Neuronal Oscillations in the Visual Cortex: $\Gamma$-Convergence to the Riemannian Mumford--Shah Functional

DOI10.1137/S0036141002398673zbMath1058.49010OpenAlexW2035159403WikidataQ115246839 ScholiaQ115246839MaRDI QIDQ4652451

Alessandro Sarti, Maria Manfredini, Giovanna Citti

Publication date: 28 February 2005

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0036141002398673

zbMATH Keywords

variational problems\(\Gamma\)-convergenceGamma-convergenceMumford-Shah functionalRiemannian metricsneural oscillatorsCauchy problem for a difference equation

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Neural biology (92C20) Methods involving semicontinuity and convergence; relaxation (49J45) Difference operators (39A70)

Related Items (13)

Sub-Riemannian calculus on hypersurfaces in Carnot groups ⋮ A cortical based model of perceptual completion in the roto-translation space ⋮ Fundamental solutions for non-divergence form operators on stratified groups ⋮ From Functional Architectures to Percepts: A Neuromathematical Approach ⋮ Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2 ⋮ Compact embeddings, eigenvalue problems, and subelliptic Brezis-Nirenberg equations involving singularity on stratified Lie groups ⋮ Smooth approximation for intrinsic Lipschitz functions in the Heisenberg group ⋮ Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups ⋮ Potential analysis for a class of diffusion equations: a Gaussian bounds approach ⋮ Unnamed Item ⋮ Minimal surfaces in the roto-translation group with applications to a neuro-biological image completion model ⋮ Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups ⋮ IMPLICIT FUNCTION THEOREM IN CARNOT–CARATHÉODORY SPACES

This page was built for publication: Neuronal Oscillations in the Visual Cortex: $\Gamma$-Convergence to the Riemannian Mumford--Shah Functional