no code implementations • 11 Feb 2024 • Minglang Yin, Nicolas Charon, Ryan Brody, Lu Lu, Natalia Trayanova, Mauro Maggioni

DIMON is based on transporting a given problem (initial/boundary conditions and domain $\Omega_{\theta}$) to a problem on a reference domain $\Omega_{0}$, where training data from multiple problems is used to learn the map to the solution on $\Omega_{0}$, which is then re-mapped to the original domain $\Omega_{\theta}$.

no code implementations • 7 Nov 2023 • Emmanuel Hartman, Emery Pierson, Martin Bauer, Mohamed Daoudi, Nicolas Charon

The use of such bases allows to simplify the representation of the corresponding shape space to a finite dimensional latent space.

no code implementations • ICCV 2023 • Emmanuel Hartman, Emery Pierson, Martin Bauer, Nicolas Charon, Mohamed Daoudi

We present Basis Restricted Elastic Shape Analysis (BaRe-ESA), a novel Riemannian framework for human body scan representation, interpolation and extrapolation.

no code implementations • 9 Nov 2022 • Ravi Shankar, Hsi-Wei Hsieh, Nicolas Charon, Archana Venkataraman

We term this new architecture a variational CycleGAN (VCGAN).

1 code implementation • 8 Apr 2022 • Emmanuel Hartman, Yashil Sukurdeep, Eric Klassen, Nicolas Charon, Martin Bauer

This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics.

1 code implementation • 13 Jan 2021 • Emmanuel Hartman, Yashil Sukurdeep, Nicolas Charon, Eric Klassen, Martin Bauer

Motivated by applications from computer vision to bioinformatics, the field of shape analysis deals with problems where one wants to analyze geometric objects, such as curves, while ignoring actions that preserve their shape, such as translations, rotations, or reparametrizations.

no code implementations • 25 Jul 2020 • Ravi Shankar, Hsi-Wei Hsieh, Nicolas Charon, Archana Venkataraman

Finally, the predictor uses the original spectrum and the modified F0 contour to generate a corresponding target spectrum.

1 code implementation • 20 Jun 2020 • Martin Bauer, Nicolas Charon, Philipp Harms, Hsi-Wei Hsieh

Square root normal fields (SRNF) considerably simplify the computation of certain elastic distances between parametrized surfaces.

no code implementations • 9 Jan 2020 • Yashil Sukurdeep, Martin Bauer, Nicolas Charon

This paper introduces a new mathematical formulation and numerical approach for the computation of distances and geodesics between immersed planar curves.

2 code implementations • 27 Mar 2019 • Hsi-Wei Hsieh, Nicolas Charon

We study in detail the construction of kernel metrics on varifold spaces and the resulting topological properties of those metrics, then propose a mathematical model for diffeomorphic registration of varifolds under a specific group action which we formulate in the framework of optimal control theory.

Optimization and Control

no code implementations • 15 Jul 2018 • Evan Schwab, Benjamin D. Haeffele, René Vidal, Nicolas Charon

In the classical setting, signals are represented as vectors and the dictionary learning problem is posed as a matrix factorization problem where the data matrix is approximately factorized into a dictionary matrix and a sparse matrix of coefficients.

1 code implementation • 29 Jan 2018 • Hsi-Wei Hsieh, Nicolas Charon

This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors.

Optimization and Control Classical Analysis and ODEs 49M25, 49Q20, 49J15

no code implementations • 21 Jul 2017 • Evan Schwab, René Vidal, Nicolas Charon

Advanced diffusion magnetic resonance imaging (dMRI) techniques, like diffusion spectrum imaging (DSI) and high angular resolution diffusion imaging (HARDI), remain underutilized compared to diffusion tensor imaging because the scan times needed to produce accurate estimations of fiber orientation are significantly longer.

no code implementations • CVPR 2017 • Irene Kaltenmark, Benjamin Charlier, Nicolas Charon

This paper introduces a general setting for the construction of data fidelity metrics between oriented or non-oriented geometric shapes like curves, curve sets or surfaces.

no code implementations • 18 Dec 2016 • Evan Schwab, René Vidal, Nicolas Charon

High angular resolution diffusion imaging (HARDI) can produce better estimates of fiber orientation than the popularly used diffusion tensor imaging, but the high number of samples needed to estimate diffusivity requires longer patient scan times.

no code implementations • 1 Dec 2016 • Kwame S. Kutten, Nicolas Charon, Michael I. Miller, J. T. Ratnanather, Jordan Matelsky, Alexander D. Baden, Kunal Lillaney, Karl Deisseroth, Li Ye, Joshua T. Vogelstein

Due to the novelty of this microscopy technique it is impractical to use absolute intensity values to align these images to existing standard atlases.

1 code implementation • 5 Aug 2016 • Nicolas Charon, Benjamin Charlier, Alain Trouvé

In this paper, we describe in detail a model of geometric-functional variability between fshapes.

Optimization and Control Differential Geometry 49M25, 49Q20, 58B32, 58E50, 68U05, 68U10

1 code implementation • 6 May 2016 • Kwame S. Kutten, Joshua T. Vogelstein, Nicolas Charon, Li Ye, Karl Deisseroth, Michael I. Miller

Therefore, we developed a method (Mask-LDDMM) for registering CLARITY images, that automatically find the brain boundary and learns the optimal deformation between the brain and atlas masks.

no code implementations • 24 Apr 2014 • Benjamin Charlier, Nicolas Charon, Alain Trouvé

This article introduces a full mathematical and numerical framework for treating functional shapes (or fshapes) following the landmarks of shape spaces and shape analysis.

no code implementations • 22 Apr 2013 • Nicolas Charon, Alain Trouvé

More specifically, problems occur with structures like acute pikes because of canceling effects of currents or with data that consists in many disconnected pieces like fiber bundles for which currents require a consistent orientation of all pieces.

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