Are mirror-symmetric objects of special importance for 3D shape perception? A reply to Sawada and Pizlo (2022).

Yu, Todd, and Petrov (2021) and Yu, Petrov, and Todd (2021) investigated failures of shape constancy that occur when objects are viewed stereoscopically at different distances. Although this result has been reported previously with simple objects such as pyramids or cylinders, we examined more complex objects with bilateral symmetry to test the claim by Li, Sawada, Shi, Kwon, and Pizlo (2011) that the perception of those objects is veridical. Sawada and Pizlo (2022) offer several criticisms of our experiments, but they seem to suggest that the concept of shape is defined by what is computable by their model. If stimuli are used that cannot be discriminated by their model, they are dismissed as degenerate, and tasks that cannot be performed by their model are assumed to be based on something other than shape. This allows them to disregard empirical evidence that is inconsistent with their model. We argue, in contrast, that all reliable aspects of shape perception are deserving of explanation. We also argue that there are many different attributes of shape and many different sources of information about shape that may be relevant in different contexts. It is unlikely that all of them can be explained by a single model.

The many facets of shape.

Shape is an interesting property of objects because it is used in ordinary discourse in ways that seem to have little connection to how it is typically defined in mathematics. The present article describes how the concept of shape can be grounded within Euclidean and non-Euclidean geometry and also to human perception. It considers the formal methods that have been proposed for measuring the differences among shapes and how the performance of those methods compares with shape difference thresholds of human observers. It discusses how different types of shape change can be perceptually categorized. It also evaluates the specific data structures that have been used to represent shape in models of both human and machine vision, and it reviews the psychophysical evidence about the extent to which those models are consistent with human perception. Based on this review of the literature, we argue that shape is not one thing but rather a collection of many object attributes, some of which are more perceptually salient than others. Because the relative importance of these attributes can be context dependent, there is no obvious single definition of shape that is universally applicable in all situations.

Bilateral Symmetry Has No Effect on Stereoscopic Shape Judgments.

A single experiment is reported that measured the apparent stereoscopic shapes of symmetric and asymmetric objects at different viewing distances. The symmetric stimuli were specifically designed to satisfy the minimal conditions for computing veridical shape from symmetry. That is to say, they depicted complex, bilaterally symmetric, plane-faced polyhedra whose symmetry planes were oriented at an angle of 45° relative to the line of sight. The asymmetric stimuli were distorted versions of the symmetric ones in which the 3D position of each vertex was randomly displaced. Prior theoretical analyses have shown that it is mathematically possible to compute the 3D shapes of symmetric stimuli under these conditions, but those algorithms are useless for asymmetric objects. The results revealed that the apparent shapes of both types of objects were expanded or compressed in depth as a function of viewing distance, in exactly the same way as has been reported in many other studies, and that the presence or absence of symmetry had no detectable effect on performance.

Failures of stereoscopic shape constancy over changes of viewing distance and size for bilaterally symmetric polyhedra.

Two shape matching experiments examined the effects of viewing distance and object size on observers' judgments of 3D metric shape under binocular viewing. Unlike previous studies on this topic, the stimuli were specifically designed to satisfy the minimal conditions for computing veridical shape from symmetry. Concretely, the stimuli were complex, mirror-symmetric polyhedra whose symmetry planes were oriented at an angle of 45o relative to the line of sight in a shape-matching task. Although it is mathematically possible to accurately compute the 3D shapes of these stimuli using relatively simple algorithms, the results indicated that human observers are unable to do so. Indeed, the apparent shapes of the objects were systematically expanded or compressed in depth as a function of viewing distance, in exactly the same way as has been reported for simpler stimuli that do not satisfy the minimal conditions for an accurate computational analysis. For objects presented at near distances, we also obtained statistically significant effects of object size on observers' shape judgments.

Non-steady-state photo-EMF in ß-Ga2O3 crystals at λ = 457 nm.

The non-steady-state photoelectromotive force is excited in a monoclinic gallium oxide crystal at wavelength λ = 457 nm. The crystal grown in an oxygen atmosphere is insulating and highly transparent for a visible light, nevertheless, the formation of dynamic space-charge gratings and observation of the photo-EMF signal is achieved without application of any electric field to the sample. The dependencies of the signal amplitude on the frequency of phase modulation, light intensity, spatial frequency and light polarization are measured. The material demonstrates the anisotropy along the [100] and [010] directions, namely, there is a small difference in the transport parameters and a pronounced polarization dependence of the signal. The crystal's photoconductivity, responsivity and diffusion length of electrons are estimated for the chosen light wavelength and compared with the ones for other wide-bandgap crystals.

The divisive normalization model of V1 neurons: a comprehensive comparison of physiological data and model predictions.

The physiological responses of simple and complex cells in the primary visual cortex (V1) have been studied extensively and modeled at different levels. At the functional level, the divisive normalization model (DNM; Heeger DJ. Vis Neurosci 9: 181-197, 1992) has accounted for a wide range of single-cell recordings in terms of a combination of linear filtering, nonlinear rectification, and divisive normalization. We propose standardizing the formulation of the DNM and implementing it in software that takes static grayscale images as inputs and produces firing rate responses as outputs. We also review a comprehensive suite of 30 empirical phenomena and report a series of simulation experiments that qualitatively replicate dozens of key experiments with a standard parameter set consistent with physiological measurements. This systematic approach identifies novel falsifiable predictions of the DNM. We show how the model simultaneously satisfies the conflicting desiderata of flexibility and falsifiability. Our key idea is that, while adjustable parameters are needed to accommodate the diversity across neurons, they must be fixed for a given individual neuron. This requirement introduces falsifiable constraints when this single neuron is probed with multiple stimuli. We also present mathematical analyses and simulation experiments that explicate some of these constraints.

Mapping and correcting the influence of gaze position on pupil size measurements.

Pupil size is correlated with a wide variety of important cognitive variables and is increasingly being used by cognitive scientists. Pupil data can be recorded inexpensively and non-invasively by many commonly used video-based eye-tracking cameras. Despite the relative ease of data collection and increasing prevalence of pupil data in the cognitive literature, researchers often underestimate the methodological challenges associated with controlling for confounds that can result in misinterpretation of their data. One serious confound that is often not properly controlled is pupil foreshortening error (PFE)-the foreshortening of the pupil image as the eye rotates away from the camera. Here we systematically map PFE using an artificial eye model and then apply a geometric model correction. Three artificial eyes with different fixed pupil sizes were used to systematically measure changes in pupil size as a function of gaze position with a desktop EyeLink 1000 tracker. A grid-based map of pupil measurements was recorded with each artificial eye across three experimental layouts of the eye-tracking camera and display. Large, systematic deviations in pupil size were observed across all nine maps. The measured PFE was corrected by a geometric model that expressed the foreshortening of the pupil area as a function of the cosine of the angle between the eye-to-camera axis and the eye-to-stimulus axis. The model reduced the root mean squared error of pupil measurements by 82.5 % when the model parameters were pre-set to the physical layout dimensions, and by 97.5 % when they were optimized to fit the empirical error surface.

Pupil Diameter Tracks the Exploration-Exploitation Trade-off during Analogical Reasoning and Explains Individual Differences in Fluid Intelligence.

The ability to adaptively shift between exploration and exploitation control states is critical for optimizing behavioral performance. Converging evidence from primate electrophysiology and computational neural modeling has suggested that this ability may be mediated by the broad norepinephrine projections emanating from the locus coeruleus (LC) [Aston-Jones, G., & Cohen, J. D. An integrative theory of locus coeruleus-norepinephrine function: Adaptive gain and optimal performance. Annual Review of Neuroscience, 28, 403-450, 2005]. There is also evidence that pupil diameter covaries systematically with LC activity. Although imperfect and indirect, this link makes pupillometry a useful tool for studying the locus coeruleus norepinephrine system in humans and in high-level tasks. Here, we present a novel paradigm that examines how the pupillary response during exploration and exploitation covaries with individual differences in fluid intelligence during analogical reasoning on Raven's Advanced Progressive Matrices. Pupillometry was used as a noninvasive proxy for LC activity, and concurrent think-aloud verbal protocols were used to identify exploratory and exploitative solution periods. This novel combination of pupillometry and verbal protocols from 40 participants revealed a decrease in pupil diameter during exploitation and an increase during exploration. The temporal dynamics of the pupillary response was characterized by a steep increase during the transition to exploratory periods, sustained dilation for many seconds afterward, and followed by gradual return to baseline. Moreover, the individual differences in the relative magnitude of pupillary dilation accounted for 16% of the variance in Advanced Progressive Matrices scores. Assuming that pupil diameter is a valid index of LC activity, these results establish promising preliminary connections between the literature on locus coeruleus norepinephrine-mediated cognitive control and the literature on analogical reasoning and fluid intelligence.

Do We Really Become Smarter When Our Fluid-Intelligence Test Scores Improve?

Recent reports of training-induced gains on fluid intelligence tests have fueled an explosion of interest in cognitive training-now a billion-dollar industry. The interpretation of these results is questionable because score gains can be dominated by factors that play marginal roles in the scores themselves, and because intelligence gain is not the only possible explanation for the observed control-adjusted far transfer across tasks. Here we present novel evidence that the test score gains used to measure the efficacy of cognitive training may reflect strategy refinement instead of intelligence gains. A novel scanpath analysis of eye movement data from 35 participants solving Raven's Advanced Progressive Matrices on two separate sessions indicated that one-third of the variance of score gains could be attributed to test-taking strategy alone, as revealed by characteristic changes in eye-fixation patterns. When the strategic contaminant was partialled out, the residual score gains were no longer significant. These results are compatible with established theories of skill acquisition suggesting that procedural knowledge tacitly acquired during training can later be utilized at posttest. Our novel method and result both underline a reason to be wary of purported intelligence gains, but also provide a way forward for testing for them in the future.

Motion aftereffect duration is not changed by perceptual learning: evidence against the representation modification hypothesis.

The representation modification hypothesis of perceptual learning attributes the practice-induced improvements in sensitivity and/or discriminability to changes in the early visual areas. We used motion aftereffects (MAE) to probe the representations of motion direction. In two experiments, four practice sessions on a fine direction-discrimination task caused large stimulus-specific improvements in d' but no significant stimulus-specific changes in either static or dynamic MAE duration at posttest relative to a pretest. Power analysis indicated that the data were approximately 100 times more likely given the hypothesis of no MAE change than the hypothesis of a 10% relative change. In light of converging evidence in the MAE literature, this suggests that little or no change occurred in the cortical representations of visual motion up to and including area MT. The task specificity of the learning effect challenges the representation modification hypothesis and supports an alternative-selective reweighting.

The visual identification of relational categories.

An experiment was performed to investigate the ability of human observers to identify configural relations among three dots. Four stimulus categories were defined on the basis of whether or not the dots were arranged collinearly and whether or not the central dot was equally spaced relative to the two flanking dots. Observers were initially trained with feedback to identify these categories at a single orientation with a fixed uniform background, and then they were tested with variable orientations and backgrounds without feedback. The results revealed almost perfect generalization. We also simulated the same task using a recent feature hierarchy model (J. Mutch & D. G. Lowe, 2008) that is among the most successful for object recognition. This model performed well for fixed orientations and backgrounds, but it could not accurately identify these categories with variable orientations and backgrounds even when given training with those conditions. These findings suggest that feature hierarchy models represent the spatial relations within an image quite differently than human observers.

A novel method for analyzing sequential eye movements reveals strategic influence on Raven's Advanced Progressive Matrices.

Eye movements are an important data source in vision science. However, the vast majority of eye movement studies ignore sequential information in the data and utilize only first-order statistics. Here, we present a novel application of a temporal-difference learning algorithm to construct a scanpath successor representation (SR; P. Dayan, 1993) that captures statistical regularities in temporally extended eye movement sequences. We demonstrate the effectiveness of the scanpath SR on eye movement data from participants solving items from Raven's Advanced Progressive Matrices Test. Analysis of the SRs revealed individual differences in scanning patterns captured by two principal components that predicted individual Raven scores much better than existing methods. These scanpath SR components were highly interpretable and provided new insight into the role of strategic processing on the Raven test. The success of the scanpath SR in terms of prediction and interpretability suggests that this method could prove useful in a much broader context.

Category rating is based on prototypes and not instances: evidence from feedback-dependent context effects.

Context effects in category rating on a 7-point scale are shown to reverse direction depending on feedback. Context (skewed stimulus frequencies) was manipulated between and feedback within subjects in two experiments. The diverging predictions of prototype- and exemplar-based scaling theories were tested using two representative models: ANCHOR and INST. To gain coverage on one side of the continuum, a prototype-based category must lose on the opposite side. ANCHOR can exhibit both assimilative and compensatory context effects depending on feedback. INST always exhibits assimilative effects. The human data show a significant context-by-feedback interaction. The main context effect is assimilative in one data set and compensatory in the other. This pattern is consistent with ANCHOR but rules out INST, which fails to account for the compensatory effect and the interaction. This suggests that human category rating is based on unitary representations.

Dissociable perceptual-learning mechanisms revealed by diffusion-model analysis.

Performance on perceptual tasks improves with practice. Most theories address only accuracy data and tacitly assume that perceptual learning is a monolithic phenomenon. The present study pioneers the use of response time distributions in perceptual learning research. The 27 observers practiced a visual motion-direction discrimination task with filtered-noise textures for four sessions with feedback. Session 5 tested whether the learning effects transferred to the orthogonal direction. The diffusion model (Ratcliff, Psychological Review, 85, 59-108, 1978) achieved good fits to the individual response time distributions from each session and identified two distinct learning mechanisms with markedly different specificities. A stimulus-specific increase in the drift-rate parameter indicated improved sensory input to the decision process, and a stimulus-general decrease in nondecision time variability suggested improved timing of the decision process onset relative to stimulus onset (which was preceded by a beep). A traditional d' analysis would miss the latter effect, but the diffusion-model analysis identified it in the response time data.

Asymmetric transfer of perceptual learning of luminance- and contrast-modulated motion.

Perceptual learning was used as a tool for studying motion perception. The pattern of transfer of learning of luminance- (LM) and contrast-modulated (CM) motion is diagnostic of how their respective processing pathways are integrated. Twenty observers practiced fine direction discrimination with either additive (LM) or multiplicative (CM) mixtures of a dynamic noise carrier and a radially isotropic texture modulator. The temporal frequency was 10 Hz, speed was 10 deg/s, and duration was 400 ms, with feedback. Group 1 pre-tested CM for 2 blocks, trained LM for 16 blocks, and post-tested CM for 6 blocks during 6 sessions on separate days. In Group 2, the LM and CM roles were reversed. The d' improved almost twofold in both groups. There seemed to be full transfer from CM to LM but no significant transfer from LM to CM. The pattern of post-switch improvement was asymmetric as well-no further learning during the LM post-test versus rapid relearning during the CM post-test. These strong asymmetries suggest a dual-pathway architecture with Fourier channels sensitive only to LM signals and non-Fourier channels sensitive to both LM and CM. We hypothesize that the channels tuned for the same motion direction but different carriers are integrated using a MAX operation.

Symmetry-based methodology for decision-rule identification in same--different experiments.

The standard practice of reducing every same-different data set to two numbers (hits and false alarms) is wasteful, because the response pattern to all four stimulus pairs carries information about the decision rule adopted by the observer. We describe eight rules organized in three families: differencing, covert classification, and likelihood ratio. We prove that each family produces a characteristic pattern of (in)equalities among the response probabilities. We propose two simple qualitative tests. Is the performance on stimulus pairs AA and BB statistically indistinguishable? If not, differencing and likelihood-ratio strategies can be rejected. Is the performance on pairs AB and BA indistinguishable? If not, covert classification can be rejected. We present algorithms for fitting two covert-classification models and illustrate the new methodology in a perceptual learning experiment on visual motion-direction discrimination. The standard assumption of symmetric decision criteria was violated.

Perceptual learning without feedback in non-stationary contexts: data and model.

The role of feedback in perceptual learning is probed in an orientation discrimination experiment under destabilizing non-stationary conditions, and explored in a neural-network model. Experimentally, perceptual learning was examined with periodic alteration of a strong external noise context. The speed of learning, the performance loss at each change in external noise context (switch cost), and the asymptotic accuracy d' without feedback were very similar or identical to those with feedback. However, lack of feedback led to higher decision bias (error responses matching the external noise context). In the model, the stimulus representations are constant, whereas the read-out connections to a decision unit learn by a Hebbian plasticity rule that may be augmented by additional feedback input and criterion control of decision bias.

The dynamics of perceptual learning: an incremental reweighting model.

The mechanisms of perceptual learning are analyzed theoretically, probed in an orientation-discrimination experiment involving a novel nonstationary context manipulation, and instantiated in a detailed computational model. Two hypotheses are examined: modification of early cortical representations versus task-specific selective reweighting. Representation modification seems neither functionally necessary nor implied by the available psychophysical and physiological evidence. Computer simulations and mathematical analyses demonstrate the functional and empirical adequacy of selective reweighting as a perceptual learning mechanism. The stimulus images are processed by standard orientation- and frequency-tuned representational units, divisively normalized. Learning occurs only in the "read-out" connections to a decision unit; the stimulus representations never change. An incremental Hebbian rule tracks the task-dependent predictive value of each unit, thereby improving the signal-to-noise ratio of their weighted combination. Each abrupt change in the environmental statistics induces a switch cost in the learning curves as the system temporarily works with suboptimal weights.

The dynamics of scaling: a memory-based anchor model of category rating and absolute identification.

A memory-based scaling model--ANCHOR--is proposed and tested. The perceived magnitude of the target stimulus is compared with a set of anchors in memory. Anchor selection is probabilistic and sensitive to similarity, base-level strength, and recency. The winning anchor provides a reference point near the target and thereby converts the global scaling problem into a local comparison. An explicit correction strategy determines the final response. Two incremental learning mechanisms update the locations and base-level activations of the anchors. This gives rise to sequential, context, transfer, practice, and other dynamic effects. The scale unfolds as an adaptive map. A hierarchy of models is tested on a battery of quantitative measures from 2 experiments in absolute identification and category rating.