A cortical based model of perceptual completion in the roto-translation space

We present a mathematical model of perceptual completion and formation of subjective surfaces, which is at the same time inspired by the architecture of the visual cortex, and is the lifting in the 3-dimensional rototranslation group of the phenomenological variational models based on elastica functional. The initial image is lifted by the simple cells to a surface in the rototraslation group and the completion process is modelled via a diffusion driven motion by curvature. The convergence of the motion to a minimal surface is proved. Results are presented both for modal and amodal completion in classic Kanizsa images

Neurogeometry of Perception: Isotropic and Anisotropic Aspects

In this paper we first recall geometrical models of neurogeometical in Lie groups and we show that geometrical properties of horizontal cortical connectivity can be considered as a neural correlate of a geometry of the visual plane. Then we introduce a new model of non isotropic cortical connectivity modeled on statistics of images. In this way we are able to justify oblique phenomena comparable with experimental findings

A model of natural image edge co-occurrence in the rototranslation group

n/

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

Geometrical optical illusion via sub-Riemannian geodesics in the roto-translation group

We present a neuro-mathematical model for geometrical optical illusions (GOIs), a class of illusory phenomena that consists in a mismatch of geometrical properties of the visual stimulus and its associated percept. They take place in the visual areas V1/V2 whose functional architecture have been modeled in previous works by Citti and Sarti as a Lie group equipped with a sub-Riemannian (SR) metric. Here we extend their model proposing that the metric responsible for the cortical connectivity is modulated by the modeled neuro-physiological response of simple cells to the visual stimulus, hence providing a more biologically plausible model that takes into account a presence of visual stimulus. Illusory contours in our model are described as geodesics in the new metric. The model is confirmed by numerical simulations, where we compute the geodesics via SR-Fast Marching

Basic properties of nonsmooth Hormander's vector fields and Poincare's inequality

We consider a family of vector fields defined in some bounded domain of R^p, and we assume that they satisfy Hormander's rank condition of some step r, and that their coefficients have r-1 continuous derivatives. We extend to this nonsmooth context some results which are well-known for smooth Hormander's vector fields, namely: some basic properties of the distance induced by the vector fields, the doubling condition, Chow's connectivity theorem, and, under the stronger assumption that the coefficients belong to C^{r-1,1}, Poincare's inequality. By known results, these facts also imply a Sobolev embedding. All these tools allow to draw some consequences about second order differential operators modeled on these nonsmooth Hormander's vector fields.Comment: 60 pages, LaTeX; Section 6 added and Section 7 (6 in the previous version) changed. Some references adde

Levi umbilical surfaces in complex space

We define a complex connection on a real hypersurface of \C^{n+1} which is naturally inherited from the ambient space. Using a system of Codazzi-type equations, we classify connected real hypersurfaces in \C^{n+1}, $n\ge 2$, which are Levi umbilical and have non zero constant Levi curvature. It turns out that such surfaces are contained either in a sphere or in the boundary of a complex tube domain with spherical section.Comment: 18 page

Submanifolds of Fixed Degree in Graded Manifolds for Perceptual Completion

We extend to a Engel type structure a cortically inspired model of perceptual completion initially proposed in the Lie group of positions and orientations with a sub-Riemannian metric. According to this model, a given image is lifted in the group and completed by a minimal surface. The main obstacle in extending the model to a higher dimensional group, which can code also curvatures, is the lack of a good definition of codimension 2 minimal surface. We present here this notion, and describe an application to image completion

Kratom: The analytical challenge of an emerging herbal drug

Mitragyna speciosa or kratom is emerging worldwide as a “legal” herbal drug of abuse. An increasing number of papers is appearing in the scientific literature regarding its pharmacological profile and the analysis of its chemical constituents, mainly represented by alkaloids. However, its detection and identification are not straightforward as the plant material is not particularly distinctive. Hyphenated techniques are generally preferred for the identification and quantification of these compounds, especially the main purported psychoactive substances, mitragynine (MG) and 7-hydroxymitragynine (7-OH-MG), in raw and commercial products. Considering the vast popularity of this recreational drug and the growing concern about its safety, the analysis of alkaloids in biological specimens is also of great importance for forensic and toxicological laboratories. The review addresses the analytical aspects of kratom spanning the extraction techniques used to isolate the alkaloids, the qualitative and quantitative analytical methods and the strategies for the distinction of the naturally occurring isomers