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Monochromaticity of orientation maps in v1 implies minimum variance for hypercolumn size.

Afgoustidis A - J Math Neurosci (2015)

Bottom Line: The repartition of preferred orientations of neurons in some areas is remarkable: a repetitive, non-periodic, layout.We discuss the relationship between the notion of column spacing and the structure of correlation spectra; we prove formulas for the mean value and variance of column spacing, and we use numerical analysis of exact analytic formulae to study the variance.The minimum variance property associated to thin spectra could be useful for information processing, provide optimal modularity for V1 hypercolumns, and be a first step toward a mathematical definition of hypercolumns.

View Article: PubMed Central - PubMed

Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris 7 Denis Diderot, 75013 Paris, France.

ABSTRACT
In the primary visual cortex of many mammals, the processing of sensory information involves recognizing stimuli orientations. The repartition of preferred orientations of neurons in some areas is remarkable: a repetitive, non-periodic, layout. This repetitive pattern is understood to be fundamental for basic non-local aspects of vision, like the perception of contours, but important questions remain about its development and function. We focus here on Gaussian Random Fields, which provide a good description of the initial stage of orientation map development and, in spite of shortcomings we will recall, a computable framework for discussing general principles underlying the geometry of mature maps. We discuss the relationship between the notion of column spacing and the structure of correlation spectra; we prove formulas for the mean value and variance of column spacing, and we use numerical analysis of exact analytic formulae to study the variance. Referring to studies by Wolf, Geisel, Kaschube, Schnabel, and coworkers, we also show that spectral thinness is not an essential ingredient to obtain a pinwheel density of π, whereas it appears as a signature of Euclidean symmetry. The minimum variance property associated to thin spectra could be useful for information processing, provide optimal modularity for V1 hypercolumns, and be a first step toward a mathematical definition of hypercolumns. A measurement of this property in real maps is in principle possible, and comparison with the results in our paper could help establish the role of our minimum variance hypothesis in the development process.

No MeSH data available.


Related in: MedlinePlus

Layout of orientation preferences in the visual cortex of a tree shrew (modified from Bosking et al. [10]). Here orientation preference is color-coded (for instance neurons in blue regions are more sensitive to vertical stimuli). Maps of sensitivity to different stimulus angles were obtained by optical imaging; summing these with appropriate complex phases yields Fig. 1: see Swindale [11]. In particular, at singular points (pinwheels), all orientations meet (see the upper right corner); for a fine-scale experimental study of the neighbourhood of such points, see [8]
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Fig1: Layout of orientation preferences in the visual cortex of a tree shrew (modified from Bosking et al. [10]). Here orientation preference is color-coded (for instance neurons in blue regions are more sensitive to vertical stimuli). Maps of sensitivity to different stimulus angles were obtained by optical imaging; summing these with appropriate complex phases yields Fig. 1: see Swindale [11]. In particular, at singular points (pinwheels), all orientations meet (see the upper right corner); for a fine-scale experimental study of the neighbourhood of such points, see [8]

Mentions: Neurons in the primary visual cortex (V1, V2) of mammals have stronger responses to stimuli that have a specific orientation [1–3]. In many species including primates and carnivores (but no rodent, even though some of them have rather elaborated vision [4, 5]), these orientation preferences are arranged in an ordered map along the cortical surface. Moving orthogonally to the cortical surface, one meets neurons with the same orientation preference; traveling along the cortical surface, however, reveals a striking arrangement in smooth, quasi-periodic maps, with singular points known as pinwheels where all orientations are present [6–8]; see Fig. 1. All these orientation maps look similar, even in distantly related species [5, 9]; the main difference between any two orientation preference maps (OPM) seems to be a matter of global scaling. Fig. 1


Monochromaticity of orientation maps in v1 implies minimum variance for hypercolumn size.

Afgoustidis A - J Math Neurosci (2015)

Layout of orientation preferences in the visual cortex of a tree shrew (modified from Bosking et al. [10]). Here orientation preference is color-coded (for instance neurons in blue regions are more sensitive to vertical stimuli). Maps of sensitivity to different stimulus angles were obtained by optical imaging; summing these with appropriate complex phases yields Fig. 1: see Swindale [11]. In particular, at singular points (pinwheels), all orientations meet (see the upper right corner); for a fine-scale experimental study of the neighbourhood of such points, see [8]
© Copyright Policy - OpenAccess
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4388110&req=5

Fig1: Layout of orientation preferences in the visual cortex of a tree shrew (modified from Bosking et al. [10]). Here orientation preference is color-coded (for instance neurons in blue regions are more sensitive to vertical stimuli). Maps of sensitivity to different stimulus angles were obtained by optical imaging; summing these with appropriate complex phases yields Fig. 1: see Swindale [11]. In particular, at singular points (pinwheels), all orientations meet (see the upper right corner); for a fine-scale experimental study of the neighbourhood of such points, see [8]
Mentions: Neurons in the primary visual cortex (V1, V2) of mammals have stronger responses to stimuli that have a specific orientation [1–3]. In many species including primates and carnivores (but no rodent, even though some of them have rather elaborated vision [4, 5]), these orientation preferences are arranged in an ordered map along the cortical surface. Moving orthogonally to the cortical surface, one meets neurons with the same orientation preference; traveling along the cortical surface, however, reveals a striking arrangement in smooth, quasi-periodic maps, with singular points known as pinwheels where all orientations are present [6–8]; see Fig. 1. All these orientation maps look similar, even in distantly related species [5, 9]; the main difference between any two orientation preference maps (OPM) seems to be a matter of global scaling. Fig. 1

Bottom Line: The repartition of preferred orientations of neurons in some areas is remarkable: a repetitive, non-periodic, layout.We discuss the relationship between the notion of column spacing and the structure of correlation spectra; we prove formulas for the mean value and variance of column spacing, and we use numerical analysis of exact analytic formulae to study the variance.The minimum variance property associated to thin spectra could be useful for information processing, provide optimal modularity for V1 hypercolumns, and be a first step toward a mathematical definition of hypercolumns.

View Article: PubMed Central - PubMed

Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris 7 Denis Diderot, 75013 Paris, France.

ABSTRACT
In the primary visual cortex of many mammals, the processing of sensory information involves recognizing stimuli orientations. The repartition of preferred orientations of neurons in some areas is remarkable: a repetitive, non-periodic, layout. This repetitive pattern is understood to be fundamental for basic non-local aspects of vision, like the perception of contours, but important questions remain about its development and function. We focus here on Gaussian Random Fields, which provide a good description of the initial stage of orientation map development and, in spite of shortcomings we will recall, a computable framework for discussing general principles underlying the geometry of mature maps. We discuss the relationship between the notion of column spacing and the structure of correlation spectra; we prove formulas for the mean value and variance of column spacing, and we use numerical analysis of exact analytic formulae to study the variance. Referring to studies by Wolf, Geisel, Kaschube, Schnabel, and coworkers, we also show that spectral thinness is not an essential ingredient to obtain a pinwheel density of π, whereas it appears as a signature of Euclidean symmetry. The minimum variance property associated to thin spectra could be useful for information processing, provide optimal modularity for V1 hypercolumns, and be a first step toward a mathematical definition of hypercolumns. A measurement of this property in real maps is in principle possible, and comparison with the results in our paper could help establish the role of our minimum variance hypothesis in the development process.

No MeSH data available.


Related in: MedlinePlus