Search Results for author:
Found 20 papers, 7 papers with code
DIMON: Learning Solution Operators of Partial Differential Equations on a Diffeomorphic Family of Domains
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 $\Omega_{\theta}$.
Basis restricted elastic shape analysis on the space of unregistered surfaces
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
We present Basis Restricted Elastic Shape Analysis (BaRe-ESA), a novel Riemannian framework for human body scan representation, interpolation and extrapolation.
A Diffeomorphic Flow-based Variational Framework for Multi-speaker Emotion Conversion
We term this new architecture a variational CycleGAN (VCGAN).
Elastic shape analysis of surfaces with second-order Sobolev metrics: a comprehensive numerical framework
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
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
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
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
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
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
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.
Diffeomorphic registration of discrete geometric distributions
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
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
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
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.
A Large Deformation Diffeomorphic Approach to Registration of CLARITY Images via Mutual Information
Due to the novelty of this microscopy technique it is impractical to use absolute intensity values to align these images to existing standard atlases.
Metamorphoses of functional shapes in Sobolev spaces
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
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
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
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.
