The effect of variation of frame shape on the angular function of the rod-and-frame illusion

The angular function of the rod-and-frame illusion was studied under conditions of variation in frame shape. The results support predictions arising from the hypothesis that as a frame is varied in tilt, vertical settings of a rod will be in error in the direction of the major frame axis closest to true vertical.     

Determinants of the rod and frame effect: The role of retinal size

In Experiment 1, base-out prisms were used to alter perceived size and distance to a luminous rod and frame while the retinal size remained unchanged. The rod-and-frame effect (RFE) was the same, whether the display was viewed directly or through the prisms. In Experiment 2, one large and one small rod-and-frame display were placed at distances such that they produced identical retinal angles. This was replicated at three different sets of distances. Perceived size and distance of the large and small frame of identical retinal angle interacted with the observation distance, such that at near distances the large frame was perceived as larger and farther than the small frame while, at far distances, both types of estimates converged to a constant value. In contrast, the RFE was identical for the large and small frames matched in retinal angle, but diminished with distance. In both experiments, the RFE varied precisely with variation in retinal angle. Implications of the role of retinal angle in the RFE and for the interpretation of individual differences were discussed.     

The role of frame size on vertical and horizontal observers in the rod-and-frame illusion.

The rod-and-frame illusion was used to examine a proposed distinction between the mechanism responsible for frame effects on rod-adjustment errors with large displays and the mechanism responsible for errors with small displays. It was suggested that visual-vestibular mechanisms are involved only when the rod is surrounded by a large tilted frame. Errors in the perceived vertical with small frame would instead be due to purely visual mechanisms. To examine this dual process model, we compared errors at small and large frame when the body was vertical or horizontal. There is evidence to suggest that tilting the body affects visual-vestibular interactions, but there is no reason to expect that body tilt would affect intravisual interactions. Hence, we hypothesized that body tilt would increase errors for large frame, but not for small frame. Eight subjects were tested in four different conditions, corresponding to the combination of two body orientations (vertical versus horizontal) and two frame sizes (47.5 versus 10.5 deg of visual angle). Fourier analysis of data was performed. Repeated measures ANOVA tested the hypothesis about frame size and body orientation. The hypothesis was not confirmed. More specifically, we found that tilting the body increased errors for the small frame as well as for the large frame. The interaction between frame size and body orientation was not significant. Results are discussed in relation to the proposed dual-process model.     

The role of cognitive factors in the rod-and-frame effect

We compared the contribution and the effectiveness of modulating the orientation perception of two types of visual information: the visual frame and the visual polarity of objects. In experiment 1, we examined the effect of a square frame, a mouse, an elephant, and a map of France on the apparent vertical. In the upright position, despite the presence of tilted individual component features, the visual objects had no illusory visual tilt effects. When tilted, these objects had a substantial effect on the direction that appeared to be vertical. However, rod-setting errors were smaller in the inducing objects than when observed with the frame display. In the second experiment, the results of experiment 1 were replicated with a meaningful circular contour--a porthole and a clock. The presence of the external circular contour did not abolish the illusion on the apparent vertical. Moreover, in experiment 3, a clock whose numbers were displaced and not tilted--to avoid the possible tilt influence of visual cues--was also able to deflect the subjective visual vertical. This finding suggests that through top-down processing shapes can act as a framework which serves as a reference influencing the perceived orientation of the inner objects.     

The relation between horizontality and rod-and-frame and vestibular navigational performance

Sex differences on Piaget's water-level (horizontality) test are well established but poorly understood. In this article, correlates of female horizontality performance are systematically explored. Across the five experiments reported, it was found that female subjects who failed the water-level test (poor-horizontality female subjects) were selectively impaired on tasks that required processing information from the otolith organs. In Experiment 1, poor-horizontality female subjects were found to be impaired relative to good-horizontality subjects on the rod-and-frame test. In Experiment 2, a relation was found between female horizontality performance and the ability to process vestibular information in a passive transport task. Experiment 3 ruled out poor spatial updating as a mediating factor in this relation. The results of Experiments 4 and 5 indicated that poor-horizontality female subjects perform randomly on vestibular navigation because they cannot judge linear displacement under conditions of passive transport. The linear transport task is similar to the rod-and-frame task in that both require the central processing of otolith signals. It is proposed that one way to solve the water-level test is to imagine, on the basis of prior perceptual experiences, what the water level looks like inside tilted containers. Because of complex visual-otolith interactions, poor-horizontality female subjects may experience these events differently than good-horizontality subjects.     

The rod and frame effect and induced head tilt as a function of observation distance

Several experiments investigated the influence of a tilted luminous frame on the rod and frame effect (RFE) and on adjustments of the head to apparent vertical, while observation distance to the frame was varied between 1 and 5 m. Comparisons of repeated measures from the same subjects as well as between independent groups showed that distance was a highly effective variable. Both the RFE and the apparent head tilt varied inversely with distance to the frame, diminishing Lo zero at about 5 m. Since head settings were in the direction of the tilted frame, the latter may be inferred to have caused an induced head tilt (IHT) opposite in direction to the tilted frame, when the head was objectively upright. Issues discussed were the role of IHT in the RFE and factors underlying the role of distance in both phenomena.     

Modulation of the rod and frame effect: Retinal angle vs apparent size

Summary Two rod and frame displays, constructed in a 3:1 linear ratio, were used to assess the apparent vertical. When viewed at the common distance of 1.5 m, the larger-appearing frame also produced the greater retinal angle. With the small frame at .5 m and the large one at 4.5 m, the smaller-appearing frame produced the greater retinal angle. In both cases the rod and frame effect increased with increasing retinal size, rather than with the apparent size of the frame.This research was supported by NIH Grant EY 02264 from the National Eye Institute to the first author.     

The rod-and-frame effect: the whole is less than the sum of its parts

Since the discovery of the influence of the tilted frame on the visual perception of the orientation perceived as vertical (VPV), the frame has been treated as a unitary object-a Gestalt. We evaluated the effect of 1-line, 2-line, 3-line, and 4-line (square frame) stimuli of two different sizes, and asked whether the influence of the square frame on VPV is any greater than the additive combination of separate influences produced by the individual lines constituting the frame. We found that, for each size, the square frame is considerably less influential than the additive combination of the influences of the individual lines. The results conform to a mass action rule, in which the lengths and orientations of the individual line components are what matters and the organization of the lines into a square does not-no higher-level Gestalt property is involved in the induction effect on VPV.     

Observer pitch and roll influence: The rod and frame illusion

Observers misperceive the orientation of a vertical rod when it is viewed in the context of a tilted frame (therod and frame illusion, or RFI). The pitch and roll of the surrounding surfaces have independent influences on this illusion (Nelson & Prinzmetal, 2003). Experiment 1 measured the RFI when the pitch and roll of the floor that supported the observer was varied, and the observer was either seated in a chair or standing upright. There were additive influences of pitch and roll on the RFI of seated but not standing observers. Experiments 2 and 3 decoupled body roll and head roll in order to isolate the vestibular and proprioceptive contributions to these effects. The results are interpreted in support of a hierarchy of influence on the RFI: Visual input is given top priority, followed by vestibular input, and then proprioceptive input.     

Determinants of the rod-and-frame effect: Role of organization and subjective contour

In Experiment 1, performance on a conventional (full) rod and frame was compared with that on three other displays. These included a closure condition in which only the corners of a luminous frame were present, a subjective contour condition in which the rod was seen against ablack square subjective surface, and a pattern condition in which four luminous disks were arranged to form the corners of a square pattern. In all cases, a square-like form was perceived. The rod-and-frame effect (RFE) was greatest on the full frame, which differed significantly from all the rest. Closure produced the next greatest influence, while the responses to subjective and pattern conditions did not differ from each other. Experiment 2 showed that a subjective frame was no more effective than the subjective surface of Experiment 1, and verified the importance of 90-deg corner elements in the rod-and-frame display. The conclusion drawn was that equivalent form organizations are not sufficient to produce equivalent levels of the RFE, but certain luminance-difference contours appear to be essential.     

A signal detection analysis of the rod and frame test

To help determine hut what Witkin’s Rod and Frame Test measures, the task was modified by presenting the luminous rod in one of two fixed positions, either vertical or not vertical, within a titled frame. S responded on a four-category scale representing his certainty that the rod was vertical Receiver operating characteristic (ROC) curves were calculated for each of 17 Ss and compared to traditional measures of titer field dependence-independence. The results showed that Witkin’s test is not contaminated to any great extent by response bias. However, the ROC analysis did reveal significant differences between field dependents and independents, not only in their sensitivity to verticality, but also in their- characteristic manner of responding.     

Enumeration of small and large numerosities: The effect of element visibility

Precise enumeration is associated with small numerosities within the subitizing range (<4 items), while approximate enumeration is associated with large numerosities (>4 items). To date, there is still debate on whether a single continuous process or dual mutually exclusive processes mediate enumeration of small and large numerosities. Here, we evaluated a compromise between these two notions: that the precise representation of number is limited to small numerosities, but that the approximate representation of numerosity spans across both small and large numerosities. We assessed the independence of precise and approximate enumeration by looking at how luminance contrast affected enumeration of elements that differ by ones (1–8) or by tens (10–80). We found that enumeration functions of ones and tens have different characteristics, which is consistent with the presence of two number systems. Subitizing was preserved for small numerosities. However, simply decreasing element visibility changed the variability signatures of small numerosities to match those of large numerosities. Together, our results suggest that small numerosities are mediated by both precise and approximate representations of numerosity.     

Wayfinding: The effects of large displays and 3-D perception

Large displays and stereopsis have been shown to improve performance in several virtual navigation tasks. In the present research, we sought to determine whether wayfinding could benefit from these factors. Participants were tested in a virtual town. There were three viewing conditions: a desktop, a large screen, and a large screen on which the virtual environment was viewed in three dimensions (3-D) using polarized glasses. Participants explored the town and had to remember the location of several landmarks. Their memory of the layout of the town was tested by asking them to navigate from one landmark to another, taking the shortest route possible. All groups performed equally well in terms of the distance traveled to target locations. From this result, we concluded that large displays and 3-D perception do not significantly contribute to wayfinding. Thus, experimental paradigms and training programs that utilize wayfinding are as valuable when administered on standard desktops as on more sophisticated and costly equipment and do not induce simulator sickness as large displays tend to do.     

Dissociation between small and large numerosities in newborn infants

In the first year of life, infants possess two cognitive systems encoding numerical information: one for processing the numerosity of sets of 4 or more items, and the second for tracking up to 3 objects in parallel. While a previous study showed the former system to be already present a few hours after birth, it is unknown whether the latter system is functional at this age. Here, we adapt the auditory‐visual matching paradigm that previously revealed sensitivity to large numerosities to test sensitivity to numerosities spanning the range from 2 to 12. Across studies, newborns discriminated pairs of large numerosities in a 3:1 ratio, even when the smaller numerosity was 3 (3 vs. 9). In contrast, newborn infants failed to discriminate pairs including the numerosity 2, even at the same ratio (2 vs. 6). These findings mirror the dissociation that has been reported with older infants, albeit with a discontinuity situated between numerosities 2 and 3. Two alternative explanations are compatible with our results: either newborn infants have a separate system for processing small sets, and the capacity of this system is limited to 2 objects; or newborn infants possess only one system to represent numerosities, and this system either is not functional or is extremely imprecise when it is applied to small numerosities.     

Obesity as a variable affecting performance on the rod and frame test

Apparent similarities between S. Schachter's stimulus binding construct and H. A. Witkin's construct of psychological differentiation, specifically field dependence, have been noted in the literature. The present study examined field dependence on the rod-and-frame test among 20 obese and 42 average-weight subjects. Obese subjects were more field-dependent than were average-weight subjects. Women were slightly more field-dependent than were men. The author concluded that obese persons are more field-dependent and speculated that the constructs may be describing similar phenomena.     

Enumeration of small and large numerosities: the effect of element visibility

Precise enumeration is associated with small numerosities within the subitizing range (<4 items), while approximate enumeration is associated with large numerosities (>4 items). To date, there is still debate on whether a single continuous process or dual mutually exclusive processes mediate enumeration of small and large numerosities. Here, we evaluated a compromise between these two notions: that the precise representation of number is limited to small numerosities, but that the approximate representation of numerosity spans across both small and large numerosities. We assessed the independence of precise and approximate enumeration by looking at how luminance contrast affected enumeration of elements that differ by ones (1-8) or by tens (10-80). We found that enumeration functions of ones and tens have different characteristics, which is consistent with the presence of two number systems. Subitizing was preserved for small numerosities. However, simply decreasing element visibility changed the variability signatures of small numerosities to match those of large numerosities. Together, our results suggest that small numerosities are mediated by both precise and approximate representations of numerosity.     

The effect of frame figure type and frame size on the line and the circle Ponzo illusions

Abstract:   To examine the determinants of the Ponzo illusion, we compared the perceived size of lines and circles presented within three different frames: two converging lines, two circles, and two squares. Twenty stimulus figures, consisting of two types of objects (lines/circles) × three types of frame figures (Ponzo/circles/squares) × three sizes of lower frames (small/medium/large), and two control figures were presented on a personal computer display. Twelve students performed three measurements (upper-object/lower-object/illusion) for each stimulus figure using the method of adjustment. To analyze the relationship between single object perception and the Ponzo illusion, we compared the calculated values of overestimation magnitude differences between the upper and lower objects with the actual obtained illusion values of the six object-frame conditions. The calculated values of the circle and the square frame figures corresponded to the difference between the upper single object and the lower single object. In contrast, the results of the Ponzo figure need an additional factor to explain the differences between the obtained and the calculated values. These results indicate that two factors are involved in the Ponzo illusion: (a) the framing effect affects the perceived size of the individual single objects, and (b) the comparison factor affects the comparison process of the two objects within the converging lines.     

The gap effect for eye and hand movements

A temporal gap between fixation point offset and stimulus onset typically yields shorter saccadic latencies to the stimulus than if the fixation stimulus remained on. Several researchers have explored the extent to which this gap also reduces latencies of other responses but have failed to find a gap effect isolated from general warning effects. Experiment 1, however, showed a robust gap effect for aimed hand movements (which required determination of a precise spatial location), regardless of whether the hand moved alone or was accompanied by a saccadic eye movement. Experiment 2 replicated this aimed hand gap effect and also showed a smaller effect for choice manual keypress responses (which required determination of the direction of response only). Experiment 3 showed no gap effect for simple manual keypress responses (which required no spatial determination). The results are consistent with an interpretation of the gap effect in terms of facilitation of spatially oriented responses.