A Ring Model for Direction-Selective Simple Cells in the Visual Cortex

Perception ◽  
1997 ◽  
Vol 26 (1_suppl) ◽  
pp. 164-164
Author(s):  
T Hamada ◽  
K Kato ◽  
M Yamashima
Keyword(s):  
Visual Cortex ◽  
Experimental Studies ◽  
Receptive Fields ◽  
Lateral Geniculate Body ◽  
Neural Model ◽  
Cortical Cells ◽  
Simple Cells ◽  
Ring Model ◽  
Gabor Functions

Experimental studies have shown that (1) direction-selective simple cells in the visual cortex have spatiotemporally inseparable receptive fields, whose spatial profiles at a given time are described by Gabor functions: a sinusoid multiplied by a Gaussian, with a phase parameter; (2) among simple cells, the phases are distributed not merely at 0 and pi/2 as for sine and cosine Gabor functions, but uniformly between 0 and 2pi (DeAngelis et al, 1993 Journal of Neurophysiology69 1091 – 1117); (3) anatomically, these simple cells receive inputs more from other cortical cells than from the lateral geniculate body (LGN) (Ahmed et al, 1994 Journal of Comparative Neurology341 39 – 49). We accordingly propose here a neural model for the simple cells whose receptive fields are assumed to be of the same spatial position and orientation. In the model, several cortical cells are arranged in a ring with mutual excitatory and inhibitory connections, and receive afferent signals from lagged and nonlagged cells in LGN (Saul and Humphrey, 1990 Journal of Neurophysiology64 206 – 224). Computer simulation shows that the cortical cells have spatiotemporally inseparable receptive fields with spatial profiles described by Gabor functions, and are directionally selective to a moving grating. The cells are found to be arranged so that their Gabor phases vary regularly from 0 to 2pi with rotation along the ring. The connection among the cortical cells has a role of amplification as in the canonical microcircuit model (Douglas et al, 1989 Neural Computation1 480 – 488).

Generalized signal-tuned Gabor approach for signal representation and analysis

2017 ◽  
Vol 28 (01) ◽  
pp. 1750001 ◽  
Author(s):  
José R. A. Torreão
Keyword(s):  
Fourier Transform ◽  
Visual Cortex ◽  
Fourier Transforms ◽  
Fractional Fourier Transform ◽  
Receptive Fields ◽  
Gabor Functions ◽  
Plausible Model ◽  
Spectral Signal ◽  
Potential Applications ◽  
Space Frequency

The signal-tuned Gabor approach is based on spatial or spectral Gabor functions whose parameters are determined, respectively, by the Fourier and inverse Fourier transforms of a given “tuning” signal. The sets of spatial and spectral signal-tuned functions, for all possible frequencies and positions, yield exact representations of the tuning signal. Moreover, such functions can be used as kernels for space-frequency transforms which are tuned to the specific features of their inputs, thus allowing analysis with high conjoint spatio-spectral resolution. Based on the signal-tuned Gabor functions and the associated transforms, a plausible model for the receptive fields and responses of cells in the primary visual cortex has been proposed. Here, we present a generalization of the signal-tuned Gabor approach which extends it to the representation and analysis of the tuning signal’s fractional Fourier transform of any order. This significantly broadens the scope and the potential applications of the approach.

Spatial properties of neurons in the monkey striate cortex

1987 ◽  
Vol 231 (1263) ◽  
pp. 251-288 ◽  
Keyword(s):  
Receptive Field ◽  
Contrast Sensitivity ◽  
Visual Processing ◽  
Striate Cortex ◽  
Receptive Fields ◽  
Spatial Filter ◽  
Cortical Cells ◽  
Simple Cells ◽  
Gabor Function ◽  
Difference Of Gaussians

Contrast sensitivity as a function of spatial frequency was determined for 138 neurons in the foveal region of primate striate cortex. The accuracy of three models in describing these functions was assessed by the method of least squares. Models based on difference-of-Gaussians (DOG) functions were shown to be superior to those based on the Gabor function or the second differential of a Gaussian. In the most general case of the DOG models, each subregion of a simple cell’s receptive field was constructed from a single DOG function. All the models are compatible with the classical observation that the receptive fields of simple cells are made up of spatially discrete ‘on’ and ‘off’ regions. Although the DOG-based models have more free parameters, they can account better for the variety of shapes of spatial contrast sensitivity functions observed in cortical cells and, unlike other models, they provide a detailed description of the organization of subregions of the receptive field that is consistent with the physiological constraints imposed by earlier stages in the visual pathway. Despite the fact that the DOG-based models have spatially discrete components, the resulting amplitude spectra in the frequency domain describe complex cells just as well as simple cells. The superiority of the DOG-based models as a primary spatial filter is discussed in relation to popular models of visual processing that use the Gabor function or the second differential of a Gaussian.

The Joint Development of Orientation and Ocular Dominance: Role of Constraints

1997 ◽  
Vol 9 (5) ◽  
pp. 959-970 ◽  
Author(s):  
Christian Piepenbrock ◽  
Helge Ritter ◽  
Klaus Obermayer
Keyword(s):  
Visual Cortex ◽  
Primary Visual Cortex ◽  
Ocular Dominance ◽  
Receptive Fields ◽  
Simple Cell ◽  
Orientation Preference ◽  
Joint Development ◽  
Independent Work ◽  
Insight Into

Correlation-based learning (CBL) has been suggested as the mechanism that underlies the development of simple-cell receptive fields in the primary visual cortex of cats, including orientation preference (OR) and ocular dominance (OD) (Linsker, 1986; Miller, Keller, & Stryker, 1989). CBL has been applied successfully to the development of OR and OD individually (Miller, Keller, & Stryker, 1989; Miller, 1994; Miyashita & Tanaka, 1991; Erwin, Obermayer, & Schulten, 1995), but the conditions for their joint development have not been studied (but see Erwin & Miller, 1995, for independent work on the same question) in contrast to competitive Hebbian models (Obermayer, Blasdel, & Schulten, 1992). In this article, we provide insight into why this has been the case: OR and OD decouple in symmetric CBL models, and a joint development of OR and OD is possible only in a parameter regime that depends on nonlinear mechanisms.

Self-Organization of Binocular Disparity Tuning by Reciprocal Corticogeniculate Interactions

1998 ◽  
Vol 10 (2) ◽  
pp. 199-215 ◽  
Author(s):  
Alexander Grunewald ◽  
Stephen Grossberg
Keyword(s):  
Learning Process ◽  
Visual Processing ◽  
Neural Model ◽  
Image Features ◽  
Cortical Cells ◽  
Simple Cells ◽  
Complex Cells ◽  
Matching Process ◽  
Tuning Width ◽  
Opposite Contrast

This article develops a neural model of how sharp disparity tuning can arise through experience-dependent development of cortical complex cells. This learning process clarifies how complex cells can binocularly match left and right eye image features with the same contrast polarity, yet also pool signals with opposite contrast polarities. Antagonistic rebounds between LGN ON and OFF cells and cortical simple cells sensitive to opposite contrast polarities enable anticorrelated simple cells to learn to activate a shared set of complex cells. Feedback from binocularly tuned cortical cells to monocular LGN cells is proposed to carry out a matching process that dynamically stabilizes the learning process. This feedback represents a type of matching process that is elaborated at higher visual processing areas into a volitionally controllable type of attention. We show stable learning when both of these properties hold. Learning adjusts the initially coarsely tuned disparity preference to match the disparities present in the environment, and the tuning width decreases to yield high disparity selectivity, which enables the model to quickly detect image disparities. Learning is impaired in the absence of either antagonistic rebounds or corticogeniculate feedback. The model also helps to explain psychophysical and neurobiological data about adult 3-D vision.

scholarly journals Learning receptive field properties of complex cells in V1

2020 ◽  
Author(s):  
Yanbo Lian ◽  
Ali Almasi ◽  
David B. Grayden ◽  
Tatiana Kameneva ◽  
Anthony N. Burkitt ◽  
...  
Keyword(s):  
Visual Cortex ◽  
Experimental Studies ◽  
Learning Rule ◽  
Energy Model ◽  
Learning Ability ◽  
Simple Cells ◽  
Complex Cells ◽  
Spatial Phase ◽  
Model Complex ◽  
The Brain

AbstractThere 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.Author summaryMany cortical functions originate from the learning ability of the brain. How the properties of cortical cells are learned is vital for understanding how the brain works. There are many models that explain how V1 simple cells can be learned. However, how V1 complex cells are learned still remains unclear. In this paper, we propose a model of learning in complex cells based on the Bienenstock, Cooper, and Munro (BCM) rule. We demonstrate that properties of receptive fields of complex cells can be learned using this biologically plausible learning rule. Quantitative comparisons between the model and experimental data are performed. Results show that model complex cells can account for the diversity of complex cells found in experimental studies. In summary, this study provides a plausible explanation for how complex cells can be learned using biologically plausible plasticity mechanisms. Our findings help us to better understand biological vision processing and provide us with insights into the general signal processing principles that the visual cortex employs to process visual information.

Internal Spatial Organization of Receptive Fields of Complex Cells in the Early Visual Cortex

2007 ◽  
Vol 98 (3) ◽  
pp. 1194-1212 ◽  
Author(s):  
Kota S. Sasaki ◽  
Izumi Ohzawa
Keyword(s):  
Visual Cortex ◽  
Minimal Model ◽  
Spatial Organization ◽  
Receptive Fields ◽  
Simple Cell ◽  
Complex Cell ◽  
Linear Filters ◽  
Simple Cells ◽  
Complex Cells ◽  
Early Visual Cortex

The receptive fields of complex cells in the early visual cortex are economically modeled by combining outputs of a quadrature pair of linear filters. For actual complex cells, such a minimal model may be insufficient because many more simple cells are thought to make up a complex cell receptive field. To examine the minimalist model physiologically, we analyzed spatial relationships between the internal structure (subunits) and the overall receptive fields of individual complex cells by a two-stimulus interaction technique. The receptive fields of complex cells are more circular and only slightly larger than their subunits in size. In addition, complex cell subunits occupy spatial extents similar to those of simple cell receptive fields. Therefore in these respects, the minimalist schema is a fair approximation to actual complex cells. However, there are violations against the minimal model. Simple cell receptive fields have significantly fewer subregions than complex cell subunits and, in general, simple cell receptive fields are elongated more horizontally than vertically. This bias is absent in complex cell subunits and receptive fields. Thus simple cells cannot be equated to individual complex cell subunits and spatial pooling of simple cells may occur anisotropically to constitute a complex cell subunit. Moreover, when linear filters for complex cell subunits are examined separately for bright and dark responses, there are significant imbalances and position displacements between them. This suggests that actual complex cell receptive fields are constructed by a richer combination of linear filters than proposed by the minimalist model.

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