THE CORTICAL MAGNIFICATION FACTOR AND PHOTOPIC VISION

1. The concept of a topographical representation of sensory surfaces on the mammalian cerebral cortex is now well established. Furthermore, there is claimed an expanded representation for those sensory surfaces associated with behavioural specializations.
2. In the case of the visual system, the field of view associated with the retina is projected on to the striate cortex, with the central fovea or point of most acute vision occupying a disproportionately large area of representation.
3. The term 'cortical magnification factor', denoted by M, has been introduced to indicate, for a given eccentricity and meridian, the linear distance in mm along the primary visual cortex concerned with each degree of visual field.
4. The quantitative accuracy of this function subsequently has been improved and a relationship established between cortical magnification and visual acuity in man.
5. On the basis of spatio-temporal investigations across the visual field under levels of photopic adaptation, visual scientists have utilized retino-cortical magnification to reconcile aspects of structure and function in the human visual system.     

Spatial mapping in the primate sensory projection: Analytic structure and relevance to perception

The retinotopic mapping of the visual field to the surface of the striate cortex is characterized as a longarithmic conformal mapping. This summarizes in a concise way the observed curve of cortical magnification, the linear scaling of receptive field size with eccentricity, and the mapping of global visual field landmarks. It is shown that if this global structure is reiterated at the local level, then the sequence regularity of the simple cells of area 17 may be accounted for as well. Recently published data on the secondary visual area, the medial visual area, and the inferior pulvinar of the owl monkey suggests that same global logarithmic structure holds for these areas as well. The available data on the structure of the somatotopic mapping (areaS-1) supports a similar analysis. The possible relevance of the analytical form of the cortical receptotopic maps to perception is examined and a brief discussion of the developmental implications of these findings is presented.This work was supported by Grant No. 1 F32MH05367-01 from the USPHS, ADAMHA     

The effect of viewing eccentricity on enumeration

Visual acuity and contrast sensitivity progressively diminish with increasing viewing eccentricity. Here we evaluated how visual enumeration is affected by visual eccentricity, and whether subitizing capacity, the accurate enumeration of a small number (～3) of items, decreases with more eccentric viewing. Participants enumerated gratings whose (1) stimulus size was constant across eccentricity, and (2) whose stimulus size scaled by a cortical magnification factor across eccentricity. While we found that enumeration accuracy and precision decreased with increasing eccentricity, cortical magnification scaling of size neutralized the deleterious effects of increasing eccentricity. We found that size scaling did not affect subitizing capacities, which were nearly constant across all eccentricities. We also found that size scaling modulated the variation coefficients, a normalized metric of enumeration precision, defined as the standard deviation divided by the mean response. Our results show that the inaccuracy and imprecision associated with increasing viewing eccentricity is due to limitations in spatial resolution. Moreover, our results also support the notion that the precise number system is restricted to small numerosities (represented by the subitizing limit), while the approximate number system extends across both small and large numerosities (indexed by variation coefficients) at large eccentricities.     

Crowding: a cortical constraint on object recognition

The external world is mapped retinotopically onto the primary visual cortex (V1). We show here that objects in the world, unless they are very dissimilar, can be recognized only if they are sufficiently separated in visual cortex: specifically, in V1, at least 6mm apart in the radial direction (increasing eccentricity) or 1mm apart in the circumferential direction (equal eccentricity). Objects closer together than this critical spacing are perceived as an unidentifiable jumble. This is called 'crowding'. It severely limits visual processing, including speed of reading and searching. The conclusion about visual cortex rests on three findings. First, psychophysically, the necessary 'critical' spacing, in the visual field, is proportional to (roughly half) the eccentricity of the objects. Second, the critical spacing is independent of the size and kind of object. Third, anatomically, the representation of the visual field on the cortical surface is such that the position in V1 (and several other areas) is the logarithm of eccentricity in the visual field. Furthermore, we show that much of this can be accounted for by supposing that each 'combining field', defined by the critical spacing measurements, is implemented by a fixed number of cortical neurons.     

Characteristics of the receptive fields of neurons of the posterior temporal area of the cortex of the cat

In records of 219 single units in the posterotemporal cortical area (field 21) of nonanaesthetized cats, 51% of cells reacted to visual stimulation. The neurones had receptive fields (RFs) with central (0-10 degrees) or peripheral (10-52 degrees) localization in the visual field, their size increasing with eccentricity. Carting of RFs by a light bar scanning the visual field revealed a considerable variability of RFs shape, size and orientation in different cells. RFs sizes of the majority of recorded cells (100-1000 grad) were very large and exceeded the size of large RFs of neurones in the primary projection zone of the visual cortex.     

Somatosensory and visual cortical unit activity in rabbits during receptive field testing and food-getting behavior

Somatosensory and visual cortical unit activity was compared in experiments on unrestrained rabbits during receptive field testing and natural "self-stimulation" of the receptive surfaces of surrounding objects in the course of food-getting behavior. Unit activity evoked by receptive field testing may correspond completely, partially, or not at all to its activity during food-getting behavior, i.e., neurons demonstrating connection during testing with particular receptive fields (parts of the body or retina) may preserve it, modify it, or lose it during food-getting behavior. Differences of activity during food-getting behavior were observed even in the case of neurons with identical receptive fields during testing. The possible nonidentity of the overall firing pattern of the neurons during food-getting behavior with the pattern which can be simulated by receptive field testing is discussed.Institute of Psychology, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 16, No. 2, pp. 254–262, March–April, 1984.     

A model of the early stages of the human visual system: Functional and topological transformations performed in the peripheral visual field

A model of the early stages of the visual system is presented, with particular reference to the region of the visual field outside the fovea and to the class of retinal and lateral geniculate nucleus cells which are most active in the processing of pattern information (X-cells). The main neuroanatomical and neurophysiological properties taken into account are: the linear increase of the receptive fields diameter with eccentricity, the constancy of the overlap factor and the topological transformation operated upon the retinal image by the retino-cortical connection. The type of filtering taking place between the retina and the visual cortex is analyzed and some simulations are presented. It is shown that such a filtering is of a band-pass space variant type, with center frequencies that decrease from the center (i.e. the fovea) toward the periphery of the visual field. This processing is form invariant under linear scaling of the input. Moreover, considering the properties of the retino-cortical connection, it is shown that the cortical images undergo simple shifts whenever the retinal images are scaled or rotated.     

Generalized spin models for coupled cortical feature maps obtained by coarse graining correlation based synaptic learning rules

We derive generalized spin models for the development of feedforward cortical architecture from a Hebbian synaptic learning rule in a two layer neural network with nonlinear weight constraints. Our model takes into account the effects of lateral interactions in visual cortex combining local excitation and long range effective inhibition. Our approach allows the principled derivation of developmental rules for low-dimensional feature maps, starting from high-dimensional synaptic learning rules. We incorporate the effects of smooth nonlinear constraints on net synaptic weight projected from units in the thalamic layer (the fan-out) and on the net synaptic weight received by units in the cortical layer (the fan-in). These constraints naturally couple together multiple feature maps such as orientation preference and retinotopic organization. We give a detailed illustration of the method applied to the development of the orientation preference map as a special case, in addition to deriving a model for joint pattern formation in cortical maps of orientation preference, retinotopic location, and receptive field width. We show that the combination of Hebbian learning and center-surround cortical interaction naturally leads to an orientation map development model that is closely related to the XY magnetic lattice model from statistical physics. The results presented here provide justification for phenomenological models studied in Cowan and Friedman (Advances in neural information processing systems 3, 1991), Thomas and Cowan (Phys Rev Lett 92(18):e188101, 2004) and provide a developmental model realizing the synaptic weight constraints previously assumed in Thomas and Cowan (Math Med Biol 23(2):119–138, 2006).     

Predicting functional properties of visual cortex from an evolutionary scaling law

The number of neurons in the primary visual cortex (V1) is, across primate species, related to the number of neurons in the visual thalamus (the lateral geniculate nucleus [LGN]) by a power law with an exponent of 3/2. This evolutionary scaling law is explained by a simple relation according to which the fineness of resolution in cortex is related to the number of neurons in the area of cortex used to process the information from a single point of light (the point-spread area). The same theory provides a link between two functional properties of the visual cortex, the areal cortical magnification factor (ACMF) and the receptive field (RF) area.     

用脑光学成像精确测定猫初级视皮层视野拓扑投射关系

利用基于脑内源信号的光学成像和二维互相关分析的方法,对猫初级视皮层17区的视野拓扑离心度(即视网膜-皮层拓扑关系)进行了精确测量。当采用在同一屏幕内处于上下视野的、方位互相垂直的两个相邻光栅刺激时,皮层中一部分区域的绝大部分细胞因同时兴奋而导致方位功能图模糊不清。将这种方位功能图和用单一方位(水平或垂直)全屏光栅刺激所得到的功能图进行比较,通过计算每一像素的互相关系数,从而获得皮层的精确视野拓扑离心度。同时用电生理的方法测量了同一视皮层内的单细胞的感受野位置,证明这种方法得到的视野离心度和光学记录方法得到的相同。因此,本研究为大面积地确定视皮层细胞感受野在视野中的位置提供了一种快速和较准确的方法。     

A neural network model on self-organizing emergence of simple-cell receptive field with orientation selectivity in visual cortex

In order to probe into the self-organizing emergence of simple cell orientation selectivity, we tried to construct a neural network model that consists of LGN neurons and simple cells in visual cortex and obeys the Hebbian learning rule. We investigated the neural coding and representation of simple cells to a natural image by means of this model. The results show that the structures of their receptive fields are determined by the preferred orientation selectivity of simple cells. However, they are also decided by the emergence of self-organization in the unsupervision learning process. This kind of orientation selectivity results from dynamic self-organization based on the interactions between LGN and cortex.     

A neural network model on self-organizing emergence of simple-cell receptive field with orientation selectivity in visual cortex

In order to probe into the self-organizing emergence of simple cell orientation selectivity, we tried to construct a neural network model that consists of LGN neurons and simple cells in visual cortex and obeys the Hebbian learning rule. We investigated the neural coding and representation of simple cells to a natural image by means of this model. The results show that the structures of their receptive fields are determined by the preferred orientation selectivity of simple cells. However, they are also decided by the emergence of self-organization in the unsupervision learning process. This kind of orientation selectivity results from dynamic self-organization based on the interactions between LGN and cortex.     

Motion parallax contribution to perception of self-motion and depth

The object of this study is to mathematically specify important characteristics of visual flow during translation of the eye for the perception of depth and self-motion. We address various strategies by which the central nervous system may estimate self-motion and depth from motion parallax, using equations for the visual velocity field generated by translation of the eye through space. Our results focus on information provided by the movement and deformation of three-dimensional objects and on local flow behavior around a fixated point. All of these issues are addressed mathematically in terms of definite equations for the optic flow. This formal characterization of the visual information presented to the observer is then considered in parallel with other sensory cues to self-motion in order to see how these contribute to the effective use of visual motion parallax, and how parallactic flow can, conversely, contribute to the sense of self-motion. This article will focus on a central case, for understanding of motion parallax in spacious real-world environments, of monocular visual cues observable during pure horizontal translation of the eye through a stationary environment. We suggest that the global optokinetic stimulus associated with visual motion parallax must converge in significant fashion with vestibular and proprioceptive pathways that carry signals related to self-motion. Suggestions of experiments to test some of the predictions of this study are made.     

The peri-saccadic perception of objects and space

Eye movements affect object localization and object recognition. Around saccade onset, briefly flashed stimuli appear compressed towards the saccade target, receptive fields dynamically change position, and the recognition of objects near the saccade target is improved. These effects have been attributed to different mechanisms. We provide a unifying account of peri-saccadic perception explaining all three phenomena by a quantitative computational approach simulating cortical cell responses on the population level. Contrary to the common view of spatial attention as a spotlight, our model suggests that oculomotor feedback alters the receptive field structure in multiple visual areas at an intermediate level of the cortical hierarchy to dynamically recruit cells for processing a relevant part of the visual field. The compression of visual space occurs at the expense of this locally enhanced processing capacity.     

Lateral spike conduction velocity in the visual cortex affects spatial range of synchronization and receptive field size without visual experience: a learning model with spiking neurons

Classical receptive fields (cRF) increase in size from the retina to higher visual centers. The present work shows how temporal properties, in particular lateral spike velocity and spike input correlation, can affect cRF size and position without visual experience. We demonstrate how these properties are related to the spatial range of cortical synchronization if Hebbian learning dominates early development. For this, a largely reduced model of two successive levels of the visual cortex is developed (e.g., areas V1 and V2). It consists of retinotopic networks of spiking neurons with constant spike velocity in lateral connections. Feedforward connections between level 1 and 2 are additive and determine cRF size and shape, while lateral connections within level 1 are modulatory and affect the cortical range of synchronization. Input during development is mimicked by spike trains with spatially homogeneous properties and a confined temporal correlation width. During learning, the homogeneous lateral coupling shrinks to limited coupling structures defining synchronization and related association fields (AF). The size of level-1 synchronization fields determines the lateral coupling range of developing level-1-to-2 connections and, thus, the size of level-2 cRFs, even if the feedforward connections have distance-independent delays. AFs and cRFs increase with spike velocity in the lateral network and temporal correlation width of the input. Our results suggest that AF size of V1 and cRF size of V2 neurons are confined during learning by the temporal width of input correlations and the spike velocity in lateral connections without the need of visual experience. During learning from visual experience, a similar influence of AF size on the cRF size may be operative at successive levels of processing, including other parts of the visual system.     

Emergence of spatiotemporal receptive fields and its application to motion detection

A model of motion sensitivity as observed in some cells of area V1 of the visual cortex is proposed. Motion sensitivity is achieved by a combination of different spatiotemporal receptive fields, in particular, spatial and temporal differentiators. The receptive fields emerge if a Hebbian learning rule is applied to the network. Similar to a Linsker model the network has a spatially convergent, linear feedforward structure. Additionally, however, delays omnipresent in the brain are incorporated in the model. The emerging spatiotemporal receptive fields are derived explicitly by extending the approach of MacKay and Miller. The response characteristic of the network is calculated in frequency space and shows that the network can be considered as a spacetime filter for motion in one direction. The emergence of different types of receptive field requires certain structural constraints regarding the spatial and temporal arborisation. These requirements can be derived from the theoretical analysis and might be compared with neuroanatomical data. In this way an explicit link between structure and function of the network is established.     

Local non-linear interactions in the visual cortex may reflect global decorrelation

The classical receptive field in the primary visual cortex have been successfully explained by sparse activation of relatively independent units, whose tuning properties reflect the statistical dependencies in the natural environment. Robust surround modulation, emerging from stimulation beyond the classical receptive field, has been associated with increase of lifetime sparseness in the V1, but the system-wide modulation of response strength have currently no theoretical explanation. We measured fMRI responses from human visual cortex and quantified the contextual modulation with a decorrelation coefficient (d), derived from a subtractive normalization model. All active cortical areas demonstrated local non-linear summation of responses, which were in line with hypothesis of global decorrelation of voxels responses. In addition, we found sensitivity to surrounding stimulus structure across the ventral stream, and large-scale sensitivity to the number of simultaneous objects. Response sparseness across voxel population increased consistently with larger stimuli. These data suggest that contextual modulation for a stimulus event reflect optimization of the code and perhaps increase in energy efficiency throughout the ventral stream hierarchy. Our model provides a novel prediction that average suppression of response amplitude for simultaneous stimuli across the cortical network is a monotonic function of similarity of response strengths in the network when the stimuli are presented alone.