A Cortical Based Model of Perceptual Completion in the Roto-Translation Space

By Giovanna Citti, Alessandro Sarti. Journal of Mathematical Imaging and Vision, 2006

381 citations recorded by the source corpus.

Subfields: Biophysics, Cognitive Neuroscience, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/7a14c3643e7671835592e298664bda8ee6c0e9d1

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Citations in the corpus

Sub-Riemannian vs. Euclidean dimension comparison and fractal geometry on Carnot groups (2009, background): “Recently, the rototranslation group (a sub-Riemannian manifold locally modelled on the Heisenberg group) has emerged as a mathematical model for the neurogeometry of the first layer of the mammalian visual cortex [16].”
Differentiability of Intrinsic Lipschitz Functions within Heisenberg Groups (2011, neutral): “, [8, 9, 12]).”
An introduction to continuous optimization for imaging (2016, methodology): “The idea is based on work by Citti and Sarti (2006), who proposed representing images in the so-called roto-translation space in order to perform amodal completion.”
Schauder estimates for parabolic nondivergence operators of Hörmander type (2007, background): “These classes of operators naturally arise in some problems related to geometry in several complex variables (see [27] and references therein) as well as in some models of human vision (see [14] and references therein); moreover, these operators realize a framework where a suitable theory of nonline”
Rigid-Motion Scattering for Texture Classification (2014, background): “Taking into account the joint structure of the rigid-motion group of rotations and translations in 2 was proposed by several researchers (Citti & Sarti, 2006; Duits & Burgeth, 2007; Boscain et al., 2013), to preserve image structures in applications such as noise removal or image enhancement with…”
The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups (2008, background): “It was recognized in [8, 27] that the visual cortex V1 solves a nonisotropic diffusion problem on the group SE(2) while reconstructing a partially hidden or corrupted image.”
Sub-Riemannian calculus on hypersurfaces in Carnot groups (2006, result): “[CMS1] G. Citti, and M. Manfredini & A. Sarti, From neural oscillations to variational problems in the visual cortex, Journal of Physiology-Paris, 97 (2003), 379-385.”
B-Spline CNNs on Lie Groups (2019, positive): “These findings are mathematically modeled by sub-Riemannian geometry on Lie groups (Petitot, 2003; Citti & Sarti, 2006; Duits et al., 2014) and led to effective algorithms in image analysis (Franken & Duits, 2009; Bekkers et al., 2015b; Favali et al., 2016; Duits et al., 2018; Baspinar, 2018).”