We present a PDE-based framework that generalizes Group equivariant Convolutional
Neural Networks (G-CNNs). In this framework, a network layer is seen as a set of PDE …

We reproduce suprathreshold perception phenomena, specifically visual illusions, by Wilson–
Cowan (WC)-type models of neuronal dynamics. Our findings show that the ability to …

We consider the evolution model proposed in Bertalmío (Front Comput Neurosci 8: 71,
2014), Bertalmío et al.(IEEE Trans Image Process 16 (4): 1058–1072, 2007) to describe …

Applications of geometric flows to multi-orientation image processing require the choice of
an (affine) connection on the Lie group G of roto-translations. Typical choices of such …

Two key ideas have greatly improved techniques for image enhancement and denoising:
the lifting of image data to multi-orientation distributions and the application of nonlinear …

The reconstruction mechanisms built by the human auditory system during sound
reconstruction are still a matter of debate. The purpose of this study is to propose a …

We consider Wilson-Cowan-type models for the mathematical description of orientation-
dependent Poggendorff-like illusions. Our modelling improves two previously proposed …

In a first part, I shall explore the consequences of distinguishing the foundations of meaning
and the foundations of truth in mathematical statements, or imagination and rigor as motors …

In the paper (Sarti et al. in Biol Cyb 98: 33–48, 2008), Jean Petitot together with the authors
of the present paper describe the functional geometry of the visual cortex as the …

Convolutional Neural Networks (CNNs) have been extensively researched and used in
recent years. Ever since LeCun et al. showed how successful CNNs can be on real world …