Local reliability weighting explains identification of partially masked objects in natural images.

A fundamental natural visual task is the identification of specific target objects in the environments that surround us. It has long been known that some properties of the background have strong effects on target visibility. The most well-known properties are the luminance, contrast, and similarity of the background to the target. In previous studies, we found that these properties have highly lawful effects on detection in natural backgrounds. However, there is another important factor affecting detection in natural backgrounds that has received little or no attention in the masking literature, which has been concerned with detection in simpler backgrounds. Namely, in natural backgrounds the properties of the background often vary under the target, and hence some parts of the target are masked more than others. We began studying this factor, which we call the "partial masking factor," by measuring detection thresholds in backgrounds of contrast-modulated white noise that was constructed so that the standard template-matching (TM) observer performs equally well whether or not the noise contrast modulates in the target region. If noise contrast is uniform in the target region, then this TM observer is the Bayesian optimal observer. However, when the noise contrast modulates then the Bayesian optimal observer weights the template at each pixel location by the estimated reliability at that location. We find that human performance for modulated noise backgrounds is predicted by this reliability-weighted TM (RTM) observer. More surprisingly, we find that human performance for natural backgrounds is also predicted by the RTM observer.

Effects of target-amplitude and background-contrast uncertainty predicted by a normalized template-matching observer.

When detecting targets under natural conditions, the visual system almost always faces multiple, simultaneous, dimensions of extrinsic uncertainty. This study focused on the simultaneous uncertainty about target amplitude and background contrast. These dimensions have a large effect on detection and vary greatly in natural scenes. We measured the human performance for detecting a sine-wave target in white noise and natural-scene backgrounds for two levels of prior probability of the target being present. We derived and tested the ideal observer for white-noise backgrounds, a special case of a template-matching observer that dynamically moves its criterion with the background contrast (the DTM observer) and two simpler models with a fixed criterion: the template-matching (TM) observer and the normalized template-matching (NTM) observer that normalizes template response by background contrast. Simulations show that, when the target prior is low, the performance of the NTM observer is near optimal and the TM observer is near chance, suggesting that manipulating the target prior is valuable for distinguishing among models. Surprisingly, we found that the NTM and DTM observers better explain human performance than the TM observer for both target priors in both background types. We argue that the visual system most likely exploits contrast normalization, rather than dynamic criterion adjustment, to deal with simultaneous background contrast and target amplitude uncertainty. Finally, our findings show that the data collected under high levels of uncertainty have a rich structure capable of discriminating between models, providing an alternative approach for studying high dimensions of uncertainty.

Phase-dependent asymmetry of pattern masking in natural images explained by intrinsic position uncertainty.

A number of recent studies have been directed at measuring and modeling detection of targets at specific locations in natural backgrounds, a key subtask of visual search in natural environments. A useful approach is to bin natural background patches into joint histograms with bins along specific background dimensions. By measuring psychometric functions in a sparse subset of these bins, it is possible to estimate how the included dimensions jointly affect detectability over the whole space of natural backgrounds. In previous studies, we found that threshold is proportional to the product of the background luminance, contrast, and similarity; a result predicted by a simple template-matching observer with divisive normalization along each of the dimensions. The measure of similarity was the cosine similarity of the amplitude spectra of the target and background (SA)-a phase-invariant measure. Here, we investigated the effect of the cosine similarity of the target and background images (SI|A)-a phase-dependent measure. We found that threshold decreases monotonically with SI|A in agreement with a recent study (Rideaux et al., 2022). In contrast, the template-matching observer predicts threshold to be a U-shaped function of SI|A reaching a minimum when the target and background are orthogonal (SI|A = 0). Surprisingly, when the template-matching observer includes a small amount of intrinsic position uncertainty (measured in a separate experiment) the pattern of thresholds is explained.

Detection of targets in filtered noise: whitening in space and spatial frequency.

Most studies of detection in complex backgrounds have measured and modeled human performance for statistically uniform (stationary) backgrounds. However, natural and medical images have statistical properties that vary over space. We measured detection of various target shapes presented in Gaussian 1/f noise backgrounds that were statistically uniform over space, and in ones that modulated in contrast over space. We find that the pattern of human thresholds is not consistent with the ideal observer but is consistent with a suboptimal observer that performs partial whitening in spatial frequency and whitening (reliability-weighting) in space, and has a small level of intrinsic position uncertainty.

Stereo slant discrimination of planar 3D surfaces: Frontoparallel versus planar matching.

Binocular stereo cues are important for discriminating 3D surface orientation, especially at near distances. We devised a single-interval task where observers discriminated the slant of a densely textured planar test surface relative to a textured planar surround reference surface. Although surfaces were rendered with correct perspective, the stimuli were designed so that the binocular cues dominated performance. Slant discrimination performance was measured as a function of the reference slant and the level of uncorrelated white noise added to the test-plane images in the left and right eyes. We compared human performance with an approximate ideal observer (planar matching [PM]) and two subideal observers. The PM observer uses the image in one eye and back projection to predict a test image in the other eye for all possible slants, tilts, and distances. The estimated slant, tilt, and distance are determined by the prediction that most closely matches the measured image in the other eye. The first subideal observer (local planar matching [LPM]) applies PM over local neighborhoods and then pools estimates across the test plane. The second suboptimal observer (local frontoparallel matching [LFM]) uses only location disparity. We find that the ideal observer (PM) and the first subideal observer (LPM) outperforms the second subideal observer (LFM), demonstrating the additional benefit of pattern disparities. We also find that all three model observers can account for human performance, if two free parameters are included: a fixed small level of internal estimation noise, and a fixed overall efficiency scalar on slant discriminability.

Similar masking effects of natural backgrounds on detection performances in humans, macaques, and macaque-V1 population responses.

Visual systems evolve to process the stimuli that arise in the organism's natural environment, and hence, to fully understand the neural computations in the visual system, it is important to measure behavioral and neural responses to natural visual stimuli. Here, we measured psychometric and neurometric functions in the macaque monkey for detection of a windowed sine-wave target in uniform backgrounds and in natural backgrounds of various contrasts. The neurometric functions were obtained by near-optimal decoding of voltage-sensitive-dye-imaging (VSDI) responses at the retinotopic scale in primary visual cortex (V1). The results were compared with previous human psychophysical measurements made under the same conditions. We found that human and macaque behavioral thresholds followed the generalized Weber's law as function of contrast, and that both the slopes and the intercepts of the threshold as a function of background contrast match each other up to a single scale factor. We also found that the neurometric thresholds followed the generalized Weber's law with slopes and intercepts matching the behavioral slopes and intercepts up to a single scale factor. We conclude that human and macaque ability to detect targets in natural backgrounds are affected in the same way by background contrast, that these effects are consistent with population decoding at the retinotopic scale by down-stream circuits, and that the macaque monkey is an appropriate animal model for gaining an understanding of the neural mechanisms in humans for detecting targets in natural backgrounds. Finally, we discuss limitations of the current study and potential next steps.NEW & NOTEWORTHY We measured macaque detection performance in natural images and compared their performance to the detection sensitivity of neurophysiological responses recorded in the primary visual cortex (V1), and to the performance of human subjects. We found that 1) human and macaque behavioral performances are in quantitative agreement and 2) are consistent with near-optimal decoding of V1 population responses.

A method to integrate and classify normal distributions.

Univariate and multivariate normal probability distributions are widely used when modeling decisions under uncertainty. Computing the performance of such models requires integrating these distributions over specific domains, which can vary widely across models. Besides some special cases where these integrals are easy to calculate, there exist no general analytical expressions, standard numerical methods, or software for these integrals. Here we present mathematical results and open-source software that provide (a) the probability in any domain of a normal in any dimensions with any parameters; (b) the probability density, cumulative distribution, and inverse cumulative distribution of any function of a normal vector; (c) the classification errors among any number of normal distributions, the Bayes-optimal discriminability index, and relation to the receiver operating characteristic (ROC); (d) dimension reduction and visualizations for such problems; and (e) tests for how reliably these methods may be used on given data. We demonstrate these tools with vision research applications of detecting occluding objects in natural scenes and detecting camouflage.

Constrained sampling experiments reveal principles of detection in natural scenes.

A fundamental everyday visual task is to detect target objects within a background scene. Using relatively simple stimuli, vision science has identified several major factors that affect detection thresholds, including the luminance of the background, the contrast of the background, the spatial similarity of the background to the target, and uncertainty due to random variations in the properties of the background and in the amplitude of the target. Here we use an experimental approach based on constrained sampling from multidimensional histograms of natural stimuli, together with a theoretical analysis based on signal detection theory, to discover how these factors affect detection in natural scenes. We sorted a large collection of natural image backgrounds into multidimensional histograms, where each bin corresponds to a particular luminance, contrast, and similarity. Detection thresholds were measured for a subset of bins spanning the space, where a natural background was randomly sampled from a bin on each trial. In low-uncertainty conditions, both the background bin and the amplitude of the target were fixed, and, in high-uncertainty conditions, they varied randomly on each trial. We found that thresholds increase approximately linearly along all three dimensions and that detection accuracy is unaffected by background bin and target amplitude uncertainty. The results are predicted from first principles by a normalized matched-template detector, where the dynamic normalizing gain factor follows directly from the statistical properties of the natural backgrounds. The results provide an explanation for classic laws of psychophysics and their underlying neural mechanisms.

Detection of occluding targets in natural backgrounds.

Detection of target objects in the surrounding environment is a common visual task. There is a vast psychophysical and modeling literature concerning the detection of targets in artificial and natural backgrounds. Most studies involve detection of additive targets or of some form of image distortion. Although much has been learned from these studies, the targets that most often occur under natural conditions are neither additive nor distorting; rather, they are opaque targets that occlude the backgrounds behind them. Here, we describe our efforts to measure and model detection of occluding targets in natural backgrounds. To systematically vary the properties of the backgrounds, we used the constrained sampling approach of Sebastian, Abrams, and Geisler (2017). Specifically, millions of calibrated gray-scale natural-image patches were sorted into a 3D histogram along the dimensions of luminance, contrast, and phase-invariant similarity to the target. Eccentricity psychometric functions (accuracy as a function of retinal eccentricity) were measured for four different occluding targets and 15 different combinations of background luminance, contrast, and similarity, with a different randomly sampled background on each trial. The complex pattern of results was consistent across the three subjects, and was largely explained by a principled model observer (with only a single efficiency parameter) that combines three image cues (pattern, silhouette, and edge) and four well-known properties of the human visual system (optical blur, blurring and downsampling by the ganglion cells, divisive normalization, intrinsic position uncertainty). The model also explains the thresholds for additive foveal targets in natural backgrounds reported in Sebastian et al. (2017).

Nonlinear Lateral Interactions in V1 Population Responses Explained by a Contrast Gain Control Model.

How do cortical responses to local image elements combine to form a spatial pattern of population activity in primate V1? Here, we used voltage-sensitive dye imaging, which measures summed membrane potential activity, to examine the rules that govern lateral interactions between the representations of two small local-oriented elements in macaque (Macaca mulatta) V1. We find strong subadditive and mostly orientation-independent interactions for nearby elements [2-4 mm interelement cortical distance (IED)] that gradually become linear at larger separations (>6 mm IED). These results are consistent with a population gain control model describing nonlinear V1 population responses to single oriented elements. However, because of the membrane potential-to-spiking accelerating nonlinearity, the model predicts supra-additive lateral interactions of spiking responses for intermediate separations at a range of locations between the two elements, consistent with some prior facilitatory effects observed in electrophysiology and psychophysics. Overall, our results suggest that population-level lateral interactions in V1 are primarily explained by a simple orientation-independent contrast gain control mechanism.SIGNIFICANCE STATEMENT Interactions between representations of simple visual elements such as oriented edges in primary visual cortex (V1) are thought to contribute to our ability to easily integrate contours and segment surfaces, but the mechanisms that govern these interactions are primarily unknown. Our study provides novel evidence that lateral interactions at the population level are governed by a simple contrast gain-control mechanism, and we show how this divisive gain-control mechanism can give rise to apparently facilitatory spiking responses.

Psychometric functions of uncertain template matching observers.

This theoretical note describes a simple equation that closely approximates the psychometric functions of template-matching observers with arbitrary levels of position and orientation uncertainty. We show that the approximation is accurate for detection of targets in white noise, 1/f noise, and natural backgrounds. In its simplest form, this equation, which we call the uncertain normal integral (UNI) function, has two parameters: one that varies only with the level of uncertainty and one that varies only with the other properties of the stimuli. The UNI function is useful for understanding and generating predictions of uncertain template matching (UTM) observers. For example, we use the UNI function to derive a closed-form expression for the detectability (d') of UTM observers in 1/f noise, as a function of target amplitude, background contrast, and position uncertainty. As a descriptive function, the UNI function is just as flexible and simple as other common descriptive functions, such as the Weibull function, and it avoids some of their undesirable properties. In addition, the estimated parameters have a clear interpretation within the family of UTM observers. Thus, the UNI function may be the better default descriptive formula for psychometric functions in detection and discrimination tasks.

Decision-variable correlation.

An extension of the signal-detection theory framework is described and demonstrated for two-alternative identification tasks. The extended framework assumes that the subject and an arbitrary model (or two subjects, or the same subject on two occasions) are performing the same task with the same stimuli, and that on each trial they both compute values of a decision variable. Thus, their joint performance is described by six fundamental quantities: two levels of intrinsic discriminability (d'), two values of decision criterion, and two decision-variable correlations (DVCs), one for each of the two categories of stimuli. The framework should be widely applicable for testing models and characterizing individual differences in behavioral and neurophysiological studies of perception and cognition. We demonstrate the framework for the well-known task of detecting a Gaussian target in white noise. We find that (a) subjects' DVCs are approximately equal to the square root of their efficiency relative to ideal (in agreement with the prediction of a popular class of models), (b) between-subjects and within-subject (double-pass) DVCs increase with target contrast and are greater for target-present than target-absent trials (rejecting many models),

Contributions of monocular and binocular cues to distance discrimination in natural scenes.

Little is known about distance discrimination in real scenes, especially at long distances. This is not surprising given the logistical difficulties of making such measurements. To circumvent these difficulties, we collected 81 stereo images of outdoor scenes, together with precisely registered range images that provided the ground-truth distance at each pixel location. We then presented the stereo images in the correct viewing geometry and measured the ability of human subjects to discriminate the distance between locations in the scene, as a function of absolute distance (3 m to 30 m) and the angular spacing between the locations being compared (2°, 5°, and 10°). Measurements were made for binocular and monocular viewing. Thresholds for binocular viewing were quite small at all distances (Weber fractions less than 1% at 2° spacing and less than 4% at 10° spacing). Thresholds for monocular viewing were higher than those for binocular viewing out to distances of 15-20 m, beyond which they were the same. Using standard cue-combination analysis, we also estimated what the thresholds would be based on binocular-stereo cues alone. With two exceptions, we show that the entire pattern of results is consistent with what one would expect from classical studies of binocular disparity thresholds and separation/size discrimination thresholds measured with simple laboratory stimuli. The first exception is some deviation from the expected pattern at close distances (especially for monocular viewing). The second exception is that thresholds in natural scenes are lower, presumably because of the rich figural cues contained in natural images.

Estimating 3D tilt from local image cues in natural scenes.

Estimating three-dimensional (3D) surface orientation (slant and tilt) is an important first step toward estimating 3D shape. Here, we examine how three local image cues from the same location (disparity gradient, luminance gradient, and dominant texture orientation) should be combined to estimate 3D tilt in natural scenes. We collected a database of natural stereoscopic images with precisely co-registered range images that provide the ground-truth distance at each pixel location. We then analyzed the relationship between ground-truth tilt and image cue values. Our analysis is free of assumptions about the joint probability distributions and yields the Bayes optimal estimates of tilt, given the cue values. Rich results emerge: (a) typical tilt estimates are only moderately accurate and strongly influenced by the cardinal bias in the prior probability distribution; (b) when cue values are similar, or when slant is greater than 40°, estimates are substantially more accurate; (c) when luminance and texture cues agree, they often veto the disparity cue, and when they disagree, they have little effect; and (d) simplifying assumptions common in the cue combination literature is often justified for estimating tilt in natural scenes. The fact that tilt estimates are typically not very accurate is consistent with subjective impressions from viewing small patches of natural scene. The fact that estimates are substantially more accurate for a subset of image locations is also consistent with subjective impressions and with the hypothesis that perceived surface orientation, at more global scales, is achieved by interpolation or extrapolation from estimates at key locations.

Defocus blur discrimination in natural images with natural optics.

The lens system in the human eye is able to best focus light from only one distance at a time.Therefore, many objects in the natural environment are not imaged sharply on the retina. Furthermore, light from objects in the environment is subject to the particular aberrations of the observer's lens system (e.g., astigmatism and chromatic aberration). We refer to blur created by the observer's optics as "natural" or "defocus" blur as opposed to "on-screen" blur created by software on a display screen. Although blur discrimination has been studied extensively, human ability to discriminate defocus blur in images of natural scenes has not been systematically investigated. Here, we measured discrimination of defocus blur for a collection of natural image patches, sampled from well-focused photographs. We constructed a rig capable of presenting stimuli at three physical distances simultaneously. In Experiment 1, subjects viewed monocularly two simultaneously presented natural image patches through a 4-mm artificial pupil at ±1° eccentricity. The task was to identify the sharper patch. Discrimination thresholds varied substantially between stimuli but were correlated between subjects. The lowest thresholds were at or below the lowest thresholds ever reported. In a second experiment, we paralyzed accommodation and retested a subset of conditions from Experiment 1. A third experiment showed that removing contrast as a cue to defocus blur had only a modest effect on thresholds. Finally, we describe a simple masking model and evaluate how well it can explain our experimental results and the results from previous blur discrimination experiments.

Optimal defocus estimation in individual natural images.

Defocus blur is nearly always present in natural images: Objects at only one distance can be perfectly focused. Images of objects at other distances are blurred by an amount depending on pupil diameter and lens properties. Despite the fact that defocus is of great behavioral, perceptual, and biological importance, it is unknown how biological systems estimate defocus. Given a set of natural scenes and the properties of the vision system, we show from first principles how to optimally estimate defocus at each location in any individual image. We show for the human visual system that high-precision, unbiased estimates are obtainable under natural viewing conditions for patches with detectable contrast. The high quality of the estimates is surprising given the heterogeneity of natural images. Additionally, we quantify the degree to which the sign ambiguity often attributed to defocus is resolved by monochromatic aberrations (other than defocus) and chromatic aberrations; chromatic aberrations fully resolve the sign ambiguity. Finally, we show that simple spatial and spatio-chromatic receptive fields extract the information optimally. The approach can be tailored to any environment-vision system pairing: natural or man-made, animal or machine. Thus, it provides a principled general framework for analyzing the psychophysics and neurophysiology of defocus estimation in species across the animal kingdom and for developing optimal image-based defocus and depth estimation algorithms for computational vision systems.

Optimal disparity estimation in natural stereo images.

A great challenge of systems neuroscience is to understand the computations that underlie perceptual constancies, the ability to represent behaviorally relevant stimulus properties as constant even when irrelevant stimulus properties vary. As signals proceed through the visual system, neural states become more selective for properties of the environment, and more invariant to irrelevant features of the retinal images. Here, we describe a method for determining the computations that perform these transformations optimally, and apply it to the specific computational task of estimating a powerful depth cue: binocular disparity. We simultaneously determine the optimal receptive field population for encoding natural stereo images of locally planar surfaces and the optimal nonlinear units for decoding the population responses into estimates of disparity. The optimal processing predicts well-established properties of neurons in cortex. Estimation performance parallels important aspects of human performance. Thus, by analyzing the photoreceptor responses to natural images, we provide a normative account of the neurophysiology and psychophysics of absolute disparity processing. Critically, the optimal processing rules are not arbitrarily chosen to match the properties of neurophysiological processing, nor are they fit to match behavioral performance. Rather, they are dictated by the task-relevant statistical properties of complex natural stimuli. Our approach reveals how selective invariant tuning-especially for properties not trivially available in the retinal images-could be implemented in neural systems to maximize performance in particular tasks.

Retina-V1 model of detectability across the visual field.

A practical model is proposed for predicting the detectability of targets at arbitrary locations in the visual field, in arbitrary gray scale backgrounds, and under photopic viewing conditions. The major factors incorporated into the model include (a) the optical point spread function of the eye, (b) local luminance gain control (Weber's law), (c) the sampling array of retinal ganglion cells, (d) orientation and spatial frequency-dependent contrast masking, (e) broadband contrast masking, and (f) efficient response pooling. The model is tested against previously reported threshold measurements on uniform backgrounds (the ModelFest data set and data from Foley, Varadharajan, Koh, & Farias, 2007) and against new measurements reported here for several ModelFest targets presented on uniform, 1/f noise, and natural backgrounds at retinal eccentricities ranging from 0° to 10°. Although the model has few free parameters, it is able to account quite well for all the threshold measurements.

Human vision is attuned to the diffuseness of natural light.

All images are highly ambiguous, and to perceive 3-D scenes, the human visual system relies on assumptions about what lighting conditions are most probable. Here we show that human observers' assumptions about lighting diffuseness are well matched to the diffuseness of lighting in real-world scenes. We use a novel multidirectional photometer to measure lighting in hundreds of environments, and we find that the diffuseness of natural lighting falls in the same range as previous psychophysical estimates of the visual system's assumptions about diffuseness. We also find that natural lighting is typically directional enough to override human observers' assumption that light comes from above. Furthermore, we find that, although human performance on some tasks is worse in diffuse light, this can be largely accounted for by intrinsic task difficulty. These findings suggest that human vision is attuned to the diffuseness levels of natural lighting conditions.

Neural correlates of perceptual similarity masking in primate V1.

Visual detection is a fundamental natural task. Detection becomes more challenging as the similarity between the target and the background in which it is embedded increases, a phenomenon termed 'similarity masking'. To test the hypothesis that V1 contributes to similarity masking, we used voltage sensitive dye imaging (VSDI) to measure V1 population responses while macaque monkeys performed a detection task under varying levels of target-background similarity. Paradoxically, we find that during an initial transient phase, V1 responses to the target are enhanced, rather than suppressed, by target-background similarity. This effect reverses in the second phase of the response, so that in this phase V1 signals are positively correlated with the behavioral effect of similarity. Finally, we show that a simple model with delayed divisive normalization can qualitatively account for our findings. Overall, our results support the hypothesis that a nonlinear gain control mechanism in V1 contributes to perceptual similarity masking.