Global shape versus local feature: an angle illusion.

We have shown previously that the precision of angle judgments depends strongly on the global stimulus configuration: discrimination thresholds for angles that form part of isosceles triangles are up to 3 times lower than for those that form part of scalene triangles [Kennedy, G. J., Orbach, H. S., & Loffler, G. (2006). Effects of global shape on angle discrimination. VisionResearch, 46(8-9), 1530-1539]. Here, we investigated whether or not the perceived size of an angle (accuracy) is also affected by the overall shape of which it forms a part. Observers compared the relative sizes of angles contained in isosceles triangles with those of angles in scalene triangles and points of subjective equality were determined. For a reference angle of 60 degrees , angles embedded in isosceles triangles were judged to be on average 14 degrees larger than angles embedded in scalene triangles. This result is largely independent of the reference angle, triangle orientation and triangle size. Moreover, the effect is present whether or not triangles of different shapes enclose the same area, whether or not the side of the triangle opposite the angle is present and whether the triangle is outlined or defined by dots at its vertexes. In sum, our results provide evidence for a novel illusion where an angle embedded in an isosceles triangle is judged substantially larger than the same angle embedded in a scalene triangle. This finding demonstrates that mechanisms for computing angles are sensitive to the context within which angles are presented.

Judging the shape of moving objects: discriminating dynamic angles.

Studies of shape perception have typically focused on static shapes. Studies of motion perception have mainly investigated speed and direction. None have addressed performance for judging the shape of moving objects. We investigated this by determining the discrimination of geometric angles under various dynamic conditions (translation, rotation, and expansion). Angles were parts of imaginary triangles, defined by three vertex dots. Compared to static angles, results show no significant decline in the precision of angle judgments for any of the three motion types, up to speeds high enough to impair target visibility. Additional experiments provide evidence against a uniform mechanism underlying static and dynamic performance, which could rely on "snapshots" when processing moving angles. Rather, we find support for distinct mechanisms. Firstly, adding noise dots to the display affects rotating and expanding angles substantially more than those which are translating or static. Secondly, the ability to judge angles is unaffected when vertex dots are occluded for short periods. Given the dependence of dot trajectories on the overall triangle motion, the ability to precisely extrapolate the future position of a dot requires distinct computations for translating, expanding, and rotating shapes.

Is there a mismatch negativity during change blindness?

The mismatch negativity is an event-related potential that represents a preattentive change detection process. The aim of this study was to determine whether the mismatch negativity was present during 'change blindness', a striking phenomenon in which surprisingly large changes in a complex scene are not seen when they occur during a blink or an eye movement. In this study, large orientation changes elicited a candidate mismatch negativity between 180 and 320 ms that appeared to be independent of participants' performance (uncued 76% correct, miscued 59% correct with chance performance at 50%). This negativity, however, disappeared in the miscued 'change blind' condition. In conclusion, the mismatch negativity does not appear to be present during change blindness suggesting that in complex scenes even large changes may not trigger preattentive change detection processes.

Effects of global shape on angle discrimination.

Previous studies have been inconclusive as to whether angle discrimination performance can be predicted by the sensitivity of orientation discrimination mechanisms or by that of mechanisms specialised for angle coding. However, these studies have assumed that angle discrimination is independent of the shape of the object of which the angle is a part. This assumption was tested by measuring angle discrimination using angles that were parts of different triangular shapes. Angle discrimination thresholds were lowest when angles were presented in isosceles triangles (sides forming the angle were of identical length). Performance was significantly poorer when angles were presented in scalene triangles (sides of different lengths) and as much as three times worse when the sides forming the angle varied randomly in length between presentations. Comparing orientation discrimination for single lines with angle discrimination for different stimulus conditions (isosceles, scalene and random triangles) leads to conflicting conclusions as to the mechanisms underlying angle perception: line orientation sensitivity correctly predicts angle discrimination for random triangles, but underestimates angle acuity for isosceles triangles. The fact that performance in angle discrimination tasks is strongly dependant on the overall stimulus geometry implies that geometric angles are computed by mechanisms that are sensitive to global aspects of the stimulus.

Adding rotation to translation: percepts and illusions.

This study investigated how the perception of a translating object is affected by rotation. Observers were asked to judge the motion and trajectory of objects that rotated around their centroid while linearly translating. The expected percept, consistent with the actual dynamics used to generate the movie sequences, is that of a translating and rotating object, akin to a tumbling rugby ball. Observers, however, do not always report this and, under certain circumstances, perceive the object to translate on an illusory curved trajectory, similar to a car driving on a curved road. The prevalence of veridical versus nonveridical percepts depends on a number of factors. First, if the object's orientation remains within a limited range relative to the axis of translation, the illusory, curved percept dominates. If the orientation, at any point of the movie sequence, differs sufficiently from the axis of translation, the percept switches to linear translation with rotation. The angle at which the switch occurs is dependent upon a number of factors that relate to an object's elongation and, with it, the prominence of its orientation. For an ellipse with an aspect ratio of 3, the switch occurs at approximately 45 degrees. Higher aspect ratios increase the range; lower ratios decrease it. This applies similarly to rectangular shapes. A line is more likely to be perceived on a curved trajectory than an elongated rectangle, which, in turn, is more likely seen on a curved path than a square. This is largely independent of rotational and translational speeds. Measuring perceived directions of motion at different instants in time allows the shape of the perceived illusory curved path to be extrapolated. This results in a trajectory that is independent of object size and corresponds closely to the actual object orientation at different points during the movie sequence. The results provide evidence for a perceptual transition from an illusory curved trajectory to a veridical linear trajectory (with rotation) for the same object. Both are consistent with special real-world cases such as objects rotating around a centre outside of the object so that their orientation remains tangent to the trajectory (cheetahs running along a curve, sailboats) or objects tumbling along simple trajectories (a monkey spinning in air, spinning cars on ice). In certain cases, the former is an illusion.

Set-size effects for sampled shapes: experiments and model.

The location of imperfections or heterogeneities in shapes and contours often correlates with points of interest in a visual scene. Investigating the detection of such heterogeneities provides clues as to the mechanisms processing simple shapes and contours. We determined set-size effects (e.g., sensitivity to single target detection as distractor number increases) for sampled contours to investigate how the visual system combines information across space. Stimuli were shapes sampled by oriented Gabor patches: circles and high-amplitude RF4 and RF8 radial frequency patterns with Gabor orientations tangential to the shape. Subjects had to detect a deviation in orientation of one element ("heterogeneity"). Heterogeneity detection sensitivity was measured for a range (7-40) of equally spaced (2.3-0.4°) elements. In a second condition, performance was measured when elements sampled a part of the shapes. We either varied partial contour length for a fixed (7) set-size, co-varying inter-element spacing, or set-size for a fixed spacing (0.7°), co-varying partial contour length. Surprisingly, set-size effects (poorer performance with more elements) are rarely seen. Set-size effects only occur for shapes containing concavities (RF4 and RF8) and when spacing is fixed. When elements are regularly spaced, detection performance improves with set-size for all shapes. When set-size is fixed and spacing varied, performance improves with decreasing spacing. Thus, when an increase in set-size and a decrease in spacing co-occur, the effect of spacing dominates, suggesting that inter-element spacing, not set-size, is the critical parameter for sampled shapes. We propose a model for the processing of simple shapes based on V4 curvature units with late noise, incorporating spacing, average shape curvature, and the number of segments with constant sign of curvature contained in the shape, which accurately accounts for our experimental results, making testable predictions for a variety of simple shapes.

Motion trajectories and object properties influence perceived direction of motion.

Judging the motion of objects is a fundamental task that the visual system executes in everyday life in order for us to navigate and interact safely with our surroundings. A number of strategies have been suggested to explain how the visual system uses motion information from different points of an object to compute veridical directions of motion. These include combining ambiguous signals from object contours via a vector summation (VS) or intersection of constraints (IOC) calculation, pooling information using a maximum likelihood or tracking object features. We measured the perceived direction of motion for a range of cross-shaped stimuli (composed of two superimposed lines) to test how accurately humans perceive their motion and compared data to predictions from these strategies. Crosses of different shapes (defined by the angle between the component lines) translated along 16 directions of motion with constant speed. The crosses either moved along one of their symmetry axes (balanced conditions with line components equidistant to the direction of motion) or had their symmetry axis tilted relative to the motion (unbalanced conditions) Data show reproducible differences between observers, including occasional bimodal behaviour, and exhibit the following common patterns. There is a general dependence on direction of motion: For all conditions, when motion is along cardinal axes (horizontal and vertical), perception is largely veridical. For non-cardinal directions, biases are typically small (<10 deg) when crosses are balanced but large biases occur (≥30 deg) when crosses are tilted relative to their direction of motion. Factors influencing the pattern of biases are the shape and tilt of the cross as well as the proximity of its direction of motion to cardinal axes. The dependence of the biases on the direction of motion is inconsistent with any isotropic mechanisms including VS, IOC, maximum likelihood or feature tracking. Instead, perception is biased by a number of intrinsic properties of the cross and external references. The strength of these cues depends on the type, with elongation producing the strongest weight, and their proximity to the direction of motion. This suggests that the visual system may rely on a number of static cues to improve the known low precision for non-cardinal directions of motion, a process which can, however, result in large perceptual biases in certain circumstances.

Non-linear global pooling in the discrimination of circular and non-circular shapes.

The ability to discriminate minute deviations from circularity is dependent upon global summation mechanisms integrating information along entire contours. The aim of this study was to determine how the strength of global summation depends on various stimulus features. To determine if the strength of global summation differs between shapes, contour discrimination for various contour shapes, generated by applying a sinusoidal modulation to the radius of a circle (radial frequency - RF - patterns), was measured. Shapes differed in frequency (number of lobes RF3, RF5 and RF20) and amplitude ('sharpness' of the lobes ranged between 0 and 20× thresholds for detecting deviation from a circle). Low amplitudes test discrimination against a circle while high amplitudes measure sensitivity for highly non-circular shapes (e.g. five-pointed star-shapes). The ability to integrate information along contours was assessed by comparing the effect of applying radial deformations to the entire contour or to only fractions (various number of cycles). Results show that discrimination thresholds remain in the hyperacuity range for low amplitudes, but increase for higher amplitudes. Concerning signal integration, discrimination, expressed as a function of the amount of contour deformed, exhibits a shallow and a steep regime. Discrimination improves only slowly as more contour cycles are deformed until the point when the entire pattern is modulated, when sensitivity increases substantially. The initial shallow regime is well captured by probability summation. The increase in sensitivity when the entire pattern is modulated compared to a single cycle provides evidence for global pooling. The pattern of integration and the existence of global pooling is dependent on shape frequency. The two-part behavior is independent of shape amplitude but is only seen for low RFs (3 and 5). Data for RF20 follow the prediction of probability summation. We next investigated various stimulus characteristics and their effect on integration strength. Global pooling exceeding probability summation is evident for different pattern sizes, presentation times and for high as well as low absolute contrasts. Only if the contrasts of different fractions of a contour shape are individually scaled to match their respective visibilities is integration strength below the level of probability summation. This explains the lack of apparent global pooling in previous studies employing mixed contrasts. The marked increase in performance for discriminating completely modulated RF patterns argues in favor of highly specialized, global shape mechanisms that are seen over a wide range of stimulus configurations. The results indicate global, non-linear mechanisms, which respond most strongly when stimulated by the entire pattern and comparatively weakly when only stimulated by parts of it.

Factors affecting motion integration.

The perceived direction of motion of a featureless contour inside a circular aperture is always perpendicular to the contour's orientation, regardless of its true motion (the aperture problem). This study investigates the circumstances under which unambiguous feature motion (of line terminators, single dots, or truncations of a D6 pattern) in adjacent apertures can alter the perceived direction of such featureless contours. We find that integration mechanisms responsible for motion capture are fairly robust against misorientations and contrast manipulations of individual components, are sensitive to differences in spatial frequencies, and scale with pattern size. Motion capture is not diminished when a D6 profile is substituted for the square-pulse profile of a line and is independent of the visibility of the apertures, indicating that object interpretations and three-dimensional analyses of a scene are less important than has been postulated previously. These results have strong implications for the neuronal hardware underlying the integration of motion signals across space and provide a framework for global motion models.

Modeling the integration of motion signals across space.

Experiments by Loffler and Orbach on the integration of motion signals across space [J. Opt. Soc. Am. A 20, 1461 (2003)] revealed that both three-dimensional analysis and object interpretation play a much smaller role than previously assumed. These results motivated the quantitative description of a low-level, bottom-up model presented here. Motion is computed in parallel at different spatial sites, and excitatory interactions operate between sites. The strength of these interactions is determined mainly by distance. Simulations correctly predict behavior for a variety of manipulations on multi-aperture stimuli: aligned and skewed lines, different presentation times, different inter-aperture gaps, and different spatial frequencies. However, strictly distance-dependent mechanisms are too simplistic to account for all experimental data. Mismatches for grossly misoriented lines suggest collinear facilitation as a promising extension. Once incorporated, collinear facilitation not only correctly predicts results for misoriented patterns but also accounts for the lack of motion integration between heterogeneous stimuli such as lines and dots.