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Your search keyword '"Aujol, J.-F."' showing total 26 results
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26 results on '"Aujol, J.-F."'

1. Study of the behaviour of Nesterov Accelerated Gradient in a non convex setting: the strongly quasar convex case

Author

Hermant, J, Aujol, J. -F, Dossal, C, and Rondepierre, A

Subjects
Mathematics - Optimization and Control
Abstract

We study the convergence of Nesterov Accelerated Gradient (NAG) minimization algorithm applied to a class of non convex functions called strongly quasar convex functions, which can exhibit highly non convex behaviour. We show that in the case of strongly quasar convex functions, NAG can achieve an accelerated convergence speed at the cost of a lower curvature assumption. We provide a continuous analysis through high resolution ODEs, in which negative friction may appear. Finally, we investigate connections with a weaker class of non convex functions (smooth Polyak-\L ojasiewicz functions) by characterizing the gap between this class and the one of smooth strongly quasar convex functions.

Published
2024

2. Batch-less stochastic gradient descent for compressive learning of deep regularization for image denoising

Author

Shi, Hui, Traonmilin, Yann, and Aujol, J-F

Subjects
Computer Science - Machine Learning, Computer Science - Computer Vision and Pattern Recognition, Computer Science - Information Theory, Electrical Engineering and Systems Science - Image and Video Processing
Abstract

We consider the problem of denoising with the help of prior information taken from a database of clean signals or images. Denoising with variational methods is very efficient if a regularizer well adapted to the nature of the data is available. Thanks to the maximum a posteriori Bayesian framework, such regularizer can be systematically linked with the distribution of the data. With deep neural networks (DNN), complex distributions can be recovered from a large training database.To reduce the computational burden of this task, we adapt the compressive learning framework to the learning of regularizers parametrized by DNN. We propose two variants of stochastic gradient descent (SGD) for the recovery of deep regularization parameters from a heavily compressed database. These algorithms outperform the initially proposed method that was limited to low-dimensional signals, each iteration using information from the whole database. They also benefit from classical SGD convergence guarantees. Thanks to these improvements we show that this method can be applied for patch based image denoising.}

Published
2023

8. Automatic visibility estimation of a LiDAR point cloud

Author

Biasutti , Pierre, Aujol , J-F, Brédif , M, Bugeau , A, Laboratoire Bordelais de Recherche en Informatique ( LaBRI ), Centre National de la Recherche Scientifique ( CNRS ) -École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université Sciences et Technologies - Bordeaux 1-Université Bordeaux Segalen - Bordeaux 2, Institut de Mathématiques de Bordeaux ( IMB ), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux ( UB ) -Institut Polytechnique de Bordeaux ( Bordeaux INP ) -Centre National de la Recherche Scientifique ( CNRS ), Méthodes d'Analyses pour le Traitement d'Images et la Stéréorestitution ( MATIS ), and Institut National de l'Information Géographique et Forestière [IGN] ( IGN )

Subjects
[ INFO.INFO-CV ] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Physics::Atmospheric and Oceanic Physics
Abstract

This paper presents a novel methodology to estimate if a point of a LiDAR point cloud is visible from a given point of viewcorresponding to the optical center of a camera. Visibility estimation is essential in order to improve LiDAR and optical data fusion. The LiDAR point cloud is first projected on the image plane of the camera. Then, a criteron on the neighborhood of each point is used to automatically estimate which points are visible from the given point of view.

Published
2018

11. Texture synthesis guided by a low-resolution image

Author

El Gheche, Mireille, Berthoumieu, R, Gheche, M. El, Aujol, J.-F, Berthoumieu, Y., Deledalle, C.-A., Fablet, Ronan, Laboratoire de l'intégration, du matériau au système (IMS), Université Sciences et Technologies - Bordeaux 1-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Institut Polytechnique de Bordeaux-Université Sciences et Technologies - Bordeaux 1, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Lab-STICC_TB_CID_TOMS, Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC), École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)-École Nationale d'Ingénieurs de Brest (ENIB)-Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Télécom Bretagne-Institut Brestois du Numérique et des Mathématiques (IBNM), and Université de Brest (UBO)-Université européenne de Bretagne - European University of Brittany (UEB)-École Nationale Supérieure de Techniques Avancées Bretagne (ENSTA Bretagne)-Institut Mines-Télécom [Paris] (IMT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Texture compression, Optimization problem, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, 02 engineering and technology, Texture (geology), Image texture, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Texture filtering, Histogram, 0202 electrical engineering, electronic engineering, information engineering, Computer vision, Wasserstein distance, Proximal algorithms, Image resolution, ComputingMilieux_MISCELLANEOUS, Mathematics, business.industry, 020206 networking & telecommunications, Texture synthesis, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], Super resolution, Computer Science::Graphics, Nonconvex optimization, Random phase texture, 020201 artificial intelligence & image processing, Artificial intelligence, business, optimization, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing
Abstract

International audience; In this paper, we aim at synthesizing a texture from a high-resolution patch and a low-resolution image. To do so, we solve a nonconvex optimization problem that involves a statistical prior and a Fourier spectrum constraint. The numerical analysis shows that the proposed approach achieves better results (in terms of visual quality) than state-of-the-art methods tailored to super-resolution or texture synthesis.

Published
2016

14. New Approximation of a Scale Space Kernel on SE(3) and Applications in Neuroimaging

Author

Portegies, J.M., Sanguinetti, G.R., Meesters, S.P.L., Duits, R., Aujol, J.-F., Nikolova, M., Papadakis, N., Center for Analysis, Scientific Computing & Appl., Medical Image Analysis, Advanced School for Computing and Imaging, and Mathematical Image Analysis

Subjects
Logarithm, 010102 general mathematics, Probability density function, 02 engineering and technology, Rigid body, 01 natural sciences, Scale space, Kernel (image processing), Homogeneous space, 0202 electrical engineering, electronic engineering, information engineering, Linear scale, Applied mathematics, Initial value problem, 020201 artificial intelligence & image processing, 0101 mathematics, Mathematics
Abstract

We provide a new, analytic kernel for scale space filtering of dMRI data. The kernel is an approximation for the Green’s function of a hypo-elliptic diffusion on the 3D rigid body motion group SE(3), for fiber enhancement in dMRI. The enhancements are described by linear scale space PDEs in the coupled space of positions and orientations embedded in SE(3). As initial condition for the evolution we use either a Fiber Orientation Distribution (FOD) or an Orientation Density Function (ODF). Explicit formulas for the exact kernel do not exist. Although approximations well-suited for fast implementation have been proposed in literature, they lack important symmetries of the exact kernel. We introduce techniques to include these symmetries in approximations based on the logarithm on SE(3), resulting in an improved kernel. Regarding neuroimaging applications, we apply our enhancement kernel (a) to improve dMRI tractography results and (b) to quantify coherence of obtained streamline bundles. Keywords: Scale space on SE(3); Contextual enhancement; Left-invariant diffusion; Group convolution; Tractography

Published
2015

15. Data-driven sub-Riemannian geodesics in SE(2)

Author

Bekkers, E.J., Duits, R., Mashtakov, A., Sanguinetti, G.R., Aujol, J.-F., Nikolova, M., Papadakis, N., Medical Image Analysis, Center for Analysis, Scientific Computing & Appl., Advanced School for Computing and Imaging, and Mathematical Image Analysis

Subjects
Physics, Maximum principle, Geodesic, Group (mathematics), Image (category theory), Mathematical analysis, Metric tensor, Equidistant, Boundary value problem, Viscosity solution
Abstract

We present a new flexible wavefront propagation algorithm for the boundary value problem for sub-Riemannian (SR) geodesics in the roto-translation group SE(2)=R2¿S1 with a metric tensor depending on a smooth external cost C:SE(2)¿[d,1] , d>0 , computed from image data. The method consists of a first step where geodesically equidistant surfaces are computed as a viscosity solution of a Hamilton-Jacobi-Bellman (HJB) system derived via Pontryagin’s Maximum Principle (PMP). Subsequent backward integration, again relying on PMP, gives the SR-geodesics. We show that our method produces geodesically equidistant surfaces. For C=1 we show that our method produces the global minimizers, and comparison with exact solutions shows a remarkable accuracy of the SR-spheres/geodesics. Finally, trackings in synthetic and retinal images show the potential of including the SR-geometry. Keywords: Roto-translation group; Hamilton-Jacobi equations; Vessel tracking; Sub-riemannian geometry; Morphological scale spaces

Published
2015

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