Richard F. Murray

Classification images: A review

Classification images have recently become a widely used tool in visual psychophysics. Here, I review the development of classification image methods over the past fifteen years. I provide some historical background, describing how classification images and related methods grew out of established statistical and mathematical frameworks and became common tools for studying biological systems. I describe key developments in classification image methods: use of optimal weighted sums based on the linear observer model, formulation of classification images in terms of the generalized linear model, development of statistical tests, use of priors to reduce dimensionality, methods for experiments with more than two response alternatives, a variant using multiplicative noise, and related methods for examining nonlinearities in visual processing, including second-order Volterra kernels and principal component analysis. I conclude with a selective review of how classification image methods have led to substantive findings in three representative areas of vision research, namely, spatial vision, perceptual organization, and visual search.

Optimal methods for calculating classification images: Weighted sums

In signal detection theory, an observers responses are often modeled as being based on a decision variable obtained by cross-correlating the stimulus with a template, possibly after corruption by external and internal noise. The response classification method estimates an observers template by measuring the influence of each pixel of external noise on the observers responses. A map that shows the influence of each pixel is called a classification image. Other authors have shown how to calculate classification images from external noise fields, but the optimal calculation has never been determined, and the quality of the resulting classification images has never been evaluated. Here we derive the optimal weighted sum of noise fields for calculating classification images in several experimental designs, and we derive the signal-to-noise ratio (SNR) of the resulting classification images. Using the expressions for the SNR, we show how to choose experimental parameters, such as the observers performance level and the external noise power, to obtain classification images with a high SNR. We discuss two-alternative identification experiments in which the stimulus is presented at one or more contrast levels, in which each stimulus is presented twice so that we can estimate the power of the internal noise from the consistency of the observers responses, and in which the observer rates the confidence of his responses. We illustrate these methods in a series of contrast increment detection experiments.

Time course of amodal completion revealed by a shape discrimination task

We measured the extent of amodal completion as a function of stimulus duration over the range of 15–210 msec, for both moving and stationary stimuli. Completion was assessed using a performancebased measure: a shape discrimination task that is easy if the stimulus is amodally completed and difficult if it is not. Specifically, participants judged whether an upright rectangle was longer horizontally or vertically, when the rectangle was unoccluded, occluded at its corners by four negative-contrast squares, or occluded at its corners by four zero-contrast squares. In the zero-contrast condition, amodal completion did not occur because there were no occlusion cues; in the unoccluded condition, the entire figure was present. Thus, comparing performance in the negative-contrast condition to these two extremes provided a quantitative measure of amodal completion. This measure revealed a rapid but measurable time course for amodal completion. Moving and stationary stimuli took the same amount of time to be completed (≈ 75 msec), but moving stimuli had slightly stronger completion at long durations.

The human visual system's assumption that light comes from above is weak

Every biological or artificial visual system faces the problem that images are highly ambiguous, in the sense that every image depicts an infinite number of possible 3D arrangements of shapes, surface colors, and light sources. When estimating 3D shape from shading, the human visual system partly resolves this ambiguity by relying on the light-from-above prior, an assumption that light comes from overhead. However, light comes from overhead only on average, and most images contain visual information that contradicts the light-from-above prior, such as shadows indicating oblique lighting. How does the human visual system perceive 3D shape when there are contradictions between what it assumes and what it sees? Here we show that the visual system combines the light-from-above prior with visual lighting cues using an efficient statistical strategy that assigns a weight to the prior and to the cues and finds a maximum-likelihood lighting direction estimate that is a compromise between the two. The prior receives surprisingly little weight and can be overridden by lighting cues that are barely perceptible. Thus, the light-from-above prior plays a much more limited role in shape perception than previously thought, and instead human vision relies heavily on lighting cues to recover 3D shape. These findings also support the notion that the visual system efficiently integrates priors with cues to solve the difficult problem of recovering 3D shape from 2D images.

Visual Memory Decay Is Deterministic

After observers see an object or pattern, their visual memory of what they have seen decays slowly over time. Nearly all current theories of vision assume that decay of short-term memory occurs because visual representations are progressively and randomly corrupted as time passes. We tested this assumption using psychophysical noise-masking methods, and we found that visual memory decays in a completely deterministic fashion. This surprising finding challenges current ideas about visual memory and sets a goal for future memory research: to characterize the deterministic “forgetting function” that describes how memories decay over time.

Cognitive neuroscience: Practice doesn't make perfect.

It may seem counterintuitive, but we are not very efficient at recognizing even the most common words. This finding suggests strict limits on how flexible we are in learning to recognize new patterns.

9 – Amodal Completion: A Case Study In Grouping

A minimum number of clock pulses required for keeping an electronic component in a waiting condition or state are intermittently applied to the electronic component, thereby minimizing the heat dissipation thereof. A control circuit, utilized in the invention, provides an output signal which permits continuous clock signals to be applied, for example, to memory chips, during read and write periods, but such control circuit reduces the number of clock signals applied to the memory chips during periods when the read and write processes are not required.

Cue combination on the circle and the sphere

Bayesian cue combination models have been used to examine how human observers combine information from several cues to form estimates of linear quantities like depth. Here we develop an analogous theory for circular quantities like planar direction. The circular theory is broadly similar to the linear theory but differs in significant ways. First, in the circular theory the combined estimate is a nonlinear function of the individual cue estimates. Second, in the circular theory the mean of the combined estimate is affected not only by the means of individual cues and the weights assigned to individual cues but also by the variability of individual cues. Third, in the circular theory the combined estimate can be less certain than the individual estimates, if the individual estimates disagree with one another. Fourth, the circular theory does not have some of the closed-form expressions available in the linear theory, so data analysis requires numerical methods. We describe a vector sum model that gives a heuristic approximation to the circular theorys behavior. We also show how the theory can be extended to deal with spherical quantities like direction in three-dimensional space.

The intrinsic constraint approach to cue combination: An empirical and theoretical evaluation

We elucidate two properties of the intrinsic constraint (IC) model of depth cue combination (F. Domini, C. Caudek, & H. Tassinari, 2006). First, we show that IC combines depth cues in a weighted sum that maximizes the signal-to-noise ratio of the combined estimate. Second, we show that IC predicts that any two depth-matched pairs of stimuli are separated by equal numbers of just noticeable differences (JNDs) in depth. That is, IC posits a strong link between perceived depth and depth discrimination, much like some Fechnerian theories of sensory scaling. We test this prediction, and we find that it does not hold. We also find that depth discrimination performance approximately follows Webers law, whereas IC assumes that depth discrimination thresholds are independent of baseline stimulus depth.

Posterior Probability Matching and Human Perceptual Decision Making

Probability matching is a classic theory of decision making that was first developed in models of cognition. Posterior probability matching, a variant in which observers match their response probabilities to the posterior probability of each response being correct, is being used increasingly often in models of perception. However, little is known about whether posterior probability matching is consistent with the vast literature on vision and hearing that has developed within signal detection theory. Here we test posterior probability matching models using two tools from detection theory. First, we examine the models’ performance in a two-pass experiment, where each block of trials is presented twice, and we measure the proportion of times that the model gives the same response twice to repeated stimuli. We show that at low performance levels, posterior probability matching models give highly inconsistent responses across repeated presentations of identical trials. We find that practised human observers are more consistent across repeated trials than these models predict, and we find some evidence that less practised observers more consistent as well. Second, we compare the performance of posterior probability matching models on a discrimination task to the performance of a theoretical ideal observer that achieves the best possible performance. We find that posterior probability matching is very inefficient at low-to-moderate performance levels, and that human observers can be more efficient than is ever possible according to posterior probability matching models. These findings support classic signal detection models, and rule out a broad class of posterior probability matching models for expert performance on perceptual tasks that range in complexity from contrast discrimination to symmetry detection. However, our findings leave open the possibility that inexperienced observers may show posterior probability matching behaviour, and our methods provide new tools for testing for such a strategy.