The effects of tilted outline frames and Intersecting line patterns on judgments of vertical

Influence of scene aspect ratio and depth cues on verticality perception bias

Perceiving verticality is crucial for accurate spatial orientation. Previous research has revealed that tilted scenes can bias verticality perception. Verticality perception bias can be represented as the sum of multiple periodic functions that play a role in the perception of visual orientation, where the specific factors affecting each periodicity remain uncertain. This study investigated the influence of the width and depth of an indoor scene on each periodic component of the bias. The participants were presented with an indoor scene showing a rectangular checkerboard room (Experiment 1), a rectangular aperture on the wall (Experiment 2), or a rectangular dotted room (Experiment 3), with various aspect ratios. The stimuli were presented with roll orientations ranging from 90° clockwise to 90° counterclockwise. The participants were asked to report their subjective visual vertical (SVV) perceptions. The contributions of 45°, 90°, and 180° periodicities to the SVV error were assessed by the weighted vector sum model. In Experiment 1, the periodic components of the SVV error increased with the aspect ratio. In Experiments 2 and 3, only the 90° component increased with the aspect ratio. These findings suggest that extended transverse surfaces may modulate the periodic components of verticality perception.

Panoramic Uncertainty in Vertical Perception

Judgments of the orientation of a visual line with respect to earth vertical are affected by panoramic visual cues. This is illustrated by the rod-and-frame effect (RFE), the finding that the perceived orientation of a luminous rod is biased by the orientation of a surrounding squared frame. In this study, we tested how the uncertainty of frame orientation affects the RFE by asking upright or tilted participants to psychometrically judge the orientation of a briefly flashed rod contained within either a circular frame, a squared frame, or either of two intermediate frame forms, called squircles, presented in various orientations. Results showed a cyclical modulation of frame-induced bias across the range of the square and squircular frame orientations. The magnitude of this bias increased with increasing squaredness of the frame, as if the more unequivocal the orientation cues of the frame, the larger the reliance on them for rod orientation judgments. These findings are explained with a Bayesian optimal integration model in which participants flexibly weigh visual panoramic cues, depending on their orientation reliability, and non-visual cues in the perception of vertical.

Visual factors affecting the rod-and-frame illusion: role of gap size and frame components

In two studies the effect of the distance between the tip of the rod and the frame sides (gap) in the rod-and-frame (RF) illusion was examined and the effect of a full-square condition was compared with that of two different frame amputations. In both studies, there were more rod-setting errors in the direction of the tilt of the inducing figure with a small gap than with a large one. These findings are consistent with the idea that in the case of small gap size local interactions contribute to determining the RF illusion. The actual length of the rod was varied in order to keep the gap constant across different frame tilts; therefore these findings cannot be due to the co-variation between gap size and frame tilt which is typical of standard apparatuses. The effect of frame amputations was compared to the full-square condition. According to Wenderoth and Beh, amputations that maintain the two orthogonal contours of the square produce the typical angular function of the RF illusion. This prediction was confirmed in both studies. However, results indicate that the full square has a stronger illusory effect in the case of a small degree of tilt of the inducing stimulus, irrespective of gap size. It is suggested that this 'square superiority' effect is related to global, not local, mechanisms. To pursue Wenderoth and Beh's observations, amputations close to the vertical meridian were used in one experiment and those close to the horizontal meridian in the second experiment. Contrary to predictions, these conditions produced overlapping results.

Direct evidence for competition between local and global mechanisms of two-dimensional orientation illusions

Orientation illusions induced by two-dimensional stimuli, such as square outline frames or plaids, have been more or less adequately accounted for in terms of repulsion of the vertical test stimulus from the axis of symmetry nearest vertical of the inducing stimulus, whether that axis is real or virtual. Recently, data have been obtained which directly suggest a more complex mechanism: one in which the observed illusion is the sum of all effects--complementary and antagonistic--induced by all axes flanking vertical which are sufficiently close to vertical to exert a significant effect. Experiments are reported in which this latter hypothesis was directly tested by using nonorthogonal plaid component gratings and varying the real-axis orientations while a virtual plaid axis remained fixed in orientation at 10 degrees from vertical. The data indicate that the real component gratings modulate the virtual-axis effect.

Possible neural substrates for orientation analysis and perception

Recent research into the response properties of extrastriate visual cortical mechanisms has revealed single-cell functional organisation which closely parallels certain global and apparently emergent properties of psychophysical observation. An attempt is made to relate previous data on orientation illusions and aftereffects to these extrastriate mechanisms and new data which cannot be explained adequately by V1 (striate) orientation channels are discussed. Conversely, properties of cells in areas such as V3, V4, MT, and others seem to provide an obvious neural substrate for global interactions. It is suggested that psychological 'explanations' couched in terms of 'hypotheses' or 'cognitive problem solving' lack heuristic value, and that, in contrast, the properties of extrastriate cells can suggest novel experimental psychophysical paradigms which are designed to probe these higher-order global mechanisms more or less selectively.

Component analysis of orientation illusions

Orientation illusions occur when the inducing figure is a line or grating (the tilt illusion) or a square outline frame (the rod-and-frame illusion). In the range of inducing figure tilts between vertical and horizontal, the tilt illusion describes one cycle of positive (direct) and negative (indirect) effects but the rod-and-frame illusion describes two such cycles. In two experiments, angular functions of illusions were measured with the six possible inducing figures which result when two of the four sides of a square inducing frame are deleted. As expected, the parallel-side frame amputations induced angular functions similar to the tilt illusion and these functions differed from those induced by the orthogonal-sided amputations. In agreement with previous findings on the nonadditivity of tilt illusions, the sum of angular functions induced by frame amputations, which together form a complete frame, were not always equivalent to the angular function induced by a complete frame, and there were asymmetries in the data fro which neither of two simple hypotheses could adequately account. The discussion focuses upon properties of inducing figures which psychophysical hypotheses might need to consider in order to account for the shapes of angular functions of orientation illusions and, in particular,a distinction is drawn between the global orientation of the inducing figure and the orientations of it (local) component features. It is suggested that it might be fruitful if the tilt illusion and the rod-and-frame illusion were conceived of as illusions resulting from inducing figures composed of all or part of n gratings of spatial frequency fn intersecting at angles of 180 degrees/n.

On the non-additivity of visual tilt illusions

In Experiment I, the visual tilt illusion induced by two orthogonal lines was found to differ from the sum of the illusions induced by each line independently. The length of one of the orthogonal-inducing lines was varied in Experiment II with the other inducing line remaining a fixed length. As length increased from zero (no line) to 100%, the size of the illusion increased monotonically. The increase in illusion was not due to the increasing length of the variable line alone since, in the absence of the line of fixed length, increasing the length of the variable line produced no significant trend in the illusion (Experiment III).

The distinction between the rod-and-frame illusion and the rod-and-frame test

Errors in vertical settings of a test rod occur when the rod is enclosed in a laterally-tilted square-outline frame. The majority of previous experiments which have investigated this rod-and-frame effect have used a single frame tilt, usually 28°, and have tabulated errors as average unsigned deviations from gravitational vertical. Evidence is presented that, when the illusion is measured by taking algebraic differences between constant (signed) errors made with and without the frame being present, illusions occur in the direction of frame tilt for frame tilts up to about 25° from vertical (repulsion effects) but that directionally opposite illusions (attraction effects) occur for frame tilts between 25° and 45°. At the frame tilts used most frequently in previous studies (25° to 30°) little or no illusion occurs. A distinction is drawn between the rod-and-frame illusion (RFI), which has an angular function similar to the simple tilt illusion and aftereffect, and the rod-and-frame test (RFT), which uses unsigned deviations from vertical as its measure of error and which probably bears little or no relationship to the RFI.