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.Comment: 25 pages, 18 figures. Added acknowledgement

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

A metric model for the functional architecture of the visual cortex

open3siThis work was supported by the Horizon 2020 Project, ref. 777822: GHAIA, PRIN 2015 ``Variational and perturbative aspects of nonlinear differential problems,"" and by the European Union's Seventh Framework Programme, ref. 607643: MAnET.The purpose of this work is to construct a model for the functional architecture of the primary visual cortex (V1), based on a structure of metric measure space induced by the underlying organization of receptive profiles (RPs) of visual cells. In order to account for the horizontal connectivity of V1 in such a context, a diffusion process compatible with the geometry of the space is defined following the classical approach of K.-T. Sturm [Ann. Probab., 26 (1998), pp. 1-55]. The construction of our distance function neither requires any group parameterization of the family of RPs nor involves any differential structure. As such, it adapts to nonparameterized sets of RPs, possibly obtained through numerical procedures; it also allows us to model the lateral connectivity arising from nondifferential metrics such as the one induced on a pinwheel surface by a family of filters of vanishing scale. On the other hand, when applied to the classical framework of Gabor filters, this construction yields a distance approximating the sub-Riemannian structure proposed as a model for V1 by Citti and Sarti [J. Math. Imaging Vision Archive, 24 (2006), pp. 307-326], thus showing itself to be consistent with existing cortex models.openMontobbio N.; Sarti A.; Citti G.Montobbio N.; Sarti A.; Citti G

Preattentive texture discrimination with early vision mechanisms

We present a model of human preattentive texture perception. This model consists of three stages: (1) convolution of the image with a bank of even-symmetric linear filters followed by half-wave rectification to give a set of responses modeling outputs of V1 simple cells, (2) inhibition, localized in space, within and among the neural-response profiles that results in the suppression of weak responses when there are strong responses at the same or nearby locations, and (3) texture-boundary detection by using wide odd-symmetric mechanisms. Our model can predict the salience of texture boundaries in any arbitrary gray-scale image. A computer implementation of this model has been tested on many of the classic stimuli from psychophysical literature. Quantitative predictions of the degree of discriminability of different texture pairs match well with experimental measurements of discriminability in human observers

Development of spatial coarse-to-fine processing in the visual pathway

The sequential analysis of information in a coarse-to-fine manner is a fundamental mode of processing in the visual pathway. Spatial frequency (SF) tuning, arguably the most fundamental feature of spatial vision, provides particular intuition within the coarse-to-fine framework: low spatial frequencies convey global information about an image (e.g., general orientation), while high spatial frequencies carry more detailed information (e.g., edges). In this paper, we study the development of cortical spatial frequency tuning. As feedforward input from the lateral geniculate nucleus (LGN) has been shown to have significant influence on cortical coarse-to-fine processing, we present a firing-rate based thalamocortical model which includes both feedforward and feedback components. We analyze the relationship between various model parameters (including cortical feedback strength) and responses. We confirm the importance of the antagonistic relationship between the center and surround responses in thalamic relay cell receptive fields (RFs), and further characterize how specific structural LGN RF parameters affect cortical coarse-to-fine processing. Our results also indicate that the effect of cortical feedback on spatial frequency tuning is age-dependent: in particular, cortical feedback more strongly affects coarse-to-fine processing in kittens than in adults. We use our results to propose an experimentally testable hypothesis for the function of the extensive feedback in the corticothalamic circuit.Comment: 20 pages, 7 figures; substantial restructuring from previous versio

A sub-Riemannian model of the visual cortex with frequency and phase

In this paper we present a novel model of the primary visual cortex (V1) based on orientation, frequency and phase selective behavior of the V1 simple cells. We start from the first level mechanisms of visual perception: receptive profiles. The model interprets V1 as a fiber bundle over the 2-dimensional retinal plane by introducing orientation, frequency and phase as intrinsic variables. Each receptive profile on the fiber is mathematically interpreted as a rotated, frequency modulated and phase shifted Gabor function. We start from the Gabor function and show that it induces in a natural way the model geometry and the associated horizontal connectivity modeling the neural connectivity patterns in V1. We provide an image enhancement algorithm employing the model framework. The algorithm is capable of exploiting not only orientation but also frequency and phase information existing intrinsically in a 2-dimensional input image. We provide the experimental results corresponding to the enhancement algorithm