Development of radial frequency pattern perception in macaque monkeys.

Infant primates see poorly, and most perceptual functions mature steadily beyond early infancy. Behavioral studies on human and macaque infants show that global form perception, as measured by the ability to integrate contour information into a coherent percept, improves dramatically throughout the first several years after birth. However, it is unknown when sensitivity to curvature and shape emerges in early life or how it develops. We studied the development of shape sensitivity in 18 macaques, aged 2 months to 10 years. Using radial frequency stimuli, circular targets whose radii are modulated sinusoidally, we tested monkeys' ability to radial frequency stimuli from circles as a function of the depth and frequency of sinusoidal modulation. We implemented a new four-choice oddity task and compared the resulting data with that from a traditional two-alternative forced choice task. We found that radial frequency pattern perception was measurable at the youngest age tested (2 months). Behavioral performance at all radial frequencies improved with age. Performance was better for higher radial frequencies, suggesting the developing visual system prioritizes processing of fine visual details that are ecologically relevant. By using two complementary methods, we were able to capture a comprehensive developmental trajectory for shape perception.

Conservation of cortical crowding distance across individuals in human V4.

Crowding is the failure to recognize an object due to insufficient spacing, which slows daily tasks such as reading and search. Across 49 observers, we found large variations in psychophysical crowding distance and retinotopic map size. These measures covary, conserving a 1.4-mm cortical crowding distance (threshold object spacing on the cortical surface) in the human V4 map, but not V1-V3. This links the spacing limit of visual recognition to overall V4 size.

Developmentally stable representations of naturalistic image structure in macaque visual cortex.

We studied visual development in macaque monkeys using texture stimuli, matched in local spectral content but varying in "naturalistic" structure. In adult monkeys, naturalistic textures preferentially drive neurons in areas V2 and V4, but not V1. We paired behavioral measurements of naturalness sensitivity with separately-obtained neuronal population recordings from neurons in areas V1, V2, V4, and inferotemporal cortex (IT). We made behavioral measurements from 16 weeks of age and physiological measurements as early as 20 weeks, and continued through 56 weeks. Behavioral sensitivity reached half of maximum at roughly 25 weeks of age. Neural sensitivities remained stable from the earliest ages tested. As in adults, neural sensitivity to naturalistic structure increased from V1 to V2 to V4. While sensitivities in V2 and IT were similar, the dimensionality of the IT representation was more similar to V4's than to V2's.

EasyEyes - A new method for accurate fixation in online vision testing.

Online methods allow testing of larger, more diverse populations, with much less effort than in-lab testing. However, many psychophysical measurements, including visual crowding, require accurate eye fixation, which is classically achieved by testing only experienced observers who have learned to fixate reliably, or by using a gaze tracker to restrict testing to moments when fixation is accurate. Alas, both approaches are impractical online as online observers tend to be inexperienced, and online gaze tracking, using the built-in webcam, has a low precision (±4 deg). EasyEyes open-source software reliably measures peripheral thresholds online with accurate fixation achieved in a novel way, without gaze tracking. It tells observers to use the cursor to track a moving crosshair. At a random time during successful tracking, a brief target is presented in the periphery. The observer responds by identifying the target. To evaluate EasyEyes fixation accuracy and thresholds, we tested 12 naive observers in three ways in a counterbalanced order: first, in the laboratory, using gaze-contingent stimulus presentation; second, in the laboratory, using EasyEyes while independently monitoring gaze using EyeLink 1000; third, online at home, using EasyEyes. We find that crowding thresholds are consistent and individual differences are conserved. The small root mean square (RMS) fixation error (0.6 deg) during target presentation eliminates the need for gaze tracking. Thus, this method enables fixation-dependent measurements online, for easy testing of larger and more diverse populations.

The Bouma law accounts for crowding in 50 observers.

Crowding is the failure to recognize an object due to surrounding clutter. Our visual crowding survey measured 13 crowding distances (or "critical spacings") twice in each of 50 observers. The survey includes three eccentricities (0, 5, and 10 deg), four cardinal meridians, two orientations (radial and tangential), and two fonts (Sloan and Pelli). The survey also tested foveal acuity, twice. Remarkably, fitting a two-parameter model-the well-known Bouma law, where crowding distance grows linearly with eccentricity-explains 82% of the variance for all 13 × 50 measured log crowding distances, cross-validated. An enhanced Bouma law, with factors for meridian, crowding orientation, target kind, and observer, explains 94% of the variance, again cross-validated. These additional factors reveal several asymmetries, consistent with previous reports, which can be expressed as crowding-distance ratios: 0.62 horizontal:vertical, 0.79 lower:upper, 0.78 right:left, 0.55 tangential:radial, and 0.78 Sloan-font:Pelli-font. Across our observers, peripheral crowding is independent of foveal crowding and acuity. Evaluation of the Bouma factor, b (the slope of the Bouma law), as a biomarker of visual health would be easier if there were a way to compare results across crowding studies that use different methods. We define a standardized Bouma factor b' that corrects for differences from Bouma's 25 choice alternatives, 75% threshold criterion, and linearly symmetric flanker placement. For radial crowding on the right meridian, the standardized Bouma factor b' is 0.24 for this study, 0.35 for Bouma (1970), and 0.30 for the geometric mean across five representative modern studies, including this one, showing good agreement across labs, including Bouma's. Simulations, confirmed by data, show that peeking can skew estimates of crowding (e.g., greatly decreasing the mean or doubling the SD of log b). Using gaze tracking to prevent peeking, individual differences are robust, as evidenced by the much larger 0.08 SD of log b across observers than the mere 0.03 test-retest SD of log b measured in half an hour. The ease of measurement of crowding enhances its promise as a biomarker for dyslexia and visual health.

EasyEyes - Accurate fixation for online vision testing of crowding and beyond.

Online methods allow testing of larger, more diverse populations, with much less effort than in-lab testing. However, many psychophysical measurements, including visual crowding, require accurate eye fixation, which is classically achieved by testing only experienced observers who have learned to fixate reliably, or by using a gaze tracker to restrict testing to moments when fixation is accurate. Alas, both approaches are impractical online since online observers tend to be inexperienced, and online gaze tracking, using the built-in webcam, has a low precision (±4 deg, Papoutsaki et al., 2016). The EasyEyes open-source software reliably measures peripheral thresholds online with accurate fixation achieved in a novel way, without gaze tracking. EasyEyes tells observers to use the cursor to track a moving crosshair. At a random time during successful tracking, a brief target is presented in the periphery. The observer responds by identifying the target. To evaluate EasyEyes fixation accuracy and thresholds, we tested 12 naive observers in three ways in a counterbalanced order: first, in the lab, using gaze-contingent stimulus presentation (Kurzawski et al., 2023; Pelli et al., 2016); second, in the lab, using EasyEyes while independently monitoring gaze; third, online at home, using EasyEyes. We find that crowding thresholds are consistent (no significant differences in mean and variance of thresholds across ways) and individual differences are conserved. The small root mean square (RMS) fixation error (0.6 deg) during target presentation eliminates the need for gaze tracking. Thus, EasyEyes enables fixation-dependent measurements online, for easy testing of larger and more diverse populations.

Sensitivity to naturalistic texture relies primarily on high spatial frequencies.

Natural images contain information at multiple spatial scales. Though we understand how early visual mechanisms split multiscale images into distinct spatial frequency channels, we do not know how the outputs of these channels are processed further by mid-level visual mechanisms. We have recently developed a texture discrimination task that uses synthetic, multi-scale, "naturalistic" textures to isolate these mid-level mechanisms. Here, we use three experimental manipulations (image blur, image rescaling, and eccentric viewing) to show that perceptual sensitivity to naturalistic structure is strongly dependent on features at high object spatial frequencies (measured in cycles/image). As a result, sensitivity depends on a texture acuity limit, a property of the visual system that sets the highest retinal spatial frequency (measured in cycles/degree) at which observers can detect naturalistic features. Analysis of the texture images using a model observer analysis shows that naturalistic image features at high object spatial frequencies carry more task-relevant information than those at low object spatial frequencies. That is, the dependence of sensitivity on high object spatial frequencies is a property of the texture images, rather than a property of the visual system. Accordingly, we find human observers' ability to extract naturalistic information (their efficiency) is similar for all object spatial frequencies. We conclude that the mid-level mechanisms that underlie perceptual sensitivity effectively extract information from all image features below the texture acuity limit, regardless of their retinal and object spatial frequency.

Deep learning-Using machine learning to study biological vision.

Many vision science studies employ machine learning, especially the version called "deep learning." Neuroscientists use machine learning to decode neural responses. Perception scientists try to understand how living organisms recognize objects. To them, deep neural networks offer benchmark accuracies for recognition of learned stimuli. Originally machine learning was inspired by the brain. Today, machine learning is used as a statistical tool to decode brain activity. Tomorrow, deep neural networks might become our best model of brain function. This brief overview of the use of machine learning in biological vision touches on its strengths, weaknesses, milestones, controversies, and current directions. Here, we hope to help vision scientists assess what role machine learning should play in their research.

Asymmetric Dichoptic Masking in Visual Cortex of Amblyopic Macaque Monkeys.

In amblyopia, abnormal visual experience leads to an extreme form of eye dominance, in which vision through the nondominant eye is degraded. A key aspect of this disorder is perceptual suppression: the image seen by the stronger eye often dominates during binocular viewing, blocking the image of the weaker eye from reaching awareness. Interocular suppression is the focus of ongoing work aimed at understanding and treating amblyopia, yet its physiological basis remains unknown. We measured binocular interactions in visual cortex of anesthetized amblyopic monkeys (female Macaca nemestrina), using 96-channel "Utah" arrays to record from populations of neurons in V1 and V2. In an experiment reported recently (Hallum et al., 2017), we found that reduced excitatory input from the amblyopic eye (AE) revealed a form of balanced binocular suppression that is unaltered in amblyopia. Here, we report on the modulation of the gain of excitatory signals from the AE by signals from its dominant fellow eye (FE). Using a dichoptic masking technique, we found that AE responses to grating stimuli were attenuated by the presentation of a noise mask to the FE, as in a normal control animal. Responses to FE stimuli, by contrast, could not be masked from the AE. We conclude that a weakened ability of the amblyopic eye to modulate cortical response gain creates an imbalance of suppression that favors the dominant eye.SIGNIFICANCE STATEMENT In amblyopia, vision in one eye is impaired as a result of abnormal early visual experience. Behavioral observations in humans with amblyopia suggest that much of their visual loss is due to active suppression of their amblyopic eye. Here we describe experiments in which we studied binocular interactions in macaques with experimentally induced amblyopia. In normal monkeys, the gain of neuronal response to stimulation of one eye is modulated by contrast in the other eye, but in monkeys with amblyopia the balance of gain modulation is altered so that the weaker, amblyopic eye has little effect while the stronger fellow eye has a strong effect. This asymmetric suppression may be a key component of the perceptual losses in amblyopia.

Altered Balance of Receptive Field Excitation and Suppression in Visual Cortex of Amblyopic Macaque Monkeys.

In amblyopia, a visual disorder caused by abnormal visual experience during development, the amblyopic eye (AE) loses visual sensitivity whereas the fellow eye (FE) is largely unaffected. Binocular vision in amblyopes is often disrupted by interocular suppression. We used 96-electrode arrays to record neurons and neuronal groups in areas V1 and V2 of six female macaque monkeys (Macaca nemestrina) made amblyopic by artificial strabismus or anisometropia in early life, as well as two visually normal female controls. To measure suppressive binocular interactions directly, we recorded neuronal responses to dichoptic stimulation. We stimulated both eyes simultaneously with large sinusoidal gratings, controlling their contrast independently with raised-cosine modulators of different orientations and spatial frequencies. We modeled each eye's receptive field at each cortical site using a difference of Gaussian envelopes and derived estimates of the strength of central excitation and surround suppression. We used these estimates to calculate ocular dominance separately for excitation and suppression. Excitatory drive from the FE dominated amblyopic visual cortex, especially in more severe amblyopes, but suppression from both the FE and AEs was prevalent in all animals. This imbalance created strong interocular suppression in deep amblyopes: increasing contrast in the AE decreased responses at binocular cortical sites. These response patterns reveal mechanisms that likely contribute to the interocular suppression that disrupts vision in amblyopes.SIGNIFICANCE STATEMENT Amblyopia is a developmental visual disorder that alters both monocular vision and binocular interaction. Using microelectrode arrays, we examined binocular interaction in primary visual cortex and V2 of six amblyopic macaque monkeys (Macaca nemestrina) and two visually normal controls. By stimulating the eyes dichoptically, we showed that, in amblyopic cortex, the binocular combination of signals is altered. The excitatory influence of the two eyes is imbalanced to a degree that can be predicted from the severity of amblyopia, whereas suppression from both eyes is prevalent in all animals. This altered balance of excitation and suppression reflects mechanisms that may contribute to the interocular perceptual suppression that disrupts vision in amblyopes.

Explicit information for category-orthogonal object properties increases along the ventral stream.

Extensive research has revealed that the ventral visual stream hierarchically builds a robust representation for supporting visual object categorization tasks. We systematically explored the ability of multiple ventral visual areas to support a variety of 'category-orthogonal' object properties such as position, size and pose. For complex naturalistic stimuli, we found that the inferior temporal (IT) population encodes all measured category-orthogonal object properties, including those properties often considered to be low-level features (for example, position), more explicitly than earlier ventral stream areas. We also found that the IT population better predicts human performance patterns across properties. A hierarchical neural network model based on simple computational principles generates these same cross-area patterns of information. Taken together, our empirical results support the hypothesis that all behaviorally relevant object properties are extracted in concert up the ventral visual hierarchy, and our computational model explains how that hierarchy might be built.

Simple Learned Weighted Sums of Inferior Temporal Neuronal Firing Rates Accurately Predict Human Core Object Recognition Performance.

To go beyond qualitative models of the biological substrate of object recognition, we ask: can a single ventral stream neuronal linking hypothesis quantitatively account for core object recognition performance over a broad range of tasks? We measured human performance in 64 object recognition tests using thousands of challenging images that explore shape similarity and identity preserving object variation. We then used multielectrode arrays to measure neuronal population responses to those same images in visual areas V4 and inferior temporal (IT) cortex of monkeys and simulated V1 population responses. We tested leading candidate linking hypotheses and control hypotheses, each postulating how ventral stream neuronal responses underlie object recognition behavior. Specifically, for each hypothesis, we computed the predicted performance on the 64 tests and compared it with the measured pattern of human performance. All tested hypotheses based on low- and mid-level visually evoked activity (pixels, V1, and V4) were very poor predictors of the human behavioral pattern. However, simple learned weighted sums of distributed average IT firing rates exactly predicted the behavioral pattern. More elaborate linking hypotheses relying on IT trial-by-trial correlational structure, finer IT temporal codes, or ones that strictly respect the known spatial substructures of IT ("face patches") did not improve predictive power. Although these results do not reject those more elaborate hypotheses, they suggest a simple, sufficient quantitative model: each object recognition task is learned from the spatially distributed mean firing rates (100 ms) of ∼60,000 IT neurons and is executed as a simple weighted sum of those firing rates. Significance statement: We sought to go beyond qualitative models of visual object recognition and determine whether a single neuronal linking hypothesis can quantitatively account for core object recognition behavior. To achieve this, we designed a database of images for evaluating object recognition performance. We used multielectrode arrays to characterize hundreds of neurons in the visual ventral stream of nonhuman primates and measured the object recognition performance of >100 human observers. Remarkably, we found that simple learned weighted sums of firing rates of neurons in monkey inferior temporal (IT) cortex accurately predicted human performance. Although previous work led us to expect that IT would outperform V4, we were surprised by the quantitative precision with which simple IT-based linking hypotheses accounted for human behavior.

Population representation of visual information in areas V1 and V2 of amblyopic macaques.

Amblyopia is a developmental disorder resulting in poor vision in one eye. The mechanism by which input to the affected eye is prevented from reaching the level of awareness remains poorly understood. We recorded simultaneously from large populations of neurons in the supragranular layers of areas V1 and V2 in 6 macaques that were made amblyopic by rearing with artificial strabismus or anisometropia, and 1 normally reared control. In agreement with previous reports, we found that cortical neuronal signals driven through the amblyopic eyes were reduced, and that cortical neurons were on average more strongly driven by the non-amblyopic than by the amblyopic eyes. We analyzed multiunit recordings using standard population decoding methods, and found that visual signals from the amblyopic eye, while weakened, were not degraded enough to explain the behavioral deficits. Thus additional losses must arise in downstream processing. We tested the idea that under monocular viewing conditions, only signals from neurons dominated by - rather than driven by - the open eye might be used. This reduces the proportion of neuronal signals available from the amblyopic eye, and amplifies the interocular difference observed at the level of single neurons. We conclude that amblyopia might arise in part from degradation in the neuronal signals from the amblyopic eye, and in part from a reduction in the number of signals processed by downstream areas.

Deep neural networks rival the representation of primate IT cortex for core visual object recognition.

The primate visual system achieves remarkable visual object recognition performance even in brief presentations, and under changes to object exemplar, geometric transformations, and background variation (a.k.a. core visual object recognition). This remarkable performance is mediated by the representation formed in inferior temporal (IT) cortex. In parallel, recent advances in machine learning have led to ever higher performing models of object recognition using artificial deep neural networks (DNNs). It remains unclear, however, whether the representational performance of DNNs rivals that of the brain. To accurately produce such a comparison, a major difficulty has been a unifying metric that accounts for experimental limitations, such as the amount of noise, the number of neural recording sites, and the number of trials, and computational limitations, such as the complexity of the decoding classifier and the number of classifier training examples. In this work, we perform a direct comparison that corrects for these experimental limitations and computational considerations. As part of our methodology, we propose an extension of "kernel analysis" that measures the generalization accuracy as a function of representational complexity. Our evaluations show that, unlike previous bio-inspired models, the latest DNNs rival the representational performance of IT cortex on this visual object recognition task. Furthermore, we show that models that perform well on measures of representational performance also perform well on measures of representational similarity to IT, and on measures of predicting individual IT multi-unit responses. Whether these DNNs rely on computational mechanisms similar to the primate visual system is yet to be determined, but, unlike all previous bio-inspired models, that possibility cannot be ruled out merely on representational performance grounds.

Binocular integration of pattern motion signals by MT neurons and by human observers.

Analysis of the movement of a complex visual stimulus is expressed in the responses of pattern-direction-selective neurons in area MT, which depend in turn on directionally selective inputs from area V1. How do MT neurons integrate their inputs? Pattern selectivity in MT breaks down when the gratings comprising a moving plaid are presented to non-overlapping regions of the (monocular) receptive field. Here we ask an analogous question, is pattern selectivity maintained when the component gratings are presented dichoptically to binocular MT neurons? We recorded from single units in area MT, measuring responses to monocular gratings and plaids, and to dichoptic plaids in which the components are presented separately to each eye. Neurons that are pattern selective when tested monocularly lose this selectivity when stimulated with dichoptic plaids. When human observers view these same stimuli, dichoptic plaids induce binocular rivalry. Yet motion signals from each eye can be integrated despite rivalry, revealing a dissociation of form and motion perception. These results reveal the role of monocular mechanisms in the computation of pattern motion in single neurons, and demonstrate that the perception of motion is not fully represented by the responses of individual MT neurons.

Nonlinear signal summation in magnocellular neurons of the macaque lateral geniculate nucleus.

Magnocellular (M-), but not parvocellular (P-), neurons of the macaque lateral geniculate nucleus (LGN) differ distinctively in their responses to counterphase-modulated and drifting gratings. Relative to stimulation with drifting gratings, counterphase modulation reduces the responses of M- cells in a band around 25 Hz, producing a "notch" in the temporal modulation transfer function (tMTF). The notch is prominent in nearly every M- cell with little variation in the temporal frequency at which it is deepest. The machinery responsible for the notch lies mostly outside the classical linear center. Directly driving the notching mechanism with annular gratings evokes no linear response but elicits a second harmonic (F2) modulation of the discharge accompanied by a drop in the mean discharge (F0). Analysis of the S- potential, which reveals inputs from ganglion cells, shows that 1) tMTFs of the afferent retinal ganglion cells are not notched and 2) during stimulation with annular gratings, the second harmonic component is present, but the drop in the F0 is largely absent from the responses of parasol ganglion cells. These results suggest that the notch is caused by the combined action of the linear response and the second harmonic response, both inherited from retina, and a suppression that originates after the retina. Our results reveal a distinctive signal transformation in the LGN and they show that nearly every M- cell exhibits a spatial nonlinearity like that observed in Y cells of the cat.

Grouping in object recognition: the role of a Gestalt law in letter identification.

The Gestalt psychologists reported a set of laws describing how vision groups elements to recognize objects. The Gestalt laws "prescribe for us what we are to recognize 'as one thing'" (Kohler, 1920). Were they right? Does object recognition involve grouping? Tests of the laws of grouping have been favourable, but mostly assessed only detection, not identification, of the compound object. The grouping of elements seen in the detection experiments with lattices and "snakes in the grass" is compelling, but falls far short of the vivid everyday experience of recognizing a familiar, meaningful, named thing, which mediates the ordinary identification of an object. Thus, after nearly a century, there is hardly any evidence that grouping plays a role in ordinary object recognition. To assess grouping in object recognition, we made letters out of grating patches and measured threshold contrast for identifying these letters in visual noise as a function of perturbation of grating orientation, phase, and offset. We define a new measure, "wiggle", to characterize the degree to which these various perturbations violate the Gestalt law of good continuation. We find that efficiency for letter identification is inversely proportional to wiggle and is wholly determined by wiggle, independent of how the wiggle was produced. Thus the effects of three different kinds of shape perturbation on letter identifiability are predicted by a single measure of goodness of continuation. This shows that letter identification obeys the Gestalt law of good continuation and may be the first confirmation of the original Gestalt claim that object recognition involves grouping.

A new code for contrast in the primate visual pathway.

We characterize a hitherto undocumented type of neuron present in the regions bordering the principal layers of the macaque lateral geniculate nucleus. Neurons of this type were distinguished by a high and unusually regular maintained discharge that was suppressed by spatiotemporal modulation of luminance or chromaticity within the receptive field. The response to any effective stimulus was a reduction in discharge, reminiscent of the "suppressed-by-contrast" cells of the cat retina. To a counterphase-modulated grating, the response was a phase-insensitive suppression modulated at twice the stimulus frequency, implying a receptive field comprised of multiple mechanisms that generate rectifying responses. This distinctive nonlinearity makes the neurons well suited to computing a measure of contrast energy; such a signal might be important in regulating sensitivity early in visual cortex.

Motion integration by neurons in macaque MT is local, not global.

Direction-selective neurons in primary visual cortex have small receptive fields that encode the motions of local features. These motions often differ from the motion of the object to which they belong and must therefore be integrated elsewhere. A candidate site for this integration is visual cortical area MT (V5), in which cells with large receptive fields compute the motion of patterns. Previous studies of motion integration in MT have used stimuli that fill the receptive field, and thus do not test whether motion information is really integrated across this whole area. For each MT neuron, we identified two regions ("patches") within the receptive field that were approximately equally effective in driving responses. We then measured responses to plaids whose component gratings overlapped within a patch, and compared them with responses to the same component gratings presented in separate patches. Cells that were selective for the direction of motion of the whole pattern when the gratings overlapped lost this selectivity when the gratings were separated and became selective instead for the direction of motion of the individual components. If MT cells simply pooled all of the inputs that endow them with a receptive field, they would encode all of the motions in the receptive field as belonging to a single object. Our results indicate instead that critical elements of the computations underlying pattern-direction selectivity in MT are done locally, on a scale smaller than the whole receptive field.

Crowding and eccentricity determine reading rate.

Bouma's law of crowding predicts an uncrowded central window through which we can read and a crowded periphery through which we cannot. The old discovery that readers make several fixations per second, rather than a continuous sweep across the text, suggests that reading is limited by the number of letters that can be acquired in one fixation, without moving one's eyes. That "visual span" has been measured in various ways, but remains unexplained. Here we show (1) that the visual span is simply the number of characters that are not crowded and (2) that, at each vertical eccentricity, reading rate is proportional to the uncrowded span. We measure rapid serial visual presentation (RSVP) reading rate for text, in both original and scrambled word order, as a function of size and spacing at central and peripheral locations. As text size increases, reading rate rises abruptly from zero to maximum rate. This classic reading rate curve consists of a cliff and a plateau, characterized by two parameters, critical print size and maximum reading rate. Joining two ideas from the literature explains the whole curve. These ideas are Bouma's law of crowding and Legge's conjecture that reading rate is proportional to visual span. We show that Legge's visual span is the uncrowded span predicted by Bouma's law. This result joins Bouma and Legge to explain reading rate's dependence on letter size and spacing. Well-corrected fluent observers reading ordinary text with adequate light are limited by letter spacing (crowding), not size (acuity). More generally, it seems that this account holds true, independent of size, contrast, and luminance, provided only that text contrast is at least four times the threshold contrast for an isolated letter. For any given spacing, there is a central uncrowded span through which we read. This uncrowded span model explains the shape of the reading rate curve. We test the model in several ways. We use a "silent substitution" technique to measure the uncrowded span during reading. These substitutions spoil letter identification but are undetectable when the letters are crowded. Critical spacing is the smallest distance between letters that avoids crowding. We find that the critical spacing for letter identification predicts both the critical spacing and the span for reading. Thus, crowding predicts the parameters that characterize both the cliff and the plateau of the reading rate curve. Previous studies have found worrisome differences across observers and laboratories in the measured peripheral reading rates for ordinary text, which may reflect differences in print exposure, but we find that reading rate is much more consistent when word order is scrambled. In all conditions tested--all sizes and spacings, central and peripheral, ordered and scrambled--reading is limited by crowding. For each observer, at each vertical eccentricity, reading rate is proportional to the uncrowded span.