Cortical Magnification Research Articles

On the cortical mapping function – Visual space, cortical space, and crowding

The retino-cortical visual pathway is retinotopically organized: Neighbourhood relationships on the retina are preserved in the mapping. Size relationships in that mapping are also highly regular: The size of a patch in the visual field that maps onto a cortical patch of fixed size follows, along any radius and over a wide range, simply a linear function with retinal eccentricity. As a consequence, the mapping of retinal to cortical locations follows a logarithmic function along that radius. While this has already been shown by Fischer (1973, Vision Research, 13, 2113–2120), the link between the linear function – which describes the local behaviour by the cortical magnification factor M – and the logarithmic location function for the global behaviour, has never been made explicit. The present paper provides such a link as a set of ready-to-use equations using Levi and Klein’s E2 nomenclature, and examples for their validity and applicability in the mapping literature are discussed. The equations allow estimating M in the retinotopic centre; values thus derived from the literature show enormous, hitherto unnoticed, variability. A new structural parameter, d2, is proposed to characterize the cortical map, as a counterpart to E2; it shows much more stability. One pitfall is discussed and spelt out, namely the common myth that a pure logarithmic function, without constant term, will give an adequate map. The correct equations are finally extended to describe the cortical map of Bouma’s law on visual crowding. The result contradicts recent suggestions that critical crowding distance corresponds to constant cortical distance.

Asymmetries around the visual field: From retina to cortex to behavior.

Visual performance varies around the visual field. It is best near the fovea compared to the periphery, and at iso-eccentric locations it is best on the horizontal, intermediate on the lower, and poorest on the upper meridian. The fovea-to-periphery performance decline is linked to the decreases in cone density, retinal ganglion cell (RGC) density, and V1 cortical magnification factor (CMF) as eccentricity increases. The origins of polar angle asymmetries are not well understood. Optical quality and cone density vary across the retina, but recent computational modeling has shown that these factors can only account for a small percentage of behavior. Here, we investigate how visual processing beyond the cone photon absorptions contributes to polar angle asymmetries in performance. First, we quantify the extent of asymmetries in cone density, midget RGC density, and V1 CMF. We find that both polar angle asymmetries and eccentricity gradients increase from cones to mRGCs, and from mRGCs to cortex. Second, we extend our previously published computational observer model to quantify the contribution of phototransduction by the cones and spatial filtering by mRGCs to behavioral asymmetries. Starting with photons emitted by a visual display, the model simulates the effect of human optics, cone isomerizations, phototransduction, and mRGC spatial filtering. The model performs a forced choice orientation discrimination task on mRGC responses using a linear support vector machine classifier. The model shows that asymmetries in a decision maker's performance across polar angle are greater when assessing the photocurrents than when assessing isomerizations and are greater still when assessing mRGC signals. Nonetheless, the polar angle asymmetries of the mRGC outputs are still considerably smaller than those observed from human performance. We conclude that cone isomerizations, phototransduction, and the spatial filtering properties of mRGCs contribute to polar angle performance differences, but that a full account of these differences will entail additional contribution from cortical representations.

Role of the Dorsal Posterior Parietal Cortex in the Accurate Perception of Object Magnitude in Peripheral Vision.

Following superior parietal lobule and intraparietal sulcus (SPL-IPS) damage, optic ataxia patients underestimate the distance of objects in the ataxic visual field such that they produce hypometric pointing errors. The metrics of these pointing errors relative to visual target eccentricity fit the cortical magnification of central vision. The SPL-IPS would therefore implement an active “peripheral magnification” to match the real metrics of the environment for accurate action. We further hypothesized that this active compensation of the central magnification by the SPL-IPS contributes to actual object’ size perception in peripheral vision. Three optic ataxia patients and 10 age-matched controls were assessed in comparing the thickness of two rectangles flashed simultaneously, one in central and another in peripheral vision. The bilateral optic ataxia patient exhibited exaggerated underestimation bias and uncertainty compared to the control group in both visual fields. The two unilateral optic ataxia patients exhibited a pathological asymmetry between visual fields: size perception performance was affected in their contralesional peripheral visual field compared to their healthy side. These results demonstrate that the SPL-IPS contributes to accurate size perception in peripheral vision.

Cortical magnification analysis of shape adaptation reveals early curvature coding mechanisms

Cortical magnification analysis of shape adaptation reveals early curvature coding mechanisms

Topological dominance in peripheral vision.

The question of what peripheral vision is good for, especially in pattern recognition, is one of the most important and controversial issues in cognitive science. In a series of experiments, we provide substantial evidence that observers’ behavioral performance in the periphery is consistently superior to central vision for topological change detection, while nontopological change detection deteriorates with increasing eccentricity. These experiments generalize the topological account of object perception in the periphery to different kinds of topological changes (i.e., including introduction, disappearance, and change in number of holes) in comparison with a broad spectrum of geometric properties (e.g., luminance, similarity, spatial frequency, perimeter, and shape of the contour). Moreover, when the stimuli were scaled according to cortical magnification factor and the task difficulty was well controlled by adjusting luminance of the background, the advantage of topological change detection in the periphery remained. The observed advantage of topological change detection in the periphery supports the view that the topological definition of objects provides a coherent account for object perception in peripheral vision, allowing pattern recognition with limited acuity.

Cross-dataset reproducibility of human retinotopic maps

Population receptive field (pRF) models fit to fMRI data are used to non-invasively measure retinotopic maps in human visual cortex, and these maps are a fundamental component of visual neuroscience experiments. Here, we examined the reproducibility of retinotopic maps across two datasets: a newly acquired retinotopy dataset from New York University (NYU) (n = 44) and a public dataset from the Human Connectome Project (HCP) (n = 181). Our goal was to assess the degree to which pRF properties are similar across datasets, despite substantial differences in their experimental protocols. The two datasets simultaneously differ in their stimulus apertures, participant pool, fMRI protocol, MRI field strength, and preprocessing pipeline. We assessed the cross-dataset reproducibility of the two datasets in terms of the similarity of vertex-wise pRF estimates and in terms of large-scale polar angle asymmetries in cortical magnification. Within V1, V2, V3, and hV4, the group-median NYU and HCP vertex-wise polar angle estimates were nearly identical. Both eccentricity and pRF size estimates were also strongly correlated between the two datasets, but with a slope different from 1; the eccentricity and pRF size estimates were systematically greater in the NYU data. Next, to compare large-scale map properties, we quantified two polar angle asymmetries in V1 cortical magnification previously identified in the HCP data. The NYU dataset confirms earlier reports that more cortical surface area represents horizontal than vertical visual field meridian, and lower than upper vertical visual field meridian. Together, our findings show that the retinotopic properties of V1, V2, V3, and hV4 can be reliably measured across two datasets, despite numerous differences in their experimental design. fMRI-derived retinotopic maps are reproducible because they rely on an explicit computational model of the fMRI response. In the case of pRF mapping, the model is grounded in physiological evidence of how visual receptive fields are organized, allowing one to quantitatively characterize the BOLD signal in terms of stimulus properties (i.e., location and size). The new NYU Retinotopy Dataset will serve as a useful benchmark for testing hypotheses about the organization of visual areas and for comparison to the HCP 7T Retinotopy Dataset.

Cortical magnification in human visual cortex parallels task performance around the visual field.

Human vision has striking radial asymmetries, with performance on many tasks varying sharply with stimulus polar angle. Performance is generally better on the horizontal than vertical meridian, and on the lower than upper vertical meridian, and these asymmetries decrease gradually with deviation from the vertical meridian. Here, we report cortical magnification at a fine angular resolution around the visual field. This precision enables comparisons between cortical magnification and behavior, between cortical magnification and retinal cell densities, and between cortical magnification in twin pairs. We show that cortical magnification in the human primary visual cortex, measured in 163 subjects, varies substantially around the visual field, with a pattern similar to behavior. These radial asymmetries in the cortex are larger than those found in the retina, and they are correlated between monozygotic twin pairs. These findings indicate a tight link between cortical topography and behavior, and suggest that visual field asymmetries are partly heritable.

Shape discrimination in peripheral vision: Addressing pragmatic limitations of M-scaling radial frequency patterns

Peripheral worsening in shape discrimination (SD) can be compensated by size-scaling of peripheral stimuli. However, such scaling results in production of large stimuli that occupy a vast range of eccentricities. We used six proportionally decreasing spatial scales to address this pragmatic limitation and to explore how shape discrimination varies with radius in the nasal visual field. Five participants with normal vision discriminated circles and radial frequency (RF) patterns presented nasally to the fixation point at 5°, 10°, 15° and 20°. Stimuli were scaled with the nasal cortical magnification factor (nCMF) from a central stimulus in six spatial scales, which varied from 0.125 to 1, where 1 corresponded to 1.2° radius. Thresholds expressed in Weber fractions remained constant at eccentricities up to 20° regardless of the spatial scale. Weber fractions for the smaller spatial scales (0.125–0.5) were higher and more variable than for the larger spatial scales (0.75–1), yet still constant across periphery. The results provide evidence that peripheral shape discrimination is constrained by low-level properties, such as eccentricity, and can be predicted by the cortical magnification theory. However, above the peripheral modulation resolution limits, RF shape discrimination is based on the proportion between the modulation amplitude and the radius for larger scales (0.75–1), and demonstrates peripheral scale invariance for these stimuli. For eccentric shape discrimination tests, stimuli with low spatial frequency, high contrast, and radii corresponding to SS 0.75–0.875 should be used to ensure constant Weber fractions, small variability, and peripheral stimuli that are not excessively magnified.

FovVideoVDP

FovVideoVDP is a video difference metric that models the spatial, temporal, and peripheral aspects of perception. While many other metrics are available, our work provides the first practical treatment of these three central aspects of vision simultaneously. The complex interplay between spatial and temporal sensitivity across retinal locations is especially important for displays that cover a large field-of-view, such as Virtual and Augmented Reality displays, and associated methods, such as foveated rendering. Our metric is derived from psychophysical studies of the early visual system, which model spatio-temporal contrast sensitivity, cortical magnification and contrast masking. It accounts for physical specification of the display (luminance, size, resolution) and viewing distance. To validate the metric, we collected a novel foveated rendering dataset which captures quality degradation due to sampling and reconstruction. To demonstrate our algorithm's generality, we test it on 3 independent foveated video datasets, and on a large image quality dataset, achieving the best performance across all datasets when compared to the state-of-the-art.

Emergence of local and global synaptic organization on cortical dendrites

Synaptic inputs on cortical dendrites are organized with remarkable subcellular precision at the micron level. This organization emerges during early postnatal development through patterned spontaneous activity and manifests both locally where nearby synapses are significantly correlated, and globally with distance to the soma. We propose a biophysically motivated synaptic plasticity model to dissect the mechanistic origins of this organization during development and elucidate synaptic clustering of different stimulus features in the adult. Our model captures local clustering of orientation in ferret and receptive field overlap in mouse visual cortex based on the receptive field diameter and the cortical magnification of visual space. Including action potential back-propagation explains branch clustering heterogeneity in the ferret and produces a global retinotopy gradient from soma to dendrite in the mouse. Therefore, by combining activity-dependent synaptic competition and species-specific receptive fields, our framework explains different aspects of synaptic organization regarding stimulus features and spatial scales.

Cytoarchitectural characteristics associated with cognitive flexibility in raccoons.

With rates of psychiatric illnesses such as depression continuing to rise, additional preclinical models are needed to facilitate translational neuroscience research. In the current study, the raccoon (Procyon lotor) was investigated due to its similarities with primate brains, including comparable proportional neuronal densities, cortical magnification of the forepaw area, and cortical gyrification. Specifically, we report on the cytoarchitectural characteristics of raccoons profiled as high, intermediate, or low solvers in a multiaccess problem-solving task. Isotropic fractionation indicated that high-solvers had significantly more cells in the hippocampus (HC) than the other solving groups; further, a nonsignificant trend suggested that this increase in cell profile density was due to increased nonneuronal (e.g., glial) cells. Group differences were not observed in the cellular density of the somatosensory cortex. Thionin-based staining confirmed the presence of von Economo neurons (VENs) in the frontoinsular cortex, although no impact of solving ability on VEN cell profile density levels was observed. Elongated fusiform cells were quantified in the HC dentate gyrus where high-solvers were observed to have higher levels of this cell type than the other solving groups. In sum, the current findings suggest that varying cytoarchitectural phenotypes contribute to cognitive flexibility. Additional research is necessary to determine the translational value of cytoarchitectural distribution patterns on adaptive behavioral outcomes associated with cognitive performance and mental health.

Topographic numerosity maps cover subitizing and estimation ranges

Numerosity, the set size of a group of items, helps guide behaviour and decisions. Non-symbolic numerosities are represented by the approximate number system. However, distinct behavioural performance suggests that small numerosities, i.e. subitizing range, are implemented differently in the brain than larger numerosities. Prior work has shown that neural populations selectively responding (i.e. hemodynamic responses) to small numerosities are organized into a network of topographical maps. Here, we investigate how neural populations respond to large numerosities, well into the ANS. Using 7 T fMRI and biologically-inspired analyses, we found a network of neural populations tuned to both small and large numerosities organized within the same topographic maps. These results demonstrate a continuum of numerosity preferences that progressively cover both the subitizing range and beyond within the same numerosity map, suggesting a single neural mechanism. We hypothesize that differences in map properties, such as cortical magnification and tuning width, underlie known differences in behaviour.

Somatotopic Arrangement of the Human Primary Somatosensory Cortex Derived From Functional Magnetic Resonance Imaging.

Functional magnetic resonance imaging (fMRI) was used to estimate neuronal activity in the primary somatosensory cortex of six participants undergoing cutaneous tactile stimulation on skin areas spread across the entire body. Differences between the accepted somatotopic maps derived from Penfield's work and those generated by this fMRI study were sought, including representational transpositions or replications across the cortex. MR-safe pneumatic devices mimicking the action of a Wartenberg wheel supplied touch stimuli in eight areas. Seven were on the left side of the body: foot, lower, and upper leg, trunk beneath ribcage, anterior forearm, middle fingertip, and neck above the collarbone. The eighth area was the glabella. Activation magnitude was estimated as the maximum cross-correlation coefficient at a certain phase shift between ideal time series and measured blood oxygen level dependent (BOLD) time courses on the cortical surface. Maximally correlated clusters associated with each cutaneous area were calculated, and cortical magnification factors were estimated. Activity correlated to lower limb stimulation was observed in the paracentral lobule and superomedial postcentral region. Correlations to upper extremity stimulation were observed in the postcentral area adjacent to the motor hand knob. Activity correlated to trunk, face and neck stimulation was localized in the superomedial one-third of the postcentral region, which differed from Penfield's cortical homunculus.

ВОЗМОЖНОСТИ И ОГРАНИЧЕНИЯ ЭКСТРАФОВЕАЛЬНОГО ВОСПРИЯТИЯ: АНАЛИТИЧЕСКИЙ ОБЗОР

The article presents an analytical review of studies in the field of extrafoveal perception. The region of extrafoveal vision combines the parafovea and periphery of the retina, so extrafoveal perception is the perception of objects which projections are outside of the fovea. For a long time, it has been believed that extrafoveal vision, in contrast to foveal, has a lower acuity and resolution and is used mainly for preliminary analysis of the visual field and selection of relevant objects for their more thorough analysis in fovea. However, the literature shows that extrafoveal perception is much more interesting and autonomous process as it has been previously considered. The paper analyzes a number of works showing that it is possible to identify both specific features of simple stimuli and rather complex objects, such as faces or whole scenes, up to the possibility of their semantic analysis, even in extrafoveal vision. The review considers the history of studies on extrafoveal perception, from the earliest works (Hueck, 1840; Aubert, Foerster, 1857) to the most recent ones of the last 5 years. These works have analyzed the main factors influencing the effectiveness of extrafoveal vision, for example, cortical magnification factor, which reflects differences in the number of neurons in the visual cortex responsible for processing stimuli depending on the region of the retina: the closer the object is to the fovea, the more neurons are involved in its processing, and vice versa. Other factors determining the efficacy of extrafoveal perception include the following: crowding effect when the target object on the periphery surrounded by distractors is identified worse than a separately located stimulus; specific characteristics of a target and distractors (for example, contexts evoking pop-out effect). Crowding effect is also related to the question of correlating two forms of processing extrafoveal information: preattentive processing (parallel “bottom up” processing) and covert attention (moving the point of deeper analysis along the visual field without eye movements) which can be controlled up to some degree. The other factors influencing the effectiveness of extrafoveal perception concern the context of a task (categorical search in laboratory conditions, analysis of the real world scenes, reactions to extrafoveal stimuli during definite activity) and individual differences. Additionally, we have analyzed the works on the possibilities of training extrafoveal perception, which can affect both higher-level processes, for example, identification of the context of complex scenes, perception of emotions and categorical visual search, and lower-level visual functions, such as identification of spatial orientation, contrast perception and reduction of crowding effect.

The effect of the stimulus eccentricity on the main component of the steady‐state visual evoked potential

PurposeFor electrophysiological functional diagnostics, the main component of steady‐state visual evoked potentials (SSVEP) at stimulation frequency (SF) is mainly used. However, some studies reported the main component at the second harmonic of the SF. A possible cause are signal components of the single responses that differ from the SF when the responses overlap during steady‐state stimulations, but the origin is not fully understood. The aim of our study was to investigate the effect of the stimulus eccentricity on the occurrence of the main component of SSVEP.MethodsWe studied 14 healthy subjects (5 m, 28 ± 5.0 years) using a circular layout (r1 = 0–1.6°, r2 = 1.6–3.5°, r3 = 3.5–6.4°, r4 = 6.4–10.9°, r5 = 10.9–18°). The dimensions of the stimuli were scaled according to the cortical magnification. The stimuli (luminance: 350 cd/m2, contrast: 99%) were presented in a random order at 7.5Hz for 75 cycles for each eccentricity. This procedure was repeated 10 times in total (750 cycles per eccentricity). A background luminance of 30 cd/m2 was added to supress foveal stray light effects. The electrodes were placed at Oz (active), FCz (reference) and FPz (ground). The recorded SSVEP were transformed using Fourier analysis. The medians (M) of the normalized amplitude ratios for amplitudes at first and second harmonic were calculated. Friedman's test (α = 0.05) and the probability of the occurrence of the main component at the second harmonic (P(MCSH)) were used for statistical analysis.ResultsThe normalized amplitude ratios showed a significant difference for the 5 stimulus eccentricities (Mr1 = 0.45, Mr2 = 0.41, Mr3 = 0.72, Mr4 = 0.72 Mr5 = 0.67; p = 0.0002*). P(MCSH) showed an increase for stimulus eccentricities for ≥r3 (P(MCSH)r1 = 0.07, P(MCSH)r2 = 0.07, P(MCSH)r3 = 0.36, P(MCSH)r4 = 0.29, P(MCSH)r5 = 0.36).ConclusionsThe stimulus eccentricity has an influence on the main component of SSVEP. An increase in stimulus eccentricity leads to an increased occurrence of the main component at second harmonic.

Spatial clustering of orientation preference in primary visual cortex of the large rodent agouti.

SummaryAll rodents investigated so far possess orientation-selective neurons in the primary visual cortex (V1) but – in contrast to carnivores and primates – no evidence of periodic maps with pinwheel-like structures. Theoretical studies debating whether phylogeny or universal principles determine development of pinwheels point to V1 size as a critical constraint. Thus, we set out to study maps of agouti, a big diurnal rodent with a V1 size comparable to cats'. In electrophysiology, we detected interspersed orientation and direction-selective neurons with a bias for horizontal contours, corroborated by homogeneous activation in optical imaging. Compatible with spatial clustering at short distance, nearby neurons tended to exhibit similar orientation preference. Our results argue against V1 size as a key parameter in determining the presence of periodic orientation maps. They are consistent with a phylogenetic influence on the map layout and development, potentially reflecting distinct retinal traits or interspecies differences in cortical circuitry.

Postnatal development of subfields in the core region of the mouse auditory cortex

The core region of the rodent auditory cortex has two subfields: the primary auditory area (A1) and the anterior auditory field (AAF). Although the postnatal development of A1 has been studied in several mammalian species, few studies have been conducted on the postnatal development of AAF. Using a voltage-sensitive-dye-based imaging method, we examined and compared the postnatal development of AAF and A1 in mice from postnatal day 11 (P11) to P40. We focused on the postnatal development of tonotopy, the relative position between A1 and AAF, and the properties of tone-evoked responses in the subfields. Tone-evoked responses in the mouse auditory cortex were first observed at P12, and tonotopy was found in both A1 and AAF at this age. Quantification of tonotopy using the cortical magnification factor (CMF; octave difference per unit cortical distance) revealed a rapid change from P12 to P14 in both A1 and AAF, and a stable level from P14. A similar time course of postnatal development was found for the distance between the 4 kHz site in A1 and AAF, the distance between the 16 kHz site in A1 and AAF, and the angle between the frequency axis of A1 and AAF. The maximum amplitude and rise time of tone-evoked signals in both A1 and AAF showed no significant change from P12 to P40, but the latency of the responses to both the 4 kHz and 16 kHz tones decreased during this period, with a more rapid decrease in the latency to 16 kHz tones in both subfields. The duration of responses evoked by 4 kHz tones in both A1 and AAF showed no significant postnatal change, but the duration of responses to 16 kHz tones decreased exponentially in both subfields. The cortical area activated by 4 kHz tones in AAF was always larger than that in A1 at all ages (P12-P40). Our results demonstrated that A1 and AAF developed in parallel postnatally, showing a rapid maturation of tonotopy, slow maturation of response latency and response duration, and a dorsal-to-ventral order (high-frequency site to low-frequency site) of functional maturation.

Geometry and Geodesy on the Primary Visual Cortex as a Surface of Revolution

Biological mapping of the visual field from the eye retina to the primary visual cortex, also known as occipital area V1, is central to vision and eye movement phenomena and research. That mapping is critically dependent on the existence of cortical magnification factors. Once unfolded, V1 has a convex three-dimensional shape, which can be mathematically modeled as a surface of revolution embedded in three-dimensional Euclidean space. Thus, we solve the problem of differential geometry and geodesy for the mapping of the visual field to V1, involving both isotropic and non-isotropic cortical magnification factors of a most general form. We provide illustrations of our technique and results that apply to V1 surfaces with curve profiles relevant to vision research in general and to visual phenomena such as ‘crowding’ effects and eye movement guidance in particular. From a mathematical perspective, we also find intriguing and unexpected differential geometry properties of V1 surfaces, discovering that geodesic orbits have alternative prograde and retrograde characteristics, depending on the interplay between local curvature and global topology.

Dynamics of Contrast Decrement and Increment Responses in Human Visual Cortex.

PurposeThe goal of the present experiments was to determine whether electrophysiologic response properties of the ON and OFF visual pathways observed in animal experimental models can be observed in humans.MethodsSteady-state visual evoked potentials (SSVEPs) were recorded in response to equivalent magnitude contrast increments and decrements presented within a probe-on-pedestal Westheimer sensitization paradigm. The probes were modulated with sawtooth temporal waveforms at a temporal frequency of 3 or 2.73 Hz. SSVEP response waveforms and response spectra for incremental and decremental stimuli were analyzed as a function of stimulus size and visual field location in 67 healthy adult participants.ResultsSSVEPs recorded at the scalp differ between contrast decrements and increments of equal Weber contrast: SSVEP responses were larger in amplitude and shorter in latency for contrast decrements than for contrast increments. Both increment and decrement responses were larger for displays that were scaled for cortical magnification.ConclusionsIn a fashion that parallels results from the early visual system of cats and monkeys, two key properties of ON versus OFF pathways found in single-unit recordings are recapitulated at the population level of activity that can be observed with scalp electrodes, allowing differential assessment of ON and OFF pathway activity in human.Translational RelevanceAs data from preclinical models of visual pathway dysfunction point to differential damage to subtypes of retinal ganglion cells, this approach may be useful in future work on disease detection and treatment monitoring.

Frequency ratio determines discrimination of concentric radial frequency patterns in the peripheral visual field.

Using a radial frequency discrimination task that has not been tested in many previous studies, we examined the dependence of the pattern radius (4 to 16 deg) on the radial frequency thresholds of two different types of concentric radial frequency (RF) patterns: constant circular contour frequency (CCF) RF patterns with different radii, which have the constant physical length of modulation cycle in external real-world space, and constant radial frequency magnified RF patterns with different radii, which have the constant cortical length of modulation cycles. These two types RF patterns used as the reference stimuli had an equal maximum orientation difference from circularity regardless of change in radius. The discrimination threshold expressed by the frequency ratio between RF patterns of different frequencies vs. radius functions for the constant CCF RF patterns indicated different functional forms dependent on the modulation amplitude of the RF patterns. The thresholds increased with increasing pattern radius for small modulation amplitude RF patterns but were relatively flattened for large-amplitude RF patterns. This dependence was ascribed to the eccentricity effect wherein the deformation thresholds for discriminating the RF pattern from a circle increase with increasing stimulus eccentricity (Feng et al. 2020). The discrimination thresholds vs. radius functions for the magnified RF patterns were also flattened for different modulation amplitudes and frequencies. The thresholds (frequency ratio) were similar at all eccentricities. Cortical magnification neutralized the eccentricity effect observed for the constant CCF patterns.