Design principles of columnar organization in visual cortex

Visual space is represented by cortical cells in an orderly manner. Only little variation in the cell behavior is found with changing depth below the cortical surface, that is, all cells in a column with axis perpendicular to the cortical plane have approximately the same properties (Hubel and Wiesel 1962, 1963, 1968). Therefore, the multiple features of the visual space (e.g., position in visual space, preferred orientation, and orientation tuning strength) are mapped on a two-dimensional space, the cortical plane. Such a dimension reduction leads to complex maps (Durbin and Mitchison 1990) that so far have evaded an intuitive understanding. Analyzing optical imaging data (Blasdel 1992a, b; Blasdel and Salama 1986; Grinvald et al. 1986) using a theoretical approach we will show that the most salient features of these maps can be understood from a few basic design principles: local correlation, modularity, isotropy, and homogeneity. These principles can be defined in a mathematically exact sense in the Fourier domain by a rather simple annulus-like spectral structure. Many of the models that have been developed to explain the mapping of the preferred orientations (Cooper et al. 1979; Legendy 1978; Linsker 1986a, b; Miller 1992; Nass and Cooper 1975; Obermayer et al. 1990, 1992; Soodak 1987; Swindale 1982, 1985, 1992; von der Malsburg 1973; von der Malsburg and Cowan 1982) are quite successful in generating maps that are close to experimental maps. We suggest that this success is due to these principles, which are common properties of the models and of biological maps

Generation of Direction Selectivity by Isotropic Intracortical Connections

To what extent do the mechanisms generating different receptive field properties of neurons depend on each other? We investigated this question theoretically within the context of orientation and direction tuning of simple cells in the mammalian visual cortex. In our model a cortical cell of the "simple" type receives its orientation tuning by afferent convergence of aligned receptive fields of the lateral geniculate nucleus (Hubel and Wiesel 1962). We sharpen this orientation bias by postulating a special type of radially symmetric long-range lateral inhibition called circular inhibition. Surprisingly, this isotropic mechanism leads to the emergence of a strong bias for the direction of motion of a bar. We show that this directional anisotropy is neither caused by the probabilistic nature of the connections nor is it a consequence of the specific columnar structure chosen but that it is an inherent feature of the architecture of visual cortex

Cortical column design: a link between the maps of preferred orientation and orientation tuning strength?

We demonstrate that the map of the preferred orientations and the corresponding map of the orientation tuning strengths as measured with optical imaging are not independent, but that band-pass filtering of the preferred orientation map at each location yields a good approximation of the orientation tuning strength. Band-pass filtering is performed by convolving the map of orientation preference with its own autocorrelation function. We suggest an interpretation of the autocorrelation function of the preferred orientations as synaptic coupling function, i.e., synaptic strength as a function of intracortical distance between cortical cells. In developmental models it has been shown previously that a “Mexican hat”-shaped synaptic coupling function (with a shape similar to that of the autocorrelation function) can produce a realistical-looking pattern of preferred orientations. Since optical imaging performs surface averaging, we discuss the possibility that the connection between the two maps is a measurement artifact of optical imaging. Whether this is the case can only be decided by combining electrode penetrations with optical imaging techniques for which we suggest experiments. We present a model for the generation of both maps from a single computational concept. The model is based on inverse Fourier transform of rather simple two-dimensional annulus-shaped spectra which will produce a column structure very similar to real data. Thus, our approach shows that the complex appearance of cortical orientation columns has a rather simple description in the Fourier domain. Our theoretical analysis explains why singularities in the cortex do not have vorticities other than ±1/2, a result which corresponds to recent experimental findings. This study combines the results from several modeling approaches with recently available optical imaging data to construct a model of both aspects (angle and strength) of the cortical orientation column system. This could alter ideas about cortical development if the link between the two maps can be established as a physiological result

A detailed model of the primary visual pathway in the cat: comparison of afferent excitatory and intracortical inhibitory connection schemes for orientation selectivity

In order to arrive at a quantitative understanding of the dynamics of cortical neuronal networks, we simulated a detailed model of the primary visual pathway of the adult cat. This computer model comprises a 5 degrees x 5 degrees patch of the visual field at a retinal eccentricity of 4.5 degrees and includes 2048 ON- and OFF-center retinal beta-ganglion cells, 8192 geniculate X-cells, and 4096 simple cells in layer IV in area 17. The neurons are implemented as improved integrate-and-fire units. Cortical receptive fields are determined by the pattern of afferent convergence and by inhibitory intracortical connections. Orientation columns are implemented continuously with a realistic receptive field scatter and jitter in the preferred orientations. We first show that realistic ON-OFF-responses, orientation selectivity, velocity low-pass behaviour, null response, and responses to spot stimuli can be obtained with an appropriate alignment of geniculate neurons converging onto the cortical simple cell (Hubel and Wiesel, 1962) and in the absence of intracortical connections. However, the average receptive field elongation (length to width) required to obtain realistic orientation tuning is 4.0, much higher than the average observed elongation. This strongly argues for additional intracortical mechanisms sharpening orientation selectivity. In the second stage, we simulated five different inhibitory intracortical connection patterns (random, local, sparse-local, circular, and cross-orientation) in order to investigate the connection specificity necessary to achieve orientation tuning. Inhibitory connection schemes were superimposed onto Hubel and Wiesel-type receptive fields with an elongation of 1.78. Cross-orientation inhibition gave rise to different horizontal and vertical orientation tuning curves, something not observed experimentally. A combination of two inhibitory schemes, local and circular inhibition (a weak form of cross-orientation inhibition), is in good agreement with observed receptive field properties. The specificity required to establish these connections during development is low. We propose that orientation selectivity is caused by at least three different mechanisms (“eclectic” model): a weak afferent geniculate bias, broadly tuned cross-orientation inhibition, and some iso-orientation inhibition. The most surprising finding is that an isotropic connection scheme, circular inhibition, in which a cell inhibits all of its postsynaptic target cells at a distance of approximately 500 microns, enhances orientation tuning and leads to a significant directional bias. This is caused by the embedding of cortical cells within a columnar structure and does not depend on our specific assumptions

A local algorithm for the computation of image velocity via constructive interference of global Fourier components

A novel Fourier-based technique for local motion detection from image sequences is proposed. In this method, the instantaneous velocities of local image points are inferred directly from the global 3D Fourier components of the image sequence. This is done by selecting those velocities for which the superposition of the corresponding Fourier gratings leads to constructive interference at the image point. Hence, image velocities can be assigned locally even though position is computed from the phases and amplitudes of global Fourier components (spanning the whole image sequence) that have been filtered based on the motion-constraint equation, reducing certain aperture effects typically arising from windowing in other methods. Regularization is introduced for sequences having smooth flow fields. Aperture effects and their effect on optic-flow regularization are investigated in this context. The algorithm is tested on both synthetic and real image sequences and the results are compared to those of other local methods. Finally, we show that other motion features, i.e. motion direction, can be computed using the same algorithmic framework without requiring an intermediate representation of local velocity, which is an important characteristic of the proposed method.Postprint (author’s final draft

Effects of Fixational Eye Movements on Retinal Ganglion Cell Responses: A Modelling Study

Visual response properties of retinal ganglion cells (GCs), the retinal output neurons, are shaped by numerous processes and interactions within the retina. In particular, amacrine cells are known to form microcircuits that affect GC responses in specific ways. So far, relatively little is known about the influence of retinal processing on GC responses under naturalistic viewing conditions, in particular in the presence of fixational eye movements. Here we used a detailed model of the mammalian retina to investigate possible effects of fixational eye movements on retinal GC activity. Populations of linear, sustained (parvocellular, PC) and nonlinear, transient (magnocellular, MC) GCs were simulated during fixation of a star-shaped stimulus, and two distinct effects were found: (1) a fading of complete wedges of the star and (2) an apparent splitting of stimulus lines. Both effects only occur in MC-cells, and an analysis shows that fading is caused by an expression of the aperture problem in retinal GCs, and the splitting effect by spatiotemporal nonlinearities in the MC-cell receptive field. These effects strongly resemble perceived instabilities during fixation of the same stimulus, and we propose that these illusions may have a retinal origin. We further suggest that in this case two parallel retinal streams send conflicting, rather than complementary, information to the higher visual system, which here leads to a dominant influence of the MC pathway. Similar situations may be common during natural vision, since retinal processing involves numerous nonlinearities

Learning weakly correlated cause-effects for gardening with a cognitive system

We propose a cognitive system that combines artificial intelligence techniques for planning and learning to execute tasks involving delayed and variable correlations between the actions executed and their expected effects. The system is applied to the task of controlling the growth of plants, where the evolution of the plant attributes strongly depends on different events taking place in the temporally distant past history of the plant. The main problem to tackle is how to efficiently detect these past events. This is very challenging since the inclusion of time could make the dimensionality of the search space extremely large and the collected training instances may only provide very limited information about the relevant combinations of events. To address this problem we propose a learning method that progressively identifies those events that are more likely to produce a sequence of changes under a plant treatment. Since the number of experiences is very limited compared to the size of the event space, we use a probabilistic estimate that takes into account the lack of experience to prevent biased estimations. Planning operators are generated from most accurately predicted sequences of changes. Planning and learning are integrated in a decision-making framework that operates without task interruptions by allowing a human gardener to instruct the treatments when the knowledge acquired so far is not enough to make a decision.This research was supported by the European Community Seventh Framework ProgrammeFP7/2007–2013 – Challenge 2 – Cognitive Systems, Interaction, Robotics – under Grant agreement No 247947 – GARNICS.Peer Reviewe