Morphodynamical enaction: the case of color.
Explore the source record for details and available documents.
Cognition↗
Biomedical subjects
Jean Petitot
Publications and source records attributed to Jean Petitot.
An introduction to the Mumford-Shah segmentation model.
Some papers of this special issue concern recent results on mathematical models of segmentation. As they are rather technical we propose here a pedagogical introduction for the non-mathematical reader. We briefly present the variational model of image segmentation proposed by David Mumford and we summarize some fundamental results of De Giorgi's school.
Animals↗
The neurogeometry of pinwheels as a sub-Riemannian contact structure.
We present a geometrical model of the functional architecture of the primary visual cortex (V1) and, more precisely, of its pinwheel structure. The problem is to understand from within how the internal "imminent" geometry of the visual cortex can produce the "transcendent" geometry of the external space. We use first the concept of blowing up to model V1 as a discrete approximation of a continuous fibration pi: R x P --> P with base space the space of the retina R and fiber the projective line P of the orientations of the plane. The core of the paper consists first in showing that the horizontal cortico-cortical connections of V1 implement what the geometers call the contact structure of the fibration pi, and secondly in introducing an integrability condition and the integral curves associated with it. The paper develops then three applications: (i) to Field's, Hayes', and Hess' psychophysical concept of association field, (ii) to a variational model of curved modal illusory contours (in the spirit of previous models due to Ullman, Horn, and Mumford), (iii) to Ermentrout's, Cowan's, Bressloff's, Golubitsky's models of visual hallucinations.
Animals↗
Dynamical systems and cognitive linguistics: toward an active morphodynamical semantics.
We propose a novel dynamical system approach to cognitive linguistics based on cellular automata and spiking neural networks. How can the same relationship 'in' apply to containers as different as 'box', 'tree' or 'bowl'? Our objective is to categorize the infinite diversity of schematic visual scenes into a small set of grammatical elements and elucidate the topology of language. Gestalt-inspired semantic studies have shown that spatial prepositions such as 'in' or 'above' are neutral toward the shape and size of objects. We suggest that this invariance can be explained by introducing morphodynamical transforms, which erase image details and create virtual structures or singularities (boundaries, skeleton), and call this paradigm 'active semantics'. Singularities arise from a large-scale lattice of coupled excitable units exhibiting spatiotemporal pattern formation, in particular traveling waves. This work addresses the crucial cognitive mechanisms of spatial schematization and categorization at the interface between vision and language and anchors them to expansion processes such as activity diffusion or wave propagation.
Algorithms↗