Projective invariance and visual shape constancy

As one moves about a table, the projection of its shape on the retina varies enormously, yet the table's shape appears constant. The various retinal images of a single object are nearly congruent in projective geometry. To explain apparent constancy, standard theories of vision assume that the visual system has access to this projective congruence. We present four experiments that undermine this assumption (i.e., the projective thesis). The basic result is that observers' estimates of shape in a simple production task represent gross departures from correct projection, even when observers are given aids to fixation. We manipulate both observer sample and experimental procedure in an attempt to find a source of these persistent errors. Our present hypothesis is that observers lack the sensitivity or implicit knowledge of projective geometry that has been attributed to them.     

Projective invariance and the kinetic depth effect.

Seven experiments test the assumption that, in the kinetic depth effect, observers have reliable and direct access to the equivalence of shapes in projective geometry. The assumption is implicit in 'inverse optics' approaches to visual form perception. Observers adjusted a comparison shape to match a standard shape; both standard and comparison were portrayed as in continuous rotation in space, using a graphics computer. The shapes were either plane quadrilaterals or solid prisms. The angular difference of the planes of the shapes was varied, as was the dot density of a texture in those planes. Departure from projective equivalence was measured in six studies by measuring the planar analogue of cross ratio, and in a seventh by measuring the cross ratio for points in space. Projective equivalence was not found to be perceived uniformly, except in one experiment that did not involve rotation in depth. Otherwise changes in orientation of up to 180 degrees about a single coordinate axis had no significant effect on matches in shape, while changes in orientation about more than one coordinate axis produced significant effects. The addition of texture and a change in rotation speed did not correct departures from projective equivalence.     

Context sensitivity and invariance in perception of octave-ambiguous tones

Three experiments investigated the influence of unambiguous (UA) context tones on the perception of octave-ambiguous (OA) tones. In Experiment 1, pairs of OA tones spanning a tritone interval were preceded by pairs of UA tones instantiating a rising or falling interval between the same pitch classes. Despite the inherent ambiguity of OA tritone pairs, most participants showed little or no priming when judging the OA tritone as rising or falling. In Experiments 2 and 3, participants compared the pitch heights of single OA and UA tones representing either the same pitch class or being a tritone apart. These judgments were strongly influenced by the pitch range of the UA tones, but only slightly by the spectral center of the OA tones. Thus, the perceived pitch height of single OA tones is context sensitive, but the perceived relative pitch height of two OA tones, as described in previous research on the “tritone paradox,” is largely invariant in UA tone contexts.     

Pigeon pattern perception: limits on perspective invariance

Two experiments are reported in which the response of pigeons to perspective transformations of a pattern target was measured. In the first experiment an alphabet letter was taken as the pattern target (the 'positive') and the response to its perspective transforms was compared to the response to nontarget letters ('negatives') over the course of discrimination training. In the second experiment irregular quadrilaterals were used as positives and the responses to slight perspective deformations of the prototypes were compared to the responses to random transformations of the same magnitude under steady-state conditions. The amount of differential responding depended on the type of transformation. There was no differential response to targets rotated in the picture plane or around the horizontal axis in either experiment. There was differential response to small reductions and enlargements of the target. There was also differential response to translated targets, and this was seen irrespective of the amount of displacement. Results from targets rotated around the vertical axis were erratic, some target-plus-angle combinations elicited differential responding, but most did not. The erratic responses are attributed to symmetries in pattern elements that were abstracted as critical features. Pigeons therefore exhibit no true rotation invariance, limited size invariance, and complete shift invariance. It is argued that size invariance, but not position invariance, may depend on prior exposure to the alternatives.     

Electrophysiological evidence for size invariance in masked picture repetition priming

This experiment examined invariance in object representations through measuring event-related potentials (ERPs) to pictures in a masked repetition priming paradigm. Pairs of pictures were presented where the prime was either the same size or half the size of the target object and the target was either presented in a normal orientation or was a normal sized mirror reflection of the prime object. Previous masked repetition priming studies have found a cascade of priming effect sensitive to perceptual (N190/P190) and semantic (N400) properties of the stimulus. This experiment found that both early (N190/P190 effects) and later effects (N400) were invariant to size, whereas only the N190/P190 effect was invariant to mirror reflection. The combination of a small prime and a mirror reflected target led to no significant priming effects. Taken together, the results of this set of experiments suggests that object recognition, more specifically, activating an object representation, occurs in a hierarchical fashion where overlapping perceptual information between the prime and target is necessary, although not always sufficient, to activate a higher level semantic representation.     

Emotion among women with psychopathy during picture perception

Emotional reactions in women with psychopathy were examined in a mixed-picture paradigm using psychophysiological measures. Startle probes were presented at 2.0 or 4.5 s following onset of a 6-s picture presentation. At 2.0 s, nonpsychopaths exhibited the typical pattern of eyeblink reflex magnitude: unpleasant > neutral > pleasant. Psychopaths with high general levels of anxiety also exhibited this pattern. Psychopaths with lower anxiety exhibited attenuated reflex magnitudes during unpleasant pictures. Similarly, when focusing on psychopathy components, only individuals expressing high antisocial behavior and high emotional detachment exhibited smaller reflex magnitudes during unpleasant pictures. At 4.5 s, all groups exhibited normal, potentiated reflex magnitudes during unpleasant pictures. Group differences were not observed for other measures.     

The role of pictorial convention in haptic picture perception

An investigation of tactile picture perception is reported. Blindfolded sighted subjects explored either 'line drawings' or 'textured' tactile pictures produced on Zytex swell paper. All pictures were 'two-dimensional', that is they depicted only one object face and so did not represent a third dimension. Both picture sets represented the same objects. Results revealed that the textured pictures, in which solid surfaces of depicted objects were uniformly textured, were recognised more often than tactile line drawings, in which surfaces of objects were simply bounded by lines. There were no significant correlations between imagery ability (visual, cutaneous, or kinaesthetic) and picture recognition success. Texture may be a form of 'uniform connectedness' (Palmer and Rock 1994 Psychonomic Bulletin & Review 1 29-55) or 'common region' (Palmer 1992 Cognitive Psychology 24 436-447), highlighting the global characteristics of stimuli. We argue that textured pictures may encourage the haptic system to take a more globally oriented approach to tactile picture perception, benefiting recognition.     

Useful resolution for picture perception as a function of eccentricity

Observers inspected for different lengths of time pictures which contained high-resolution information within an eye-contingent viewing window and low-resolution information outside the area of that window. A recognition test followed in which the pictures inspected were presented together with other, distractor, pictures. The time required to reach 75% picture recognition (the criterion study time) was determined as a function of window size and degree of completeness of video sampling of information outside the window. For each level of information sampling density, criterion study time decreased as window size increased up to a critical size, and then remained approximately constant beyond this size. From these critical-window sizes, a function which describes the resolution actually used by the visual system at each eccentricity (the useful-resolution function) was obtained and this decreased monotonically with eccentricity. The useful resolution at each eccentricity was coarser than the resolution available at that eccentricity as determined by visual acuity, suggesting that useful resolution is not limited by visual acuity. The relationship between useful resolution and saccade length was also analyzed.     

An empirical investigation of the visual rightness theory of picture perception

This research subjected the visual rightness theory of picture perception to experimental scrutiny. It investigated the ability of adults untrained in the visual arts to discriminate between reproductions of original abstract and representational paintings by renowned artists from two experimentally manipulated less well-organized versions of each art stimulus. Perturbed stimuli contained either minor or major disruptions in the originals' principal structural networks. It was found that participants were significantly more successful in discriminating between originals and their highly altered, but not slightly altered, perturbation than expected by chance. Accuracy of detection was found to be a function of style of painting and a viewer's way of thinking about a work as determined from their verbal reactions to it. Specifically, hit rates for originals were highest for abstract works when participants focused on their compositional style and form and highest for representational works when their content and realism were the focus of attention. Findings support the view that visually right (i.e., "good") compositions have efficient structural organizations that are visually salient to viewers who lack formal training in the visual arts.     

Relational invariance and visual space perception: On perceptual vector analysis of the optic flow

The outlines of the theory of perceptual vector analysis in visual space and motion perception in its present state of development are presented. This theory is exclusively founded on the outcome of systematic experimental research extended over more than three decades. Some informative experiments and their results are briefly described, starting with some decisive findings reported in Johansson (1950). A fundamental difference between this approach and the traditional pictorial way of describing the proximal stimulus is that it accepts abstract mathematical relations in spatial change over time in the optic flow hitting the receptor organs as specification of the proximal stimulus rather than the traditional interpretation of cues in static images. In its present form it is able to establish functionally valid mathematical correspondence between the light-reflecting environment, geometrical transformations in the optic flow at the retina and the percept.     

Measurement invariance,factor analysis and factorial invariance

Several concepts are introduced and defined: measurement invariance, structural bias, weak measurement invariance, strong factorial invariance, and strict factorial invariance. It is shown that factorial invariance has implications for (weak) measurement invariance. Definitions of fairness in employment/admissions testing and salary equity are provided and it is argued that strict factorial invariance is required for fairness/equity to exist. Implications for item and test bias are developed and it is argued that item or test bias probably depends on the existence of latent variables that are irrelevant to the primary goal of test constructers.Presidential address delivered at the Annual Meeting of the Psychometric Society in Berkeley, California, June 18–20, 1993.     

Size-distance invariance: Kinetic invariance is different from static invariance

The static form of the size-distance invariance hypothesis asserts that a given proximal stimulus size (visual angle) determines a unique and constant ratio of perceived-object size to perceived object distance. A proposed kinetic invariance hypothesis asserts that a changing proximal stimulus size (an expanding or contracting solid visual angle) produces a constant perceived size and a changing perceived distance such that the instantaneous ratio of perceived size to perceived distance is determined by the instantaneous value of visual angle. The kinetic invariance hypothesis requires a new concept, an operating constraint, to mediate between the proximal expansion or contraction pattern and the perception of rigid object motion in depth. As a consequence of the operating constraint, expansion and contraction patterns are automatically represented in consciousness as rigid objects. In certain static situations, the operation of this constraint produces the anomalous perceived-size-perceived-distance relations called the size-distance paradox.     

Size-distance invariance: kinetic invariance is different from static invariance.

The static form of the size-distance invariance hypothesis asserts that a given proximal stimulus size (visual angle) determines a unique and constant ratio of perceived object size to perceived object distance. A proposed kinetic invariance hypothesis asserts that a changing proximal stimulus size (an expanding or contracting solid visual angle) produces a constant perceived size and a changing perceived distance such that the instantaneous ratio of perceived size to perceived distance is determined by the instantaneous value of visual angle. The kinetic invariance hypothesis requires a new concept, an operating constraint, to mediate between the proximal expansion or contraction pattern and the perception of rigid object motion in depth. As a consequence of the operating constraint, expansion and contraction patterns are automatically represented in consciousness as rigid objects. In certain static situations, the operation of this constraint produces the anomalous perceived-size-perceived-distance relations called the size-distance paradox.