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

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Generalized Adaptors with Memory for Nonlinear Wave Digital Structures

The problem of modeling a nonlinear resistor in the Wave Digital domain can be seen as that of apply ing to its nonlinear characteristic the ane transforma tion that maps Khirchho variables into wave variables When dealing with nonlinear elements with memory such as nonlinear capacitors and inductors the above approach cannot be applied as ane transformations are memoryless. In this paper a new approach is proposed for modeling nonlinear elements with memory in the wave domain The method we propose denes a more general class of wave variables and adaptors with memory that un der some conditions can incorporate the memory of a nonlinear circuit and allow us to treat some nonlinear elements with memory as if they were instantaneous

Generalized Adaptors with Memory for Nonlinear Wave Digital Structures

The problem of modeling a nonlinear resistor in the Wave Digital domain can be seen as that of apply ing to its nonlinear characteristic the ane transforma tion that maps Khirchho variables into wave variables When dealing with nonlinear elements with memory such as nonlinear capacitors and inductors the above approach cannot be applied as ane transformations are memoryless. In this paper a new approach is proposed for modeling nonlinear elements with memory in the wave domain The method we propose denes a more general class of wave variables and adaptors with memory that un der some conditions can incorporate the memory of a nonlinear circuit and allow us to treat some nonlinear elements with memory as if they were instantaneous

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

Detection and identification of sparse audio tampering using distributed source coding and compressive sensing techniques

In most practical applications, for the sake of information integrity not only it is useful to detect whether a multimedia content has been modified or not, but also to identify which kind of attack has been carried out. In the case of audio streams, for example, it may be useful to localize the tamper in the time and/or frequency domain. In this paper we devise a hash-based tampering detection and localization system exploiting compressive sensing principles. The multimedia content provider produces a small hash signature using a limited number of random projections of a time-frequency representation of the original audio stream. At the content user side, the hash signature is used to estimate the distortion between the original and the received stream and, provided that the tamper is sufficiently sparse or sparsifiable in some orthonormal basis expansion or redundant dictionary (e.g. DCT or wavelet), to identify the time-frequency portion of the stream that has been manipulated. In order to keep the hash length small, the algorithm exploits distributed source coding techniques

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

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