, Top: The original 64 × 64 image (left) and the noisy version (right), Figure, vol.6
Reproducing kernel Hilbert spaces of CR functions for the Euclidean motion group, Analysis and Applications, vol.13, issue.03, pp.331-346, 2015. ,
A cortical-inspired geometry for contour perception and motion integration, Journal of Mathematical Imaging and Vision, vol.49, issue.3, pp.511-529, 2014. ,
Coherent states of the Euclidean group and activation regions of primary visual cortex, 2011. ,
An uncertainty principle underlying the functional architecture of V1, Journal of Physiology-Paris, vol.106, issue.5, pp.183-193, 2012. ,
Uniqueness of viscosity mean curvature flow solution in two sub-riemannian structures, SIAM Journal on Mathematical Analysis, vol.51, issue.3, pp.2633-2659, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02319482
A geometric model of multi-scale orientation preference maps via Gabor functions, Journal of Mathematical Imaging and Vision, vol.60, issue.6, pp.900-912, 2018. ,
Roto-translation covariant convolutional networks for medical image analysis, International Conference on Medical Image Computing and Computer-Assisted Intervention, pp.440-448, 2018. ,
On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images, The Journal of Physiology, vol.203, issue.1, p.237, 1969. ,
The functional geometry of local and horizontal connections in a model of V1, Journal of Physiology-Paris, vol.97, issue.2, pp.221-236, 2003. ,
Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex, Philosophical Transactions of the Royal Society B: Biological Sciences, vol.356, pp.299-330, 1407. ,
Myocardial deformation from local frequency estimation in tagging MRI, International Conference on Functional Imaging and Modeling of the Heart, pp.284-291, 2013. ,
Über systeme von linearen partiellen differential-gleichungen erster ordnung, The Collected Papers Of Wei-Liang Chow, pp.47-54, 2002. ,
A cortical based model of perceptual completion in the roto-translation space, Journal of Mathematical Imaging and Vision, vol.24, issue.3, pp.307-326, 2006. ,
Neuromathematics of Vision, 2014. ,
Cortical spatiotemporal dimensionality reduction for visual grouping, Neural Computation, 2015. ,
Spatiotemporal receptive fields of cells in V1 are optimally shaped for stimulus velocity estimation, JOSA A, vol.29, issue.1, pp.130-138, 2012. ,
Numerical schemes for linear and non-linear enhancement of DW-MRI, International Conference on Scale Space and Variational Methods in Computer Vision, pp.14-25, 2011. ,
Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters, JOSA A, vol.2, issue.7, pp.1160-1169, 1985. ,
Spatial-frequency-specific inhibition in cat striate cortex cells, The Journal of Physiology, vol.336, issue.1, pp.359-376, 1983. ,
Spatiotemporal organization of simple-cell receptive fields in the cat's striate cortex. i. general characteristics and postnatal development, Journal of neurophysiology, vol.69, issue.4, pp.1091-1117, 1993. ,
Perceptual organization in image analysis: a mathematical approach based on scale, orientation and curvature, vol.68, 2005. ,
Line enhancement and completion via linear left invariant scale spaces on SE(2), International Conference on Scale Space and Variational Methods in Computer Vision, pp.795-807, 2009. ,
Left-invariant parabolic evolutions on se (2) and contour enhancement via invertible orientation scores part ii: Nonlinear left-invariant diffusions on invertible orientation scores, Quarterly of Applied Mathematics, pp.293-331, 2010. ,
Left-invariant parabolic evolutions on SE(2) and contour enhancement via invertible orientation scores part i: Linear leftinvariant diffusion equations on SE(2), Quarterly of Applied Mathematics, pp.255-292, 2010. ,
Evolution equations on Gabor transforms and their applications, Applied and Computational Harmonic Analysis, vol.35, issue.3, pp.483-526, 2013. ,
Three-dimensional computer vision: a geometric viewpoint, 1993. ,
Contour integration by the human visual system: evidence for a local "association field, Vision Research, vol.33, issue.2, pp.173-193, 1993. ,
, Image structure. Series in Mathematical Imaging and Vision, 1997.
A neuromathematical model for geometrical optical illusions, Journal of Mathematical Imaging and Vision, vol.60, issue.1, pp.94-108, 2018. ,
Crossing-preserving coherence-enhancing diffusion on invertible orientation scores, International Journal of Computer Vision, vol.85, issue.3, p.253, 2009. ,
Nonlinear diffusion on the 2D Euclidean motion group. Scale Space and Variational Methods in Computer Vision pp, pp.461-472, 2007. ,
Enhancement of crossing elongated structures in images, 2008. ,
Front-end vision and multi-scale image analysis multi-scale computer vision theory and applications, Mathematica, 2003. ,
Multi-scale and multi-orientation medical image analysis, Biomedical Image Processing, pp.177-196, 2010. ,
Crossing-preserving multi-scale vesselness, International Conference on Medical Image Computing and Computer-Assisted Intervention, pp.603-610, 2014. ,
Higher visual perception as prolongation of the basic Lie transformation group, Mathematical Biosciences, vol.6, pp.437-471, 1970. ,
The visual cortex is a contact bundle, Applied Mathematics and Computation, vol.32, issue.2-3, pp.137-167, 1989. ,
Hypoelliptic second order differential equations, Acta Mathematica, vol.119, issue.1, pp.147-171, 1967. ,
Shape and arrangement of columns in cat's striate cortex, The Journal of Physiology, vol.165, issue.3, pp.559-568, 1963. ,
Receptive fields of single neurons in the cat's striate cortex, The Journal of Physiology, vol.148, issue.3, pp.574-591, 1959. ,
Receptive fields, binocular interaction and functional architecture in the cat's visual cortex, The Journal of Physiology, vol.160, pp.106-154, 1962. ,
Uniformity of monkey striate cortex: a parallel relationship between field size, scatter, and magnification factor, Journal of Comparative Neurology, vol.158, issue.3, pp.295-305, 1974. ,
Ferrier lecture: Functional architecture of macaque monkey visual cortex, Proceedings of the Royal Society of London B: Biological Sciences, vol.198, pp.1-59, 1130. ,
Spatial relationships among three columnar systems in cat area 17, The Journal of Neuroscience, vol.17, issue.23, pp.9270-9284, 1997. ,
Models and measurements of functional maps in V1, Journal of Neurophysiology, vol.99, issue.6, pp.2745-2754, 2008. ,
Spatial frequency maps in cat visual cortex, The Journal of Neuroscience, vol.20, issue.22, pp.8504-8514, 2000. ,
An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex, Journal of Neurophysiology, vol.58, issue.6, pp.1233-1258, 1987. ,
Direct myocardial strain assessment from frequency estimation in tagging MRI, International Workshop on Statistical Atlases and Computational Models of the Heart, pp.212-219, 2013. ,
Images as embedded maps and minimal surfaces: movies, color, texture, and volumetric medical images, International Journal of Computer Vision, vol.39, issue.2, pp.111-129, 2000. ,
On the geometry of texture, 2000. ,
The structure of images, Biological Cybernetics, vol.50, issue.5, pp.363-370, 1984. ,
Representation of local geometry in the visual system, Biological Cybernetics, vol.55, issue.6, pp.367-375, 1987. ,
Principles of Gestalt psychology, 2013. ,
Gestalt psychology: An introduction to new concepts in modern psychology, 1970. ,
Computational models of visual processing, 1991. ,
Ocular dominance columns and their development in layer iv of the cat's visual cortex: a quantitative study, Journal of Comparative Neurology, vol.179, issue.1, pp.223-244, 1978. ,
Spatio-temporal interactions and the spatial phase preferences of visual neurons, Experimental Brain Research, vol.80, issue.2, pp.441-445, 1990. ,
Scale-space theory: A basic tool for analyzing structures at different scales, Journal of Applied Statistics, vol.21, issue.1-2, pp.225-270, 1994. ,
Feature detection with automatic scale selection, International Journal of Computer Vision, vol.30, issue.2, pp.79-116, 1998. ,
Generalized Gaussian scale-space axiomatics comprising linear scale-space, affine scale-space and spatio-temporal scale-space, Journal of Mathematical Imaging and Vision, vol.40, issue.1, pp.36-81, 2011. ,
A computational theory of visual receptive fields, Biological Cybernetics, vol.107, issue.6, pp.589-635, 2013. ,
Spatial frequency rows in the striate visual cortex, Vision Research, vol.17, issue.2, pp.257-264, 1977. ,
Mathematical description of the responses of simple cortical cells, JOSA, vol.70, issue.11, pp.1297-1300, 1980. ,
Detection and discrimination of relative spatial phase by V1 neurons, Journal of Neuroscience, vol.22, issue.14, pp.6129-6157, 2002. ,
The neurogeometry of pinwheels as a sub-Riemannian contact structure, Journal of Physiology-Paris, vol.97, issue.2, pp.265-309, 2003. ,
Neurogéométrie de la vision, Modeles mathématiques et physiques des architectures fonctionelles. Paris:Éd.École Polytech, 2008. ,
, Vers une neurogéométrie. fibrations corticales, structures de contact et contours subjectifs modaux. Mathématiques informatique et sciences humaines, pp.5-102, 1999.
Contributionà l'étude de la représentation d'une fonction arbitraire par des intégrales définies. Rendiconti del Circolo Matematico di Palermo (1884-1940), vol.30, pp.289-335, 1910. ,
Responses of simple and complex cells to compound sine-wave gratings, Vision Research, vol.28, issue.1, pp.25-39, 1988. ,
Image processing in the semidiscrete group of rototranslations, International Conference on Geometric Science of Information, pp.627-634, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01721740
Organization and origin of spatial frequency maps in cat visual cortex, The Journal of Neuroscience, vol.33, issue.33, pp.326-339, 2013. ,
Pinwheel-dipole configuration in cat early visual cortex, NeuroImage, vol.128, pp.63-73, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01253408
A model of natural image edge cooccurrence in the rototranslation group, Journal of Vision, vol.10, issue.14, pp.37-37, 2010. ,
The symplectic structure of the primary visual cortex, Biological Cybernetics, vol.98, issue.1, pp.33-48, 2008. ,
Functional geometry of the horizontal connectivity in the primary visual cortex, Journal of Physiology-Paris, vol.103, issue.1, pp.37-45, 2009. ,
Left-invariant evolutions of wavelet transforms on the similitude group, Applied and Computational Harmonic Analysis, vol.39, issue.1, pp.110-137, 2015. ,
Ocular dominance in layer iv of the cat's visual cortex and the effects of monocular deprivation, The Journal of Physiology, vol.281, issue.1, pp.267-283, 1978. ,
The organization of orientation and spatial frequency in primary visual cortex, Proceedings of the National Academy of Sciences, vol.101, issue.48, pp.941-957, 2004. ,
Parallel development of orientation maps and spatial frequency selectivity in cat visual cortex, European Journal of Neuroscience, vol.35, issue.1, pp.44-55, 2012. ,
Splines: A perfect fit for signal and image processing, IEEE Signal Processing Magazine, vol.16, issue.6, pp.22-38, 1999. ,
Laws of organization in perceptual forms, 1938. ,
The Gaussian derivative model for spatial vision: I. Retinal mechanisms, Spatial Vision, vol.2, issue.4, pp.273-293, 1987. ,
Robust retinal vessel segmentation via locally adaptive derivative frames in orientation scores, IEEE Transactions on Medical Imaging, vol.35, issue.12, pp.2631-2644, 2016. ,