35 research outputs found
A spatialized model of textures perception using structure tensor formalism
International audienceThe primary visual cortex (V1) can be partitioned into fundamental domains or hypercolumns consisting of one set of orientation columns arranged around a singularity or ''pinwheel'' in the orientation preference map. A recent study on the specific problem of visual textures perception suggested that textures may be represented at the population level in the cortex as a second-order tensor, the structure tensor, within a hypercolumn. In this paper, we present a mathematical analysis of such interacting hypercolumns that takes into account the functional geometry of local and lateral connections. The geometry of the hypercolumn is identified with that of the Poincaré disk \D. Using the symmetry properties of the connections, we investigate the spontaneous formation of cortical activity patterns. These states are characterized by tuned responses in the feature space, which are doubly-periodically distributed across the cortex
A spatialized model of textures perception using structure tensor formalism
International audienceThe primary visual cortex (V1) can be partitioned into fundamental domains or hypercolumns consisting of one set of orientation columns arranged around a singularity or ''pinwheel'' in the orientation preference map. A recent study on the specific problem of visual textures perception suggested that textures may be represented at the population level in the cortex as a second-order tensor, the structure tensor, within a hypercolumn. In this paper, we present a mathematical analysis of such interacting hypercolumns that takes into account the functional geometry of local and lateral connections. The geometry of the hypercolumn is identified with that of the Poincaré disk \D. Using the symmetry properties of the connections, we investigate the spontaneous formation of cortical activity patterns. These states are characterized by tuned responses in the feature space, which are doubly-periodically distributed across the cortex
The hyperbolic model for edge and texture detection in the primary visual cortex
International audienceThe modeling of neural fields in the visual cortex involves geometrical structures which describe in mathematical formalism the functional architecture of this cortical area. The case of contour detection and orientation tuning has been extensively studied and has become a paradigm for the mathematical analysis of image processing by the brain. Ten years ago an attempt was made to extend these models by replacing orientation (an angle) with a second-order tensor built from the gradient of the image intensity, and it was named the structure tensor. This assumption does not follow from biological observations (experimental evidence is still lacking) but from the idea that the effectiveness of texture processing with the structure tensor in computer vision may well be exploited by the brain itself. The drawback is that in this case the geometry is not Euclidean but hyperbolic instead, which complicates the analysis substantially. The purpose of this review is to present the methodology that was developed in a series of papers to investigate this quite unusual problem, specifically from the point of view of tuning and pattern formation. These methods, which rely on bifurcation theory with symmetry in the hyperbolic context, might be of interest for the modeling of other features such as color vision or other brain functions
Pattern formation for the Swift-Hohenberg equation on the hyperbolic plane
We present an overview of pattern formation analysis for an analogue of the
Swift-Hohenberg equation posed on the real hyperbolic space of dimension two,
which we identify with the Poincar\'e disc D. Different types of patterns are
considered: spatially periodic stationary solutions, radial solutions and
traveling waves, however there are significant differences in the results with
the Euclidean case. We apply equivariant bifurcation theory to the study of
spatially periodic solutions on a given lattice of D also called H-planforms in
reference with the "planforms" introduced for pattern formation in Euclidean
space. We consider in details the case of the regular octagonal lattice and
give a complete descriptions of all H-planforms bifurcating in this case. For
radial solutions (in geodesic polar coordinates), we present a result of
existence for stationary localized radial solutions, which we have adapted from
techniques on the Euclidean plane. Finally, we show that unlike the Euclidean
case, the Swift-Hohenberg equation in the hyperbolic plane undergoes a Hopf
bifurcation to traveling waves which are invariant along horocycles of D and
periodic in the "transverse" direction. We highlight our theoretical results
with a selection of numerical simulations.Comment: Dedicated to Klaus Kirchg\"assne
Proceedings of the 7th Sound and Music Computing Conference
Proceedings of the SMC2010 - 7th Sound and Music Computing Conference, July 21st - July 24th 2010
Proceedings of the 19th Sound and Music Computing Conference
Proceedings of the 19th Sound and Music Computing Conference - June 5-12, 2022 - Saint-Étienne (France).
https://smc22.grame.f
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Words Matter: The Work of Lawrence Weiner
This dissertation explores the practice of contemporary artist Lawrence Weiner. From 1968 onwards, Weiner has presented his work using language and, as such, the artist is historically regarded as one of the pioneering practitioners of Conceptual art. The artist himself categorically refuses that designation, preferring to focus on the material aspects of his work. Nevertheless, his oeuvre has been largely received in terms of a predominantly linguistic intervention. Craig Dworkin encapsulates this position, when in discussing the Conceptual wager of Weiner's statements he writes: "Having tested the propositions that the art object might be nominal, linguistic, invisible, and on a par with its abstract initial description, the next step was to venture that it could be dispensed with altogether." By focusing equally on the linguistic and material aspects of Weiner's practice, this dissertation argues, conversely, that Weiner's work is primarily an object strategy, and not a dematerialized linguistic presentation. The first part of this discussion deals with Weiner's ground-breaking work from the mid 1960s to the early 1970s, analyzing the full implications of Weiner's extraordinary decision to present materials through language. Close comparisons are drawn with the profoundly materialist practices of contemporary artists such as Robert Rauschenberg, Carl Andre, Richard Serra and Robert Smithson. Weiner's use of language is also distinguished from the text-based works of Conceptual artists Joseph Kosuth and Douglas Huebler, problematizing the degree to which Weiner's statements can stand as an exemplar of postmodern textuality, inasmuch as their referential content remains of primary consequence. Several chapters of the dissertation focus on drawings, and in particular the artist's notebooks, an aspect of Weiner's practice that has remained largely unstudied. Crucially, the notebooks present a model of thinking which is wholly corporeal as opposed to purely analytical. Furthermore, they raise the problem of the visual in relation to a body of work that has been credited with the suppression of a traditional (optical) aesthetic. In being conceived by the artist as "maps," Weiner's drawings also invite an analysis of spatial considerations, and are thus linked to the artist's own designation of his work, not as art in general, but specifically as sculpture. Finally, the notebooks, like Weiner's films, practically dissolve the categories of reality and fiction. Indeed, Weiner himself would insist that every presentation of his essentially "realist" work is nonetheless inherently "theatrical." One of the long-standing criticisms of Conceptual art was that while it made aspects of circulation and distribution part of the work - thereby testing the limits of institutional constraint and expanding art's potential to engage in collective reception - it failed to achieve truly democratic access, in large part by neglecting issues of desire. Thus, Conceptual art's promise of collective accessibility was purportedly foreclosed by an art whose theoretical propositions lacked a democratic content. In closely considering the generic content of Weiner's work, this dissertation develops a picture not only of the concrete relationship between word and thing, but of the ways in which Weiner uses signs (drawings, text, films) to "objectify" desire, demonstrating that his "sculptures" must be seen as both conceptual and sensual, fully immersed in politicized questions of imaginary and bodily experience