Search Results for author: Nicolas Charon

Found 20 papers, 7 papers with code

DIMON: Learning Solution Operators of Partial Differential Equations on a Diffeomorphic Family of Domains

no code implementations11 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 $\Omega_{\theta}$.

Operator learning

Basis restricted elastic shape analysis on the space of unregistered surfaces

no code implementations7 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.


BaRe-ESA: A Riemannian Framework for Unregistered Human Body Shapes

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.

Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework

1 code implementation8 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.

Supervised deep learning of elastic SRV distances on the shape space of curves

1 code implementation13 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.

Multi-speaker Emotion Conversion via Latent Variable Regularization and a Chained Encoder-Decoder-Predictor Network

no code implementations25 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.


A numerical framework for elastic surface matching, comparison, and interpolation

1 code implementation20 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.

An inexact matching approach for the comparison of plane curves with general elastic metrics

no code implementations9 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.

Metrics, quantization and registration in varifold spaces

2 code implementations27 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

Global Optimality in Separable Dictionary Learning with Applications to the Analysis of Diffusion MRI

no code implementations15 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.

Denoising Dictionary Learning

Diffeomorphic registration of discrete geometric distributions

1 code implementation29 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

(k,q)-Compressed Sensing for dMRI with Joint Spatial-Angular Sparsity Prior

no code implementations21 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.

A General Framework for Curve and Surface Comparison and Registration With Oriented Varifolds

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.


Joint Spatial-Angular Sparse Coding for dMRI with Separable Dictionaries

no code implementations18 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.

Metamorphoses of functional shapes in Sobolev spaces

1 code implementation5 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

Deformably Registering and Annotating Whole CLARITY Brains to an Atlas via Masked LDDMM

1 code implementation6 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.

The fshape framework for the variability analysis of functional shapes

no code implementations24 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.

The varifold representation of non-oriented shapes for diffeomorphic registration

no code implementations22 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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