A reaction-diffusion model to capture disparity selectivity in primary visual cortex

Decades of experimental studies are available on disparity selective cells in visual cortex of macaque and cat. Recently, local disparity map for iso-orientation sites for near-vertical edge preference is reported in area 18 of cat visual cortex. No experiment is yet reported on complete disparity map in V1. Disparity map for layer IV in V1 can provide insight into how disparity selective complex cell receptive field is organized from simple cell subunits. Though substantial amounts of experimental data on disparity selective cells is available, no model on receptive field development of such cells or disparity map development exists in literature. We model disparity selectivity in layer IV of cat V1 using a reaction-diffusion two-eye paradigm. In this model, the wiring between LGN and cortical layer IV is determined by resource an LGN cell has for supporting connections to cortical cells and competition for target space in layer IV. While competing for target space, the same type of LGN cells, irrespective of whether it belongs to left-eye-specific or right-eye-specific LGN layer, cooperate with each other while trying to push off the other type. Our model captures realistic 2D disparity selective simple cell receptive fields, their response properties and disparity map along with orientation and ocular dominance maps. There is lack of correlation between ocular dominance and disparity selectivity at the cell population level. At the map level, disparity selectivity topography is not random but weakly clustered for similar preferred disparities. This is similar to the experimental result reported for macaque. The details of weakly clustered disparity selectivity map in V1 indicate two types of complex cell receptive field organization.     

视差检测：简单细胞、复杂细胞及能量模型

立体视觉信息的处理在于皮层双眼性细胞的活动.皮层中简单细胞对视差的编码方式被认为有两种：位置差（position shift）和相位差（phase shift）,但简单细胞并不适合作为视差检测器.对一些复杂细胞的视差响应特性的生理研究,发现复杂细胞是一种比较适合的视差检测器.模型的研究提出基于这类简单细胞的复杂细胞能量模型,可以很好的检测视差,并可以较好的解释一些生理现象.     

Luminance,Colour, Viewpoint and Border Enhanced Disparity Energy Model

The visual cortex is able to extract disparity information through the use of binocular cells. This process is reflected by the Disparity Energy Model, which describes the role and functioning of simple and complex binocular neuron populations, and how they are able to extract disparity. This model uses explicit cell parameters to mathematically determine preferred cell disparities, like spatial frequencies, orientations, binocular phases and receptive field positions. However, the brain cannot access such explicit cell parameters; it must rely on cell responses. In this article, we implemented a trained binocular neuronal population, which encodes disparity information implicitly. This allows the population to learn how to decode disparities, in a similar way to how our visual system could have developed this ability during evolution. At the same time, responses of monocular simple and complex cells can also encode line and edge information, which is useful for refining disparities at object borders. The brain should then be able, starting from a low-level disparity draft, to integrate all information, including colour and viewpoint perspective, in order to propagate better estimates to higher cortical areas.     

初级视觉皮层“简单”与“复杂”神经元动力学的计算建模

本文回顾了我们在哺乳动物视觉皮层的建模工作.利用初级视觉皮层的大规模神经元网络模型,我们解释了初级视觉皮层里“简单”与“复杂”神经元现象的网络机制.所谓的“简单”细胞对视觉刺激的反应近似线性,而“复杂”细胞对视觉刺激是非线性的.我们的模型成功地再现了简单和复杂细胞分布的实验数据.     

Spatial stereoresolution for depth corrugations may be set in primary visual cortex

Stereo "3D" depth perception requires the visual system to extract binocular disparities between the two eyes' images. Several current models of this process, based on the known physiology of primary visual cortex (V1), do this by computing a piecewise-frontoparallel local cross-correlation between the left and right eye's images. The size of the "window" within which detectors examine the local cross-correlation corresponds to the receptive field size of V1 neurons. This basic model has successfully captured many aspects of human depth perception. In particular, it accounts for the low human stereoresolution for sinusoidal depth corrugations, suggesting that the limit on stereoresolution may be set in primary visual cortex. An important feature of the model, reflecting a key property of V1 neurons, is that the initial disparity encoding is performed by detectors tuned to locally uniform patches of disparity. Such detectors respond better to square-wave depth corrugations, since these are locally flat, than to sinusoidal corrugations which are slanted almost everywhere. Consequently, for any given window size, current models predict better performance for square-wave disparity corrugations than for sine-wave corrugations at high amplitudes. We have recently shown that this prediction is not borne out: humans perform no better with square-wave than with sine-wave corrugations, even at high amplitudes. The failure of this prediction raised the question of whether stereoresolution may actually be set at later stages of cortical processing, perhaps involving neurons tuned to disparity slant or curvature. Here we extend the local cross-correlation model to include existing physiological and psychophysical evidence indicating that larger disparities are detected by neurons with larger receptive fields (a size/disparity correlation). We show that this simple modification succeeds in reconciling the model with human results, confirming that stereoresolution for disparity gratings may indeed be limited by the size of receptive fields in primary visual cortex.     

A binocular model for the simple cell

We authors propose a mathematical model for simple cell binocular response. It comprises two Gabor-type receptive fields (RF) having the same RF center, preferred spatial frequency, and preferred orientation. The model integrates the equally weighted signals from both eyes and performs a threshold operation. Poggio and Fischer (1977) classified binocular disparity cells in the striate cortex into four groups: tuned excitatory (TE), tuned inhibitory (TI), near, and far cells. They also found that most of the TE cells are ocularly balanced and that the other three types are usually unbalanced. This model can imitate these four types of disparity sensitivities and their ocular dominance tendency. We perform model fittings to Poggio's data using the “simulated annealing” method and discuss parameter dependence of the model's response. The model can also respond with exceptional disparity sensitivity: i.e., flat type, alternating type, and intermediate type.     

Construction of complex receptive fields in cat primary visual cortex.

In primary visual cortex, neurons are classified into simple cells and complex cells based on their response properties. Although the role of these two cell types in vision is still unknown, an attractive hypothesis is that simple cells are necessary to construct complex receptive fields. This hierarchical model puts forward two main predictions. First, simple cells should connect monosynaptically to complex cells. Second, complex cells should become silent when simple cells are inactivated. We have recently provided evidence for the first prediction, and here we do the same for the second. In summary, our results suggest that the receptive fields of most layer 2+3 complex cells are generated by a mechanism that requires simple cell inputs.     

The development of the binocular depth cells in the secondary visual cortex of the lamb.

In most respects, the response properties of cells in the secondary visual cortex of the newborn lamb were indistinguishable from those in the adult. The cells were sharply selective to orientation; the orientation preferences were the same in each eye, and they varied systematically as the electrode penetrated the cortex. The receptive-field organization did not differ noticeably from that in adults, and complex, hypercomplex, and a few simple cells were all observed. The ocular dominance distribution was similar to that in the adult. Most importantly, binocular cells were found with disparate receptive fields even in newborn, visually inexperienced animals. As in the adult, the disparities were largely horizontal, and they appeared to be arranged in columns. Many of the cells responded preferentially to a binocular stimulus at a particular disparity setting (often approximately zero), but unlike those in the adult almost all the binocular cells in the newborn lamb would also respond monocularly, and the enhancement at the optimal disparity was less than in the adult. The full development of binocular selectivity took several weeks, and was blocked by binocular deprivation. We conclude that the basic wiring of stereoscopic mechanisms is innate, but the development of mature binocular interaction may depend on an adaptive process which makes use of the visual information received during binocular stimulation.     

Receptive fields of disparity-tuned simple cells in macaque V1

Binocular simple cells in primary visual cortex (V1) are the first cells along the mammalian visual pathway to receive input from both eyes. Two models of how binocular simple cells could extract disparity information have been put forward. The phase-shift model proposes that the receptive fields in the two eyes have different subunit organizations, while the position-shift model proposes that they have different overall locations. In five fixating macaque monkeys, we recorded from 30 disparity-tuned simple cells that showed selectivity to the disparity in a random dot stereogram. High-resolution maps of the left and right eye receptive fields indicated that both phase and position shifts were common. Single cells usually showed a combination of the two, and the optimum disparity was best correlated with the sum of receptive field phase and position shift.     

Stereopsis activates V3A and caudal intraparietal areas in macaques and humans

Stereopsis, the perception of depth from small differences between the images in the two eyes, provides a rich model for investigating the cortical construction of surfaces and space. Although disparity-tuned cells have been found in a large number of areas in macaque visual cortex, stereoscopic processing in these areas has never been systematically compared using the same stimuli and analysis methods. In order to examine the global architecture of stereoscopic processing in primate visual cortex, we studied fMRI activity in alert, fixating human and macaque subjects. In macaques, we found strongest activation to near/far compared to zero disparity in areas V3, V3A, and CIPS. In humans, we found strongest activation to the same stimuli in areas V3A, V7, the V4d topolog (V4d-topo), and a caudal parietal disparity region (CPDR). Thus, in both primate species a small cluster of areas at the parieto-occipital junction appears to be specialized for stereopsis.     

Is slowness a learning principle of the visual cortex?

Slow feature analysis is an algorithm for extracting slowly varying features from a quickly varying signal. It has been shown in network simulations on one-dimensional stimuli that visual invariances to shift and other transformations can be learned in an unsupervised fashion based on slow feature analysis. More recently, we have shown that slow feature analysis applied to image sequences generated from natural images using a range of spatial transformations results in units that share many properties with complex and hypercomplex cells of the primary visual cortex. We find cells responsive to Gabor stimuli with phase invariance, sharpened or widened orientation or frequency tuning, secondary response lobes, end-stopping, and cells selective for direction of motion. These results indicate that slowness may be an important principle of self-organization in the visual cortex.     

视觉皮层复杂细胞时空编码特性

针对输入在视皮层的编码表达,在地空滤波窗口基础上构建了一个复杂细胞时空编码模型,对几种特殊的输入函数进行了编码仿真实验,结果说明了视皮层复杂细胞时空整合编码序列的精细时间结构进行视觉输入的神经表象。     

Sensory and non-sensory visual disorders in man and monkey

The posterior third of the cerebral cortex in monkeys consists of a patchwork of visual areas in each of which there is a 'map' of the retina. The details of the 'map' vary considerably from one area to another and one notable variation concerns the optimal visual feature to which the cells respond. Orientation, disparity, colour and movement are emphasized in separate areas that appear to be concerned with sensory analysis. Their existence and the possibility that brain damage is occasionally restricted chiefly to one such area may explain the rare highly selective visual sensory impairments that can follow posterior cerebral damage in man. Other areas are notable for having little or no retinotopic representation. Here the cells may have huge receptive fields and complex trigger features. When such regions are removed, the animal's visual sensory abilities are intact but its recognition of patterns and objects is not. This condition resembles human visual agnosia.     

Brain damage and global stereopsis.

When a single object lies in front of or beyond the plane of fixation its retinal image lies on disparate positions in the two eyes. This 'local' retinal disparity is an excellent cue to depth, and retinal disparties of a few seconds of arc are detectable by people and monkeys. However, most visual scenes produce a complex array of contours in each eye and we can detect the disparity in the arrays despite the ambiguous nature of the disparities, i.e. each contour in one eye could be related to any of several similar contours in the other eye. This ability, known as 'global' stereopsis, may be selectively impaired following brain damage in man. Global stereopsis was measured in rhesus monkeys before and after removing a different cortical visual area in different groups of animals. Only removal of the inferotemporal cortex impaired global stereopsis. The result is related to the findings with human patients and to receptive field properties of neurons in the inferotemporal cortex of monkeys.     

A map for horizontal disparity in monkey V2

The perception of visual depth is determined by integration of spatial disparities of inputs from the two eyes. Single cells in visual cortex of monkeys are known to respond to specific binocular disparities; however, little is known about their functional organization. We now show, using intrinsic signal optical imaging and single-unit physiology, that, in the thick stripe compartments of the second visual area (V2), there is a clustered organization of Near cells and Far cells, and moreover, there are topographic maps for Near to Far disparities within V2. Our findings suggest that maps for visual disparity are calculated in V2, and demonstrate parallels in functional organization between the thin, pale, and thick stripes of V2.     

Computational models of visual neurons specialised in the detection of periodic and aperiodic oriented visual stimuli: bar and grating cells

Computational models of periodic- and aperiodic-pattern selective cells, also called grating and bar cells, respectively, are proposed. Grating cells are found in areas V1 and V2 of the visual cortex of monkeys and respond strongly to bar gratings of a given orientation and periodicity but very weakly or not at all to single bars. This non-linear behaviour, which is quite different from the spatial frequency filtering behaviour exhibited by the other types of orientation-selective neurons such as the simple cells, is incorporated in the proposed computational model by using an AND-type non-linearity to combine the responses of simple cells with symmetric receptive field profiles and opposite polarities. The functional behaviour of bar cells, which are found in the same areas of the visual cortex as grating cells, is less well explored and documented in the literature. In general, these cells respond to single bars and their responses decrease when further bars are added to form a periodic pattern. These properties of bar cells are implemented in a computational model in which the responses of bar cells are computed as thresholded differences of the responses of corresponding complex (or simple) cells and grating cells. Bar and grating cells seem to play complementary roles in resolving the ambiguity with which the responses of simple and complex cells represent oriented visual stimuli, in that bar cells are selective only for form information as present in contours and grating cells only respond to oriented texture information. The proposed model is capable of explaining the results of neurophysiological experiments as well as the psychophysical observation that the perception of texture and the perception of form are complementary processes. Received: 4 June 1996 / Accepted in revised form: 7 October 1996     

Vertical Binocular Disparity is Encoded Implicitly within a Model Neuronal Population Tuned to Horizontal Disparity and Orientation

Primary visual cortex is often viewed as a “cyclopean retina”, performing the initial encoding of binocular disparities between left and right images. Because the eyes are set apart horizontally in the head, binocular disparities are predominantly horizontal. Yet, especially in the visual periphery, a range of non-zero vertical disparities do occur and can influence perception. It has therefore been assumed that primary visual cortex must contain neurons tuned to a range of vertical disparities. Here, I show that this is not necessarily the case. Many disparity-selective neurons are most sensitive to changes in disparity orthogonal to their preferred orientation. That is, the disparity tuning surfaces, mapping their response to different two-dimensional (2D) disparities, are elongated along the cell''s preferred orientation. Because of this, even if a neuron''s optimal 2D disparity has zero vertical component, the neuron will still respond best to a non-zero vertical disparity when probed with a sub-optimal horizontal disparity. This property can be used to decode 2D disparity, even allowing for realistic levels of neuronal noise. Even if all V1 neurons at a particular retinotopic location are tuned to the expected vertical disparity there (for example, zero at the fovea), the brain could still decode the magnitude and sign of departures from that expected value. This provides an intriguing counter-example to the common wisdom that, in order for a neuronal population to encode a quantity, its members must be tuned to a range of values of that quantity. It demonstrates that populations of disparity-selective neurons encode much richer information than previously appreciated. It suggests a possible strategy for the brain to extract rarely-occurring stimulus values, while concentrating neuronal resources on the most commonly-occurring situations.     

Cue combination in the motion correspondence problem

Image motion is a primary source of visual information about the world. However, before this information can be used the visual system must determine the spatio-temporal displacements of the features in the dynamic retinal image, which originate from objects moving in space. This is known as the motion correspondence problem. We investigated whether cross-cue matching constraints contribute to the solution of this problem, which would be consistent with physiological reports that many directionally selective cells in the visual cortex also respond to additional visual cues. We measured the maximum displacement limit (Dmax) for two-frame apparent motion sequences. Dmax increases as the number of elements in such sequences decreases. However, in our displays the total number of elements was kept constant while the number of a subset of elements, defined by a difference in contrast polarity, binocular disparity or colour, was varied. Dmax increased as the number of elements distinguished by a particular cue was decreased. Dmax was affected by contrast polarity for all observers, but only some observers were influenced by binocular disparity and others by colour information. These results demonstrate that the human visual system exploits local, cross-cue matching constraints in the solution of the motion correspondence problem.     

Learning receptive field properties of complex cells in V1

There are two distinct classes of cells in the primary visual cortex (V1): simple cells and complex cells. One defining feature of complex cells is their spatial phase invariance; they respond strongly to oriented grating stimuli with a preferred orientation but with a wide range of spatial phases. A classical model of complete spatial phase invariance in complex cells is the energy model, in which the responses are the sum of the squared outputs of two linear spatially phase-shifted filters. However, recent experimental studies have shown that complex cells have a diverse range of spatial phase invariance and only a subset can be characterized by the energy model. While several models have been proposed to explain how complex cells could learn to be selective to orientation but invariant to spatial phase, most existing models overlook many biologically important details. We propose a biologically plausible model for complex cells that learns to pool inputs from simple cells based on the presentation of natural scene stimuli. The model is a three-layer network with rate-based neurons that describes the activities of LGN cells (layer 1), V1 simple cells (layer 2), and V1 complex cells (layer 3). The first two layers implement a recently proposed simple cell model that is biologically plausible and accounts for many experimental phenomena. The neural dynamics of the complex cells is modeled as the integration of simple cells inputs along with response normalization. Connections between LGN and simple cells are learned using Hebbian and anti-Hebbian plasticity. Connections between simple and complex cells are learned using a modified version of the Bienenstock, Cooper, and Munro (BCM) rule. Our results demonstrate that the learning rule can describe a diversity of complex cells, similar to those observed experimentally.