Endstopped neurons in the visual cortex as a substrate for calculating curvature

Perceptual transitions between object rigidity and non-rigidity: Competition and cooperation among motion energy, feature tracking, and shape-based priors

Why do moving objects appear rigid when projected retinal images are deformed non-rigidly? We used rotating rigid objects that can appear rigid or non-rigid to test whether shape features contribute to rigidity perception. When two circular rings were rigidly linked at an angle and jointly rotated at moderate speeds, observers reported that the rings wobbled and were not linked rigidly, but rigid rotation was reported at slow speeds. When gaps, paint, or vertices were added, the rings appeared rigidly rotating even at moderate speeds. At high speeds, all configurations appeared non-rigid. Salient features thus contribute to rigidity at slow and moderate speeds but not at high speeds. Simulated responses of arrays of motion-energy cells showed that motion flow vectors are predominantly orthogonal to the contours of the rings, not parallel to the rotation direction. A convolutional neural network trained to distinguish flow patterns for wobbling versus rotation gave a high probability of wobbling for the motion-energy flows. However, the convolutional neural network gave high probabilities of rotation for motion flows generated by tracking features with arrays of MT pattern-motion cells and corner detectors. In addition, circular rings can appear to spin and roll despite the absence of any sensory evidence, and this illusion is prevented by vertices, gaps, and painted segments, showing the effects of rotational symmetry and shape. Combining convolutional neural network outputs that give greater weight to motion energy at fast speeds and to feature tracking at slow speeds, with the shape-based priors for wobbling and rolling, explained rigid and non-rigid percepts across shapes and speeds (R2 = 0.95). The results demonstrate how cooperation and competition between different neuronal classes lead to specific states of visual perception and to transitions between the states.

Perceptual Transitions between Object Rigidity & Non-rigidity: Competition and cooperation between motion-energy, feature-tracking and shape-based priors

Why do moving objects appear rigid when projected retinal images are deformed non-rigidly? We used rotating rigid objects that can appear rigid or non-rigid to test whether shape features contribute to rigidity perception. When two circular rings were rigidly linked at an angle and jointly rotated at moderate speeds, observers reported that the rings wobbled and were not linked rigidly but rigid rotation was reported at slow speeds. When gaps, paint or vertices were added, the rings appeared rigidly rotating even at moderate speeds. At high speeds, all configurations appeared non-rigid. Salient features thus contribute to rigidity at slow and moderate speeds, but not at high speeds. Simulated responses of arrays of motion-energy cells showed that motion flow vectors are predominantly orthogonal to the contours of the rings, not parallel to the rotation direction. A convolutional neural network trained to distinguish flow patterns for wobbling versus rotation, gave a high probability of wobbling for the motion-energy flows. However, the CNN gave high probabilities of rotation for motion flows generated by tracking features with arrays of MT pattern-motion cells and corner detectors. In addition, circular rings can appear to spin and roll despite the absence of any sensory evidence, and this illusion is prevented by vertices, gaps, and painted segments, showing the effects of rotational symmetry and shape. Combining CNN outputs that give greater weight to motion energy at fast speeds and to feature tracking at slow, with the shape-based priors for wobbling and rolling, explained rigid and nonrigid percepts across shapes and speeds (R2=0.95). The results demonstrate how cooperation and competition between different neuronal classes leads to specific states of visual perception and to transitions between the states.

Challenging deep learning models with image distortion based on the abutting grating illusion

Even state-of-the-art deep learning models lack fundamental abilities compared with humans. While many image distortions have been proposed to compare deep learning with humans, they depend on mathematical transformations instead of human cognitive functions. Here, we propose an image distortion based on the abutting grating illusion, which is a phenomenon discovered in humans and animals. The distortion generates illusory contour perception using line gratings abutting each other. We applied the method to MNIST, high-resolution MNIST, and "16-class-ImageNet" silhouettes. Many models, including models trained from scratch and 109 models pretrained with ImageNet or various data augmentation techniques, were tested. Our results show that abutting grating distortion is challenging even for state-of-the-art deep learning models. We discovered that DeepAugment models outperformed other pretrained models. Visualization of early layers indicates that better-performing models exhibit the endstopping property, which is consistent with neuroscience discoveries. Twenty-four human subjects classified distorted samples to validate the distortion.

Contributions of low- and high-level contextual mechanisms to human face perception

Contextual modulations at primary stages of visual processing depend on the strength of local input. Contextual modulations at high-level stages of (face) processing show a similar dependence to local input strength. Namely, the discriminability of a facial feature determines the amount of influence of the face context on that feature. How high-level contextual modulations emerge from primary mechanisms is unclear due to the scarcity of empirical research systematically addressing the functional link between the two. We tested (62) young adults' ability to process local input independent of the context using contrast detection and (upright and inverted) morphed facial feature matching tasks. We first investigated contextual modulation magnitudes across tasks to address their shared variance. A second analysis focused on the profile of performance across contextual conditions. In upright eye matching and contrast detection tasks, contextual modulations only correlated at the level of their profile (averaged Fisher-Z transformed r = 1.18, BF10 > 100), but not magnitude (r = .15, BF10 = .61), suggesting the functional independence but similar working principles of the mechanisms involved. Both the profile (averaged Fisher-Z transformed r = .32, BF10 = 9.7) and magnitude (r = .28, BF10 = 4.58) of the contextual modulations correlated between inverted eye matching and contrast detection tasks. Our results suggest that non-face-specialized high-level contextual mechanisms (inverted faces) work in connection to primary contextual mechanisms, but that the engagement of face-specialized mechanisms for upright faces obscures this connection. Such combined study of low- and high-level contextual modulations sheds new light on the functional relationship between different levels of the visual processing hierarchy, and thus on its functional organization.

Visually induced γ band rhythm in spatial summation beyond the receptive field in mouse primary visual cortex

Recent studies in many kinds of mammals have established the existence of multiple γ rhythms in the cerebral cortex subserving different functions. In the primary visual cortex (V1), visually induced γ rhythms are dependent on stimulus features. However, experimental findings of γ power induced by varying the size of the drifting grating are inconsistent. Here, we reinvestigated the spatial summation properties of visually induced spike and γ rhythm activities in mouse V1. Our results show that drifting sinusoidal grating stimuli mainly induce 2 γ band rhythms, including a low-frequency band (25-45 Hz) and a high-frequency band (55-75 Hz). Unlike previous findings, we discovered that visually induced γ power could also exhibit extrareceptive field (ERF) modulatory properties. The modulation by ERF stimulation could be either suppressive, countersuppressive, or nonsuppressive, mostly similar to the local spike activity. Moreover, further analysis of the neuron group exhibiting surround suppression in both spike and γ activity revealed that the strength of the surround suppression and the receptive field size showed moderate correlations between measurements by spike and γ rhythm activity. Our findings improve the understanding of the characteristics and neural mechanisms of induced γ rhythms in visual spatial summation.

Diversity of spatiotemporal coding reveals specialized visual processing streams in the mouse cortex

The cerebral cortex contains diverse neural representations of the visual scene, each enabling distinct visual and spatial abilities. However, the extent to which representations are distributed or segregated across cortical areas remains poorly understood. By determining the spatial and temporal responses of >30,000 layer 2/3 pyramidal neurons, we characterize the functional organization of parallel visual streams across eight areas of the mouse cortex. While dorsal and ventral areas form complementary representations of spatiotemporal frequency, motion speed, and spatial patterns, the anterior and posterior dorsal areas show distinct specializations for fast and slow oriented contrasts. At the cellular level, while diverse spatiotemporal tuning lies along a continuum, oriented and non-oriented spatial patterns are encoded by distinct tuning types. The identified tuning types are present across dorsal and ventral streams. The data underscore the highly specific and highly distributed nature of visual cortical representations, which drives specialization of cortical areas and streams.

The cerebral cortex contains different neural representations of the visual scene. Here, the authors show diverse and stereotyped tuning composing specialized representations in the dorsal and ventral areas of the mouse visual cortex, suggesting parallel processing channels and streams.

Neural correlates of local parallelism during naturalistic vision

Human observers can rapidly perceive complex real-world scenes. Grouping visual elements into meaningful units is an integral part of this process. Yet, so far, the neural underpinnings of perceptual grouping have only been studied with simple lab stimuli. We here uncover the neural mechanisms of one important perceptual grouping cue, local parallelism. Using a new, image-computable algorithm for detecting local symmetry in line drawings and photographs, we manipulated the local parallelism content of real-world scenes. We decoded scene categories from patterns of brain activity obtained via functional magnetic resonance imaging (fMRI) in 38 human observers while they viewed the manipulated scenes. Decoding was significantly more accurate for scenes containing strong local parallelism compared to weak local parallelism in the parahippocampal place area (PPA), indicating a central role of parallelism in scene perception. To investigate the origin of the parallelism signal we performed a model-based fMRI analysis of the public BOLD5000 dataset, looking for voxels whose activation time course matches that of the locally parallel content of the 4916 photographs viewed by the participants in the experiment. We found a strong relationship with average local symmetry in visual areas V1-4, PPA, and retrosplenial cortex (RSC). Notably, the parallelism-related signal peaked first in V4, suggesting V4 as the site for extracting paralleism from the visual input. We conclude that local parallelism is a perceptual grouping cue that influences neuronal activity throughout the visual hierarchy, presumably starting at V4. Parallelism plays a key role in the representation of scene categories in PPA.

Quality Assessment of DIBR-Synthesized Views Based on Sparsity of Difference of Closings and Difference of Gaussians

Images synthesized using depth-image-based-rendering (DIBR) techniques may suffer from complex structural distortions. The goal of the primary visual cortex and other parts of brain is to reduce redundancies of input visual signal in order to discover the intrinsic image structure, and thus create sparse image representation. Human visual system (HVS) treats images on several scales and several levels of resolution when perceiving the visual scene. With an attempt to emulate the properties of HVS, we have designed the no-reference model for the quality assessment of DIBR-synthesized views. To extract a higher-order structure of high curvature which corresponds to distortion of shapes to which the HVS is highly sensitive, we define a morphological oriented Difference of Closings (DoC) operator and use it at multiple scales and resolutions. DoC operator nonlinearly removes redundancies and extracts fine grained details, texture of an image local structure and contrast to which HVS is highly sensitive. We introduce a new feature based on sparsity of DoC band. To extract perceptually important low-order structural information (edges), we use the non-oriented Difference of Gaussians (DoG) operator at different scales and resolutions. Measure of sparsity is calculated for DoG bands to get scalar features. To model the relationship between the extracted features and subjective scores, the general regression neural network (GRNN) is used. Quality predictions by the proposed DoC-DoG-GRNN model show higher compatibility with perceptual quality scores in comparison to the tested state-of-the-art metrics when evaluated on four benchmark datasets with synthesized views, IRCCyN/IVC image/video dataset, MCL-3D stereoscopic image dataset and IST image dataset.

From boundaries to bumps: When closed (extremal) contours are critical

Invariants underlying shape inference are elusive: A variety of shapes can give rise to the same image, and a variety of images can be rendered from the same shape. The occluding contour is a rare exception: It has both image salience, in terms of isophotes, and surface meaning, in terms of surface normal. We relax the notion of occluding contour and, more accurately, the rim on the object that projects to it, to define closed extremal curves. This new shape descriptor is invariant over different renderings. It exists at the topological level, which guarantees an image-based counterpart. It surrounds bumps and dents, as well as common interior shape components, and formalizes the qualitative nature of bump perception. The invariants are biologically computable, unify shape inferences from shading and specular materials, and predict new phenomena in bump and dent perception. Most important, working at the topological level allows us to capture the elusive aspect of bump boundaries.

Complexity and diversity in sparse code priors improve receptive field characterization of Macaque V1 neurons

System identification techniques-projection pursuit regression models (PPRs) and convolutional neural networks (CNNs)-provide state-of-the-art performance in predicting visual cortical neurons' responses to arbitrary input stimuli. However, the constituent kernels recovered by these methods are often noisy and lack coherent structure, making it difficult to understand the underlying component features of a neuron's receptive field. In this paper, we show that using a dictionary of diverse kernels with complex shapes learned from natural scenes based on efficient coding theory, as the front-end for PPRs and CNNs can improve their performance in neuronal response prediction as well as algorithmic data efficiency and convergence speed. Extensive experimental results also indicate that these sparse-code kernels provide important information on the component features of a neuron's receptive field. In addition, we find that models with the complex-shaped sparse code front-end are significantly better than models with a standard orientation-selective Gabor filter front-end for modeling V1 neurons that have been found to exhibit complex pattern selectivity. We show that the relative performance difference due to these two front-ends can be used to produce a sensitive metric for detecting complex selectivity in V1 neurons.

An investigation into the relationship between stimulus property, neural response and its manifestation in the visual evoked potential involving retinal resolution

The visual evoked potential (VEP) has been shown to reflect the size of the neural population activated by a processing mechanism selective to the temporal - and spatial luminance contrast property of a stimulus. We set out to better understand how the factors determining the neural response associated with these mechanisms. To do so we recorded the VEP from 14 healthy volunteers viewing two series of pattern reversing stimuli with identical temporal-and spatial luminance contrast properties. In one series the size of the elements increased towards the edge of the image, in the other it decreased. In the former element size was congruent with receptive field size across eccentricity, in the later it was incongruent. P100 amplitude to the incongruent series exceeded that obtained to the congruent series. Using electric dipoles due the excitatory neural response we accounted for this using dipole cancellation of electric dipoles of opposite polarity originating in supra- and infragranular layers of V1. The phasic neural response in granular lamina of V1 exhibited magnocellular characteristics, the neural response outside of the granular lamina exhibited parvocellular characteristics and was modulated by re-entrant projections. Using electric current density, we identified areas of the dorsal followed by areas of the ventral stream as the source of the re-entrant signal modulating infragranular activity. Our work demonstrates that the VEP does not signal reflect the overall level of a neural response but is the result of an interaction between electric dipoles originating from neural responses in different lamina of V1.

Curvature domains in V4 of macaque monkey

An important aspect of visual object recognition is the ability to perceive object shape. Two basic components of complex shapes are straight and curved contours. A large body of evidence suggests a modular hierarchy for shape representation progressing from simple and complex orientation in early areas V1 and V2, to increasingly complex stages of curvature representation in V4, TEO, and TE. Here, we reinforce and extend the concept of modular representation. Using intrinsic signal optical imaging in Macaque area V4, we find sub-millimeter sized modules for curvature representation that are organized from low to high curvatures as well as domains with complex curvature preference. We propose a possible ‘curvature hypercolumn’ within V4. In combination with previous studies, we suggest that the key emergent functions at each stage of cortical processing are represented in systematic, modular maps.

Curvature-processing domains in primate V4

Neurons in primate V4 exhibit various types of selectivity for contour shapes, including curves, angles, and simple shapes. How are these neurons organized in V4 remains unclear. Using intrinsic signal optical imaging and two-photon calcium imaging, we observed submillimeter functional domains in V4 that contained neurons preferring curved contours over rectilinear ones. These curvature domains had similar sizes and response amplitudes as orientation domains but tended to separate from these regions. Within the curvature domains, neurons that preferred circles or curve orientations clustered further into finer scale subdomains. Nevertheless, individual neurons also had a wide range of contour selectivity, and neighboring neurons exhibited a substantial diversity in shape tuning besides their common shape preferences. In strong contrast to V4, V1 and V2 did not have such contour-shape-related domains. These findings highlight the importance and complexity of curvature processing in visual object recognition and the key functional role of V4 in this process.

Eccentricity Effect of Deformation Detection for Radial Frequency Patterns With Their Centers at Fixation Point

We measured the eccentricity effect of deformation thresholds of circular contours for two types of the radial frequency (RF) patterns with their centers at the fixation point: constant circular contour frequency (CCF) RF patterns and constant RF magnified (retino-cortical scaling) RF patterns. We varied the eccentricity by changing the mean radius of the RF patterns while keeping the centers of the RF patterns at the fixation point. Our peripheral stimulus presentation was distinguished from previous studies which have simply translated RF patterns at different locations in the visual field. Sensitivity for such shape discrimination fell off as the moderate and high CCF patterns were presented on more eccentric sites but did not as the low CCF patterns. However, sensitivity held constant as the magnified RF patterns were presented on more eccentric sites, indicating that the eccentricity effects observed for the high and moderate CCF patterns were neutralized by retinocortical mapping. Notably, sensitivity for the magnified RF patterns with large radii (4°–16°) presented in the peripheral field revealed a similar RF dependence observed for RF patterns with small radii (0.25°–1.0°) presented at the fovea in previous studies.

Intrinsic network architecture predicts the effects elicited by intracranial electrical stimulation of the human brain

Intracranial electrical stimulation (iES) of the human brain has long been known to elicit a remarkable variety of perceptual, motor and cognitive effects, but the functional-anatomical basis of this heterogeneity remains poorly understood. We conducted a whole-brain mapping of iES-elicited effects, collecting first-person reports following iES at 1,537 cortical sites in 67 participants implanted with intracranial electrodes. We found that intrinsic network membership and the principal gradient of functional connectivity strongly predicted the type and frequency of iES-elicited effects in a given brain region. While iES in unimodal brain networks at the base of the cortical hierarchy elicited frequent and simple effects, effects became increasingly rare, heterogeneous and complex in heteromodal and transmodal networks higher in the hierarchy. Our study provides a comprehensive exploration of the relationship between the hierarchical organization of intrinsic functional networks and the causal modulation of human behaviour and experience with iES.

Neural responses to dynamic adaptation reveal the dissociation between the processing of the shape of contours and textures

Shape-adaptation studies show that surround textures can inhibit the processing of contours. Using event-related potentials (ERP), we examined the time-course of neural processes involved in contour-shape and texture-shape processing following adaptation to contours and textures. Contours were made of Gabor strings whose orientations were either tangential or orthogonal to the contour path, while textures were made of a series of contours arranged in parallel. We focused on two ERP components -P1, related to low-level visual processes and N1, broadly indicative of mid-level vision- and, on ERP difference waves (no-adaptor minus with-adaptor) to isolate the effects of adaptation, which are fundamentally distinct from individual processes driving P1 and N1 components. We found that in the absence of adaptation, the N1 component for contour-tests peaked later and increased in amplitude compared to the N1 for texture-tests. Following adaptation, the ERP difference wave for contour-tests revealed an early and a late component that were differentially affected by the presence of surround texture, but critically not by its orientation. For texture-tests, the early component was of opposite polarity for contours compared to texture adaptors. From the temporal sequence of ERP modulations, we conclude that texture processing begins before contour processing and encompasses the stages of perceptual processing reflected in both the low-level P1 and the mid-level N1 vision-related components. Our study provides novel evidence on the nature of separable and temporally distinct texture and contour processing mechanisms, shown in two difference wave components, that highlights the multi-faceted nature of dynamic adaptation to shape when presented in isolation and in context.

Electrophysiological responses to regularity show specificity to global form: The case of Glass patterns

The holographic weight of evidence model (van der Helm & Leeuwenberg, J Math Psychol, 35, 1991, 151; van der Helm & Leeuwenberg, Psychol Rev, 103, 1996, 429) estimates that the perceptual goodness of moiré structures (Glass patterns), irrespective of their global form, is comparable to that of reflection symmetry. However, both behavioural and neuroscience evidences suggest that certain Glass forms (i.e. circular and radial structures) are perceptually more salient than others (i.e. translation structures) and may recruit different perceptual mechanisms. In this study, we tested whether brain responses for circular, radial and translation Glass patterns are comparable to the response for onefold bilateral reflection symmetry. We recorded an event‐related potential (ERP), called the sustained posterior negativity (SPN), which has been shown to index perceptual goodness of a range of regularities. We found that circular and radial Glass patterns generated a comparable SPN amplitude to onefold reflection symmetry (in line with the prediction of the holographic model), starting approx. 180 ms after stimulus onset. Conversely, the SPN response to translation Glass patterns had a longer latency (approx. 400 ms). These results show that Glass patterns are a special case of visual regularity, and perceptual goodness may not be fully explained by the holographic identities that constitute it. Specialised processing mechanisms might exist in the regularity‐sensitive extrastriate areas, which are tuned to global form configurations.

Differential Geometry in Edge Detection: Accurate Estimation of Position, Orientation and Curvature

The vast majority of edge detection literature has aimed at improving edge recall and precision, with relatively few addressing the accuracy of edge orientation estimates which are often based on gradient. We show that first-order estimates of orientation can have significant error and this can be remedied by employing Third-Order estimates. This paper aims at estimating differential geometry attributes of an edge, namely, localization, orientation, and curvature, as well as edge topology, and develop robust numerical techniques in gray-scale and color images, applicable to a variety of popular edge detectors, such as gradient-based, gPb and SE. Second, a combinatorial model of edge grouping in a small neighborhood is developed to capture all geometrically consistent grouping called curvels, which establish: (i) edge topology in the form of potential links between an edge and other edges; (ii) an accurate curvature estimate for each possible grouping, whose performance is comparable to methods which use global and multi-scale methods; (iii) a more accurate localization of an edge. These have been evaluated using four distinct methodologies (i) traditional human annotated datasets; (ii) using coherence measure; (iii) stability analysis under visual perturbation, and (iv) utilitarian evaluation, and show meaningful improvements.

Shape from Contour: Computation and Representation

The human visual system reliably extracts shape information from complex natural scenes in spite of noise and fragmentation caused by clutter and occlusions. A fast, feedforward sweep through ventral stream involving mechanisms tuned for orientation, curvature, and local Gestalt principles produces partial shape representations sufficient for simpler discriminative tasks. More complete shape representations may involve recurrent processes that integrate local and global cues. While feedforward discriminative deep neural network models currently produce the best predictions of object selectivity in higher areas of the object pathway, a generative model may be required to account for all aspects of shape perception. Research suggests that a successful model will account for our acute sensitivity to four key perceptual dimensions of shape: topology, symmetry, composition, and deformation.

From receptive profiles to a metric model of V1

In this work we show how to construct connectivity kernels induced by the receptive profiles of simple cells of the primary visual cortex (V1). These kernels are directly defined by the shape of such profiles: this provides a metric model for the functional architecture of V1, whose global geometry is determined by the reciprocal interactions between local elements. Our construction adapts to any bank of filters chosen to represent a set of receptive profiles, since it does not require any structure on the parameterization of the family. The connectivity kernel that we define carries a geometrical structure consistent with the well-known properties of long-range horizontal connections in V1, and it is compatible with the perceptual rules synthesized by the concept of association field. These characteristics are still present when the kernel is constructed from a bank of filters arising from an unsupervised learning algorithm.

Task Dependent Effects of Head Orientation on Perceived Gaze Direction

The perception of gaze direction involves the integration of a number of sensory cues exterior to the eye-region. The orientation of the head is one such cue, which has an overall repulsive effect on the perceived direction of gaze. However, in a recent experiment, we found the measured effect of head orientation on perceived gaze direction differed within subjects, depending on whether a single- or two-interval task design was employed. This suggests a potential difference in the way the orientation of the head is integrated into the perception of gaze direction across tasks. Four experiments were conducted to investigate this difference. The first two experiments showed that the difference was not the result of some interaction between stimuli in the two-interval task, but rather, a difference between the types of judgment being made across tasks, where observers were making a directional (left/right) judgment in the single-interval task, and a non-directional (direct/indirect gaze) judgment in the two-interval task. A third experiment showed that this difference does not arise from observers utilizing a non-directional cue to direct gaze (the circularity of the pupil/iris) in making their non-directional judgments. The fourth experiment showed no substantial differences in the duration of evidence accumulation and processing between judgments, suggesting that observers are not integrating different sensory information across tasks. Together these experiments show that the sensory information from head orientation is flexibly weighted in the perception of gaze direction, and that the purpose of the observer, in sampling gaze information, can influence the consequent perception of gaze direction.

Early sensitivity of evoked potentials to surface and volumetric structure during the visual perception of three-dimensional object shape

This study used event-related potentials (ERPs) to elucidate how the human visual system processes three-dimensional (3-D) object shape structure. In particular, we examined whether the perceptual mechanisms that support the analysis of 3-D shape are differentially sensitive to higher order surface and volumetric part structure. Observers performed a whole-part novel object matching task in which part stimuli comprised sub-regions of closed edge contour, surfaces or volumetric parts. Behavioural response latency data showed an advantage in matching surfaces and volumetric parts to whole objects over contours, but no difference between surfaces and volumes. ERPs were analysed using a convergence of approaches based on stimulus dependent amplitude modulations of evoked potentials, topographic segmentation, and spatial frequency oscillations. The results showed early differential perceptual processing of contours, surfaces, and volumetric part stimuli. This was first reliably observed over occipitoparietal electrodes during the N1 (140-200 ms) with a mean peak latency of 170 ms, and continued on subsequent P2 (220-260 ms) and N2 (260-320 ms) components. The differential sensitivity in perceptual processing during the N1 was accompanied by distinct microstate patterns that distinguished among contours, surfaces and volumes, and predominant theta band activity around 4-7 Hz over right occipitoparietal and orbitofrontal sites. These results provide the first evidence of early differential perceptual processing of higher order surface and volumetric shape structure within the first 200 ms of stimulus processing. The findings challenge theoretical models of object recognition that do not attribute functional significance to surface and volumetric object structure during visual perception.

The statistical shape of geometric reasoning

Geometric reasoning has an inherent dissonance: its abstract axioms and propositions refer to perfect, idealized entities, whereas its use in the physical world relies on dynamic perception of objects. How do abstract Euclidean concepts, dynamics, and statistics come together to support our intuitive geometric reasoning? Here, we address this question using a simple geometric task – planar triangle completion. An analysis of the distribution of participants’ errors in localizing a fragmented triangle’s missing corner reveals scale-dependent deviations from a deterministic Euclidean representation of planar triangles. By considering the statistical physics of the process characterized via a correlated random walk with a natural length scale, we explain these results and further predict participants’ estimates of the missing angle, measured in a second task. Our model also predicts the results of a categorical reasoning task about changes in the triangle size and shape even when such completion strategies need not be invoked. Taken together, our findings suggest a critical role for noisy physical processes in our reasoning about elementary Euclidean geometry.

Contextual modulation of sensitivity to naturalistic image structure in macaque V2

The stimulus selectivity of neurons in V1 is well known, as is the finding that their responses can be affected by visual input to areas outside of the classical receptive field. Less well understood are the ways selectivity is modified as signals propagate to visual areas beyond V1, such as V2. We recently proposed a role for V2 neurons in representing the higher order statistical dependencies found in images of naturally occurring visual texture. V2 neurons, but not V1 neurons, respond more vigorously to "naturalistic" images that contain these dependencies than to "noise" images that lack them. In this work, we examine the dependency of these effects on stimulus size. For most V2 neurons, the preference for naturalistic over noise stimuli was modest when presented in small patches and gradually strengthened with increasing size, suggesting that the mechanisms responsible for this enhanced sensitivity operate over regions of the visual field that are larger than the classical receptive field. Indeed, we found that surround suppression was stronger for noise than for naturalistic stimuli and that the preference for large naturalistic stimuli developed over a delayed time course consistent with lateral or feedback connections. These findings are compatible with a spatially broad facilitatory mechanism that is absent in V1 and suggest that a distinct role for the receptive field surround emerges in V2 along with sensitivity for more complex image structure. NEW & NOTEWORTHY The responses of neurons in visual cortex are often affected by visual input delivered to regions of the visual field outside of the conventionally defined receptive field, but the significance of such contextual modulations are not well understood outside of area V1. We studied the importance of regions beyond the receptive field in establishing a novel form of selectivity for the statistical dependencies contained in natural visual textures that first emerges in area V2.

Phase-specific Surround suppression in Mouse Primary Visual Cortex Correlates with Figure Detection Behavior Based on Phase Discontinuity

In the primary visual cortex (V1), neuronal responses to stimuli within the receptive field (RF) are modulated by stimuli in the RF surround. A common effect of surround modulation is surround suppression, which is dependent on the feature difference between stimuli within and surround the RF and is suggested to be involved in the perceptual phenomenon of figure-ground segregation. In this study, we examined the relationship between feature-specific surround suppression of V1 neurons and figure detection behavior based on figure-ground feature difference. We trained freely moving mice to perform a figure detection task using figure and ground gratings that differed in spatial phase. The performance of figure detection increased with the figure-ground phase difference, and was modulated by stimulus contrast. Electrophysiological recordings from V1 in head-fixed mice showed that the increase in phase difference between stimuli within and surround the RF caused a reduction in surround suppression, which was associated with an increase in V1 neural discrimination between stimuli with and without RF-surround phase difference. Consistent with the behavioral performance, the sensitivity of V1 neurons to RF-surround phase difference could be influenced by stimulus contrast. Furthermore, inhibiting V1 by optogenetically activating either parvalbumin (PV)- or somatostatin (SOM)-expressing inhibitory neurons both decreased the behavioral performance of figure detection. Thus, the phase-specific surround suppression in V1 represents a neural correlate of figure detection behavior based on figure-ground phase discontinuity.

Complex Pattern Selectivity in Macaque Primary Visual Cortex Revealed by Large-Scale Two-Photon Imaging

Visual objects contain rich local high-order patterns such as curvature, corners, and junctions. In the standard hierarchical model of visual object recognition, V1 neurons were commonly assumed to code local orientation components of those high-order patterns. Here, by using two-photon imaging in awake macaques and systematically characterizing V1 neuronal responses to an extensive set of stimuli, we found a large percentage of neurons in the V1 superficial layer responded more strongly to complex patterns, such as corners, junctions, and curvature, than to their oriented line or edge components. Our results suggest that those individual V1 neurons could play the role in detecting local high-order visual patterns in the early stage of object recognition hierarchy.

Curvature Blindness Illusion

We report a novel illusion––curvature blindness illusion: a wavy line is perceived as a zigzag line. The following are required for this illusion to occur. First, the luminance contrast polarity of the wavy line against the background is reversed at the turning points. Second, the curvature of the wavy line is somewhat low; the right angle is too steep to be perceived as an illusion. This illusion implies that, in order to perceive a gentle curve, it is necessary to satisfy more conditions––constant contrast polarity––than perceiving an obtuse corner. It is notable that observers exactly “see” an illusory zigzag line against a physically wavy line, rather than have an impaired perception. We propose that the underlying mechanisms for the gentle curve perception and those of obtuse corner perception are competing with each other in an imbalanced way and the percepts of corner might be dominant in the visual system.

End-Stopping Predicts Curvature Tuning along the Ventral Stream

Neurons in primate inferotemporal cortex (IT) are clustered into patches of shared image preferences. Functional imaging has shown that these patches are activated by natural categories (e.g., faces, body parts, and places), artificial categories (numerals, words) and geometric features (curvature and real-world size). These domains develop in the same cortical locations across monkeys and humans, which raises the possibility of common innate mechanisms. Although these commonalities could be high-level template-based categories, it is alternatively possible that the domain locations are constrained by low-level properties such as end-stopping, eccentricity, and the shape of the preferred images. To explore this, we looked for correlations among curvature preference, receptive field (RF) end-stopping, and RF eccentricity in the ventral stream. We recorded from sites in V1, V4, and posterior IT (PIT) from six monkeys using microelectrode arrays. Across all visual areas, we found a tendency for end-stopped sites to prefer curved over straight contours. Further, we found a progression in population curvature preferences along the visual hierarchy, where, on average, V1 sites preferred straight Gabors, V4 sites preferred curved stimuli, and many PIT sites showed a preference for curvature that was concave relative to fixation. Our results provide evidence that high-level functional domains may be mapped according to early rudimentary properties of the visual system.

SIGNIFICANCE STATEMENT

The macaque occipitotemporal cortex contains clusters of neurons with preferences for categories such as faces, body parts, and places. One common question is how these clusters (or "domains") acquire their cortical position along the ventral stream. We and other investigators previously established an fMRI-level correlation among these category domains, retinotopy, and curvature preferences: for example, in inferotemporal cortex, face- and curvature-preferring domains show a central visual field bias whereas place- and rectilinear-preferring domains show a more peripheral visual field bias. Here, we have found an electrophysiological-level explanation for the correlation among domain preference, curvature, and retinotopy based on neuronal preference for short over long contours, also called end-stopping.

The curvature calculation mechanism based on simple cell model

A conclusion has not yet been reached on how exactly the human visual system detects curvature. This paper demonstrates how orientation-selective simple cells can be used to construct curvature-detecting neural units. Through fixed arrangements, multiple plurality cells were constructed to simulate curvature cells with a proportional output to their curvature. In addition, this paper offers a solution to the problem of narrow detection range under fixed resolution by selecting an output value under multiple resolution. Curvature cells can be treated as concrete models of an end-stopped mechanism, and they can be used to further understand "curvature-selective" characteristics and to explain basic psychophysical findings and perceptual phenomena in current studies.

Improved Compressive Sensing of Natural Scenes Using Localized Random Sampling

Compressive sensing (CS) theory demonstrates that by using uniformly-random sampling, rather than uniformly-spaced sampling, higher quality image reconstructions are often achievable. Considering that the structure of sampling protocols has such a profound impact on the quality of image reconstructions, we formulate a new sampling scheme motivated by physiological receptive field structure, localized random sampling, which yields significantly improved CS image reconstructions. For each set of localized image measurements, our sampling method first randomly selects an image pixel and then measures its nearby pixels with probability depending on their distance from the initially selected pixel. We compare the uniformly-random and localized random sampling methods over a large space of sampling parameters, and show that, for the optimal parameter choices, higher quality image reconstructions can be consistently obtained by using localized random sampling. In addition, we argue that the localized random CS optimal parameter choice is stable with respect to diverse natural images, and scales with the number of samples used for reconstruction. We expect that the localized random sampling protocol helps to explain the evolutionarily advantageous nature of receptive field structure in visual systems and suggests several future research areas in CS theory and its application to brain imaging.

Novel Visual Illusions Related to Vasarely's ‘Nested Squares’ Show That Corner Salience Varies with Corner Angle

Vasarely's ‘nested-squares’ illusion shows that 90° corners can be more salient perceptually than straight edges. On the basis of this illusion we have developed a novel visual illusion, the ‘Alternating Brightness Star’, which shows that sharp corners are more salient than shallow corners (an effect we call ‘corner angle salience variation’) and that the same corner can be perceived as either bright or dark depending on the polarity of the angle (ie whether concave or convex: ‘corner angle brightness reversal’). Here we quantify the perception of corner angle salience variation and corner angle brightness reversal effects in twelve naive human subjects, in a two-alternative forced-choice brightness discrimination task. The results show that sharp corners generate stronger percepts than shallow corners, and that corner gradients appear bright or dark depending on whether the corner is concave or convex. Basic computational models of center – surround receptive fields predict the results to some degree, but not fully.

2D Geometry Predicts Perceived Visual Curvature in Context-Free Viewing

Planar geometry was exploited for the computation of symmetric visual curves in the image plane, with consistent variations in local parameters such as sagitta, chordlength, and the curves' height-to-width ratio, an indicator of the visual area covered by the curve, also called aspect ratio. Image representations of single curves (no local image context) were presented to human observers to measure their visual sensation of curvature magnitude elicited by a given curve. Nonlinear regression analysis was performed on both the individual and the average data using two types of model: (1) a power function where y (sensation) tends towards infinity as a function of x (stimulus input), most frequently used to model sensory scaling data for sensory continua, and (2) an “exponential rise to maximum” function, which converges towards an asymptotically stable level of y as a function of x. Both models provide satisfactory fits to subjective curvature magnitude as a function of the height-to-width ratio of single curves. The findings are consistent with an in-built sensitivity of the human visual system to local curve geometry, a potentially essential ground condition for the perception of concave and convex objects in the real world.

The visual system's internal model of the world

The Bayesian paradigm has provided a useful conceptual theory for understanding perceptual computation in the brain. While the detailed neural mechanisms of Bayesian inference are not fully understood, recent computational and neurophysiological works have illuminated the underlying computational principles and representational architecture. The fundamental insights are that the visual system is organized as a modular hierarchy to encode an internal model of the world, and that perception is realized by statistical inference based on such internal model. In this paper, I will discuss and analyze the varieties of representational schemes of these internal models and how they might be used to perform learning and inference. I will argue for a unified theoretical framework for relating the internal models to the observed neural phenomena and mechanisms in the visual cortex.

Silent suppressive surrounds and optimal spatial frequencies of single neurons in cat V1

The receptive fields of the clear majority of neurons in the primary visual cortex (V1) of cats contain silent surround regions beyond the classical receptive field (CRF). When stimulated on their own, the silent surround regions do not generate action potentials (spikes); instead, they modulate (and usually partially suppress) spike responses to stimuli presented in the CRF. In the present study, we subdivided our sample of single V1 neurons recorded from anesthetized cats into two distinct categories: surround-suppressive (SS) cells and surround-non-suppressive (SN) cells. Consistent with previous reports, we found a negative correlation between the size of the CRF and the optimal spatial frequency (SF) of circular patches of achromatic gratings presented in the cells' receptive fields. Furthermore, we found a positive correlation between the strength of the surround suppression and the optimal spatial frequency of the achromatic gratings presented in the cells' receptive fields. The correlation between the strength of surround suppression and the optimal spatial frequency was stronger in neurons with suppressive regions located in the so-called 'end' zones. The functional implications of these relationships are discussed.

Multidimensional gain control in image representation and processing in vision

A generic model of automatic gain control (AGC) is proposed as a general framework for multidimensional automatic contrast sensitivity adjustment in vision, as well as in other sensory modalities. We show that a generic feedback AGC mechanism, incorporating a nonlinear synaptic interaction into the feedback loop of a neural network, can enhance and emphasize important image attributes, such as curvature, size, depth, convexity/concavity and more, similar to its role in the adjustment of photoreceptors and retinal network sensitivity over the extremely high dynamic range of environmental light intensities, while enhancing the contrast. We further propose that visual illusions, well established by psychophysical experiments, are a by-product of the multidimensional AGC. This hypothesis is supported by simulations implementing AGC, which reproduce psychophysical data regarding size contrast effects known as the Ebbinghaus illusion, and depth contrast effects. Processing of curvature by an AGC network illustrates that it is an important mechanism of image structure pre-emphasis, which thereby enhances saliency. It is argued that the generic neural network of AGC constitutes a universal, parsimonious, unified mechanism of neurobiological automatic contrast sensitivity control. This mechanism/model can account for a wide range of physiological and psychophysical phenomena, such as visual illusions and contour completion, in cases of occlusion, by a basic neural network. Likewise, and as important, biologically motivated AGC provides attractive new means for the development of intelligent computer vision systems.

The lemon illusion: seeing curvature where there is none

Curvature is a highly informative visual cue for shape perception and object recognition. We introduce a novel illusion—the Lemon Illusion—in which subtle illusory curvature is perceived along contour regions that are devoid of physical curvature. We offer several perceptual demonstrations and observations that lead us to conclude that the Lemon Illusion is an instance of a more general illusory curvature phenomenon, one in which the presence of contour curvature discontinuities lead to the erroneous extension of perceived curvature. We propose that this erroneous extension of perceived curvature results from the interaction of neural mechanisms that operate on spatially local contour curvature signals with higher-tier mechanisms that serve to establish more global representations of object shape. Our observations suggest that the Lemon Illusion stems from discontinuous curvature transitions between rectilinear and curved contour segments. However, the presence of curvature discontinuities is not sufficient to produce the Lemon Illusion, and the minimal conditions necessary to elicit this subtle and insidious illusion are difficult to pin down.

Feature-based attention modulates surround suppression

Stimuli appearing in the surround of the classical receptive field (CRF) can reduce neuronal firing and perceived contrast of a preferred stimulus in the CRF, a phenomenon referred to as surround suppression. Suppression is greatest when the surrounding stimulus has the same orientation and spatial frequency (SF) as the central target. Although spatial attention has been shown to influence surround suppression, the effects of feature-based attention have yet to be characterized. Using behavioral contrast adaptation in humans, we examined center-surround interactions between SF and orientation, and asked whether attending to one feature dimension versus the other influenced suppression. A center-surround triplet comprised of a central target Gabor and two flanking Gabors were used for adaptation. The flankers could have the same SF and orientation as the target, or differ in one or both of the feature dimensions. Contrast thresholds were measured for the target before and after adapting to center-surround triplets, and postadaptation thresholds were taken as an indirect measure of surround suppression. Both feature dimensions contributed to surround suppression and did not summate. Moreover, when center and surround had the same feature value in one dimension (e.g., same orientation) but had different values in the other dimension (e.g., different SF), there was more suppression when attention was directed to the feature dimension that matched between center and surround than when attention was directed to the feature dimension that differed. These results demonstrate that feature-based attention can influence center-surround interactions by enhancing the effects of the attended dimension.

Tangent Bundle Elastica and Computer Vision

Visual curve completion, an early visual process that completes the occluded parts between observed boundary fragments (a.k.a. inducers), is a major problem in perceptual organization and a critical step toward higher level visual tasks in both biological and machine vision. Most computational contributions to solving this problem suggest desired perceptual properties that the completed contour should satisfy in the image plane, and then seek the mathematical curves that provide them. Alternatively, few studies (including by the authors) have suggested to frame the problem not in the image plane but rather in the unit tangent bundleR (2) × S(1), the space that abstracts the primary visual cortex, where curve completion allegedly occurs. Combining both schools, here we propose and develop a biologically plausible theory of elastica in the tangent bundle that provides not only perceptually superior completion results but also a rigorous computational prediction that inducer curvatures greatly affects the shape of the completed curve, as indeed indicated by human perception.

A conceptual framework of computations in mid-level vision

If a picture is worth a thousand words, as an English idiom goes, what should those words-or, rather, descriptors-capture? What format of image representation would be sufficiently rich if we were to reconstruct the essence of images from their descriptors? In this paper, we set out to develop a conceptual framework that would be: (i) biologically plausible in order to provide a better mechanistic understanding of our visual system; (ii) sufficiently robust to apply in practice on realistic images; and (iii) able to tap into underlying structure of our visual world. We bring forward three key ideas. First, we argue that surface-based representations are constructed based on feature inference from the input in the intermediate processing layers of the visual system. Such representations are computed in a largely pre-semantic (prior to categorization) and pre-attentive manner using multiple cues (orientation, color, polarity, variation in orientation, and so on), and explicitly retain configural relations between features. The constructed surfaces may be partially overlapping to compensate for occlusions and are ordered in depth (figure-ground organization). Second, we propose that such intermediate representations could be formed by a hierarchical computation of similarity between features in local image patches and pooling of highly-similar units, and reestimated via recurrent loops according to the task demands. Finally, we suggest to use datasets composed of realistically rendered artificial objects and surfaces in order to better understand a model's behavior and its limitations.

Contextual modulation and stimulus selectivity in extrastriate cortex

Contextual modulation is observed throughout the visual system, using techniques ranging from single-neuron recordings to behavioral experiments. Its role in generating feature selectivity within the retina and primary visual cortex has been extensively described in the literature. Here, we describe how similar computations can also elaborate feature selectivity in the extrastriate areas of both the dorsal and ventral streams of the primate visual system. We discuss recent work that makes use of normalization models to test specific roles for contextual modulation in visual cortex function. We suggest that contextual modulation renders neuronal populations more selective for naturalistic stimuli. Specifically, we discuss contextual modulation's role in processing optic flow in areas MT and MST and for representing naturally occurring curvature and contours in areas V4 and IT. We also describe how the circuitry that supports contextual modulation is robust to variations in overall input levels. Finally, we describe how this theory relates to other hypothesized roles for contextual modulation.

Contextual effects in human visual cortex depend on surface structure

Neural responses in early visual cortex depend on stimulus context. One of the most well-established context-dependent effects is orientation-specific surround suppression: the neural response to a stimulus inside the receptive field of a neuron ("target") is suppressed when it is surrounded by iso-oriented compared with orthogonal stimuli ("flankers"). Despite the importance of orientation-specific surround suppression in potentially mediating a number of important perceptual effects, including saliency, contour integration, and orientation discrimination, the underlying neural mechanisms remain unknown. The suppressive signal could be inherited from precortical areas as early as the retina and thalamus, arise from local circuits through horizontal connections, or be fed back from higher visual cortex. Here, we show, using two different methodologies, measurements of scalp-recorded event-related potentials (ERPs) and behavioral contrast adaptation aftereffects in humans, that orientation-specific surround suppression is dependent on the surface structure in an image. When the target and flankers can be grouped on the same surface (independent of their distance), orientation-specific surround suppression occurs. When the target and flankers are on different surfaces (independent of their distance), orientation-specific surround suppression does not occur. Our results demonstrate a surprising role of high-level, global processes such as grouping in determining when contextual effects occur in early visual cortex.

Visual search targeting either local or global perceptual processes differs as a function of autistic-like traits in the typically developing population

Relative to low scorers, high scorers on the autism-spectrum quotient (AQ) show enhanced performance on the embedded figures test and the radial frequency search task (RFST), which has been attributed to both enhanced local processing and differences in combining global percepts. We investigate the role of local and global processing further using the RFST in four experiments. High AQ adults maintained a consistent advantage in search speed across diverse target-distracter stimulus conditions. This advantage may reflect enhanced local processing of curvature in early stages of the form vision pathway and superior global detection of shape primitives. However, more probable is the presence of a superior search process that enables a consistent search advantage at both levels of processing.

Visual nonclassical receptive field effects emerge from sparse coding in a dynamical system

Extensive electrophysiology studies have shown that many V1 simple cells have nonlinear response properties to stimuli within their classical receptive field (CRF) and receive contextual influence from stimuli outside the CRF modulating the cell's response. Models seeking to explain these non-classical receptive field (nCRF) effects in terms of circuit mechanisms, input-output descriptions, or individual visual tasks provide limited insight into the functional significance of these response properties, because they do not connect the full range of nCRF effects to optimal sensory coding strategies. The (population) sparse coding hypothesis conjectures an optimal sensory coding approach where a neural population uses as few active units as possible to represent a stimulus. We demonstrate that a wide variety of nCRF effects are emergent properties of a single sparse coding model implemented in a neurally plausible network structure (requiring no parameter tuning to produce different effects). Specifically, we replicate a wide variety of nCRF electrophysiology experiments (e.g., end-stopping, surround suppression, contrast invariance of orientation tuning, cross-orientation suppression, etc.) on a dynamical system implementing sparse coding, showing that this model produces individual units that reproduce the canonical nCRF effects. Furthermore, when the population diversity of an nCRF effect has also been reported in the literature, we show that this model produces many of the same population characteristics. These results show that the sparse coding hypothesis, when coupled with a biophysically plausible implementation, can provide a unified high-level functional interpretation to many response properties that have generally been viewed through distinct mechanistic or phenomenological models.

Simple cells in the primary visual cortex (V1) demonstrate many response properties that are either nonlinear or involve response modulations (i.e., stimuli that do not cause a response in isolation alter the cell's response to other stimuli). These non-classical receptive field (nCRF) effects are generally modeled individually and their collective role in biological vision is not well understood. Previous work has shown that classical receptive field (CRF) properties of V1 cells (i.e., the spatial structure of the visual field responsive to stimuli) could be explained by the sparse coding hypothesis, which is an optimal coding model that conjectures a neural population should use the fewest number of cells simultaneously to represent each stimulus. In this paper, we have performed extensive simulated physiology experiments to show that many nCRF response properties are simply emergent effects of a dynamical system implementing this same sparse coding model. These results suggest that rather than representing disparate information processing operations themselves, these nCRF effects could be consequences of an optimal sensory coding strategy that attempts to represent each stimulus most efficiently. This interpretation provides a potentially unifying high-level functional interpretation to many response properties that have generally been viewed through distinct models.

Prioritization of brain MRI volumes using medical image perception model and tumor region segmentation

The objective of the present study is to explore prioritization methods in diagnostic imaging modalities to automatically determine the contents of medical images. In this paper, we propose an efficient prioritization of brain MRI. First, the visual perception of the radiologists is adapted to identify salient regions. Then this saliency information is used as an automatic label for accurate segmentation of brain lesion to determine the scientific value of that image. The qualitative and quantitative results prove that the rankings generated by the proposed method are closer to the rankings created by radiologists.

Contrast dependence and differential contributions from somatostatin- and parvalbumin-expressing neurons to spatial integration in mouse V1

A characteristic feature in the primary visual cortex is that visual responses are suppressed as a stimulus extends beyond the classical receptive field. Here, we examined the role of inhibitory neurons expressing somatostatin (SOM⁺) or parvalbumin (PV⁺) on surround suppression and preferred receptive field size. We recorded multichannel extracellular activity in V1 of transgenic mice expressing channelrhodopsin in SOM⁺ neurons or PV⁺ neurons. Preferred size and surround suppression were measured using drifting square-wave gratings of varying radii and at two contrasts. Consistent with findings in primates, we found that the preferred size was larger for lower contrasts across all cortical depths, whereas the suppression index (SI) showed a trend to decrease with contrast. We then examined the effect of these metrics on units that were suppressed by photoactivation of either SOM⁺ or PV⁺ neurons. When activating SOM⁺ neurons, we found a significant increase in SI at cortical depths >400 μm, whereas activating PV⁺ neurons caused a trend toward lower SIs regardless of cortical depth. Conversely, activating PV⁺ neurons significantly increased preferred size across all cortical depths, similar to lowering contrast, whereas activating SOM⁺ neurons had no systematic effect on preferred size across all depths. These data suggest that SOM⁺ and PV⁺ neurons contribute differently to spatial integration. Our findings are compatible with the notion that SOM⁺ neurons mediate surround suppression, particularly in deeper cortex, whereas PV⁺ activation decreases the drive of the input to cortex and therefore resembles the effects on spatial integration of lowering contrast.

Trade-off between curvature tuning and position invariance in visual area V4

Humans can rapidly recognize a multitude of objects despite differences in their appearance. The neural mechanisms that endow high-level sensory neurons with both selectivity to complex stimulus features and "tolerance" or invariance to identity-preserving transformations, such as spatial translation, remain poorly understood. Previous studies have demonstrated that both tolerance and selectivity to conjunctions of features are increased at successive stages of the ventral visual stream that mediates visual recognition. Within a given area, such as visual area V4 or the inferotemporal cortex, tolerance has been found to be inversely related to the sparseness of neural responses, which in turn was positively correlated with conjunction selectivity. However, the direct relationship between tolerance and conjunction selectivity has been difficult to establish, with different studies reporting either an inverse or no significant relationship. To resolve this, we measured V4 responses to natural scenes, and using recently developed statistical techniques, we estimated both the relevant stimulus features and the range of translation invariance for each neuron. Focusing the analysis on tuning to curvature, a tractable example of conjunction selectivity, we found that neurons that were tuned to more curved contours had smaller ranges of position invariance and produced sparser responses to natural stimuli. These trade-offs provide empirical support for recent theories of how the visual system estimates 3D shapes from shading and texture flows, as well as the tiling hypothesis of the visual space for different curvature values.

Detecting shapes in noise: tuning characteristics of global shape mechanisms

The proportion of signal elements embedded in noise needed to detect a signal is a standard tool for investigating motion perception. This paradigm was applied to the shape domain to determine how local information is pooled into a global percept. Stimulus arrays consisted of oriented Gabor elements that sampled the circumference of concentric radial frequency (RF) patterns. Individual Gabors were oriented tangentially to the shape (signal) or randomly (noise). In different conditions, signal elements were located randomly within the entire array or constrained to fall along one of the concentric contours. Coherence thresholds were measured for RF patterns with various frequencies (number of corners) and amplitudes (“sharpness” of corners). Coherence thresholds (about 10% = 15 elements) were lowest for circular shapes. Manipulating shape frequency or amplitude showed a range where thresholds remain unaffected (frequency ≤ RF4; amplitude ≤ 0.05). Increasing either parameter caused thresholds to rise. Compared to circles, thresholds increased by approximately four times for RF13 and five times for amplitudes of 0.3. Confining the signals to individual contours significantly reduced the number of elements needed to reach threshold (between 4 and 6), independent of the total number of elements on the contour or contour shape. Finally, adding external noise to the orientation of the elements had a greater effect on detection thresholds than adding noise to their position. These results provide evidence for a series of highly sensitive, shape-specific analysers which sum information globally but only from within specific annuli. These global mechanisms are tuned to position and orientation of local elements from which they pool information. The overall performance for arrays of elements can be explained by the sensitivity of multiple, independent concentric shape detectors rather than a single detector integrating information widely across space (e.g. Glass pattern detector).