Giovanna Citti

Learn More
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(More)
We consider the following nonlinear degenerate parabolic equation which arises in some recent problems of mathematical finance: ∂xxu+ u∂yu− ∂tu = f. Using a harmonic analysis technique on Lie groups, we prove that, if the solution u satisfies condition ∂xu 6= 0 in an open set Ω ⊂ R and f ∈ C∞(Ω), then u ∈ C∞(Ω).
Abstract. The functionality of the visual cortex has been described in [63] and in [50] as a contact manifold of dimension three and in [62] the Mumford and Shah functional has been proposed to segment lifting of an image in the three dimensional cortical space. Hence, we study here this functional and we provide a constructive approach to the problem,(More)
– We study the interior regularity properties of the solutions of a nonlinear degenerate equation arising in mathematical finance. We set the problem in the framework of Hörmander type operators without assuming any hypothesis on the degeneracy of the associated Lie algebra. We prove that the viscosity solutions are indeed classical solutions.  2001(More)
We present a model of the morphology of orientation maps in V1 based on the uncertainty principle of the SE(2) group. Starting from the symmetries of the cortex, suitable harmonic analysis instruments are used to obtain coherent states in the Fourier domain as minimizers of the uncertainty. Cortical activities related to orientation maps are then obtained(More)
In this paper we develop a geometrical model of functional architecture for the processing of spatio-temporal visual stimuli. The model arises from the properties of the receptive field linear dynamics of orientation and speed-selective cells in the visual cortex, that can be embedded in the definition of a geometry where the connectivity between points is(More)
We propose to model the functional architecture of the primary visual cortex V1 as a principal fiber bundle where the two-dimensional retinal plane is the base manifold and the secondary variables of orientation and scale constitute the vertical fibers over each point as a rotation–dilation group. The total space is endowed with a natural symplectic(More)