentric and object-based transformations on performance and sex differences in mental rotation. In previous work, the egocentric and object-based mental rotation tasks confounded the stimulus type (embodied vs. non-embodied) and transformation task (egocentric vs. object-based). In both experiments presented here, the same stimuli were used regardless of the type of transformation but task instructions were modified to induce either egocentric (left–right judgment) or object-based (same–different judgment) processing. Experiment 1 used pairs of letters whereas Experiment 2 presented pairs of line-drawings of human hands. For both experiments, it was hypothesized that the mental rotation slope for response time would be steeper for object-based than for egocentric transformations. This hypothesis was verified in both experiments. Furthermore, Experiment 2 showed a reduced male advantage for egocentric compared to object-based rotations, whereas this pattern was reversed for Experiment 1. In conclusion, the present study showed that the influence of the type of transformation involved in mental rotation can be examined with the same set of stimuli simply by modifying task instructions.     

Flipping and spinning: Spatial transformation procedures in the identification of rotated natural objects

The proposal that identification of inverted objects is accomplished by either a relatively slow rotation in the picture plane or a faster rotation in the depth plane about the horizontal axis was tested. In Experiment 1, subjects decided whether objects at 0° or 180° corresponded to previously learned normal views of the upright objects, or were mirror images. Instructions to mentally flip an inverted object in the depth plane to the upright produced faster decision times than did instructions to mentally spin the object in the picture plane. In Experiment 2, the effects of orientation were compared across an object-naming task and a normal-mirror task for six orientations from 0° to 300°. In the normal-mirror task, objects at 180° were cued for rotation in the picture plane or in the depth plane in equal numbers. The naming function for one group of subjects did not differ from the normalmirror function where inverted objects had been mentally rotated to the upright. For both functions, response time (RT) increased linearly from 0° to 180° and the slopes did not differ. The naming function for a second group of subjects did not differ from the normal-mirror function where inverted objects had been mentally flipped to the upright. For both functions, RT increased linearly at a similar rate from 0° to 120°, but decreased from 120° to 180°. The results are discussed in terms of theories of orientation-specific identification.