Search Results for author: Stefan Sommer

Found 21 papers, 5 papers with code

Moment evolution equations and moment matching for stochastic image EPDiff

no code implementations7 Oct 2021 Alexander Christgau, Alexis Arnaudon, Stefan Sommer

Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain.

Atlas Generative Models and Geodesic Interpolation

no code implementations30 Jan 2021 Jakob Stolberg-Larsen, Stefan Sommer

In this work we define the general class of Atlas Generative Models (AGMs), models with hybrid discrete-continuous latent space that estimate an atlas on the underlying data manifold together with a partition of unity on the data space.

Unity

Diffusion bridges for stochastic Hamiltonian systems and shape evolutions

1 code implementation3 Feb 2020 Alexis Arnaudon, Frank van der Meulen, Moritz Schauer, Stefan Sommer

Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes.

Numerical Analysis Computational Engineering, Finance, and Science Numerical Analysis Computational Physics

Horizontal Flows and Manifold Stochastics in Geometric Deep Learning

no code implementations13 Sep 2019 Stefan Sommer, Alex Bronstein

We introduce two constructions in geometric deep learning for 1) transporting orientation-dependent convolutional filters over a manifold in a continuous way and thereby defining a convolution operator that naturally incorporates the rotational effect of holonomy; and 2) allowing efficient evaluation of manifold convolution layers by sampling manifold valued random variables that center around a weighted diffusion mean.

Frame

Stochastic Image Deformation in Frequency Domain and Parameter Estimation using Moment Evolutions

no code implementations13 Dec 2018 Line Kühnel, Alexis Arnaudon, Tom Fletcher, Stefan Sommer

We apply a stochastic generalisation of the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework to model differences in the evolution of anatomical objects detected in populations of image data.

PADDIT: Probabilistic Augmentation of Data using Diffeomorphic Image Transformation

no code implementations3 Oct 2018 Mauricio Orbes Arteaga, Lauge Sørensen, M. Jorge Cardoso, Marc Modat, Sebastien Ourselin, Stefan Sommer, Mads Nielsen, Christian Igel, Akshay Pai

For proper generalization performance of convolutional neural networks (CNNs) in medical image segmentation, the learnt features should be invariant under particular non-linear shape variations of the input.

Medical Image Segmentation Semantic Segmentation

Latent Space Non-Linear Statistics

no code implementations19 May 2018 Line Kuhnel, Tom Fletcher, Sarang Joshi, Stefan Sommer

Given data, deep generative models, such as variational autoencoders (VAE) and generative adversarial networks (GAN), train a lower dimensional latent representation of the data space.

String Methods for Stochastic Image and Shape Matching

no code implementations15 May 2018 Alexis Arnaudon, Darryl Holm, Stefan Sommer

Matching of images and analysis of shape differences is traditionally pursued by energy minimization of paths of deformations acting to match the shape objects.

An Infinitesimal Probabilistic Model for Principal Component Analysis of Manifold Valued Data

no code implementations31 Jan 2018 Stefan Sommer

We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data.

Differential geometry and stochastic dynamics with deep learning numerics

2 code implementations22 Dec 2017 Line Kühnel, Alexis Arnaudon, Stefan Sommer

In this paper, we demonstrate how deterministic and stochastic dynamics on manifolds, as well as differential geometric constructions can be implemented concisely and efficiently using modern computational frameworks that mix symbolic expressions with efficient numerical computations.

Computational Geometry Computation 53A35, 53C17, 53C44, 70H05, 22E30 G.3; G.4; G.1.4

Stochastic metamorphosis with template uncertainties

no code implementations20 Nov 2017 Alexis Arnaudon, Darryl Holm, Stefan Sommer

In this paper, we investigate two stochastic perturbations of the metamorphosis equations of image analysis, in the geometrical context of the Euler-Poincar\'e theory.

Computational Anatomy in Theano

2 code implementations15 Jun 2017 Line Kühnel, Stefan Sommer

To model deformation of anatomical shapes, non-linear statistics are required to take into account the non-linear structure of the data space.

Other Computer Science 53A35

Bridge Simulation and Metric Estimation on Landmark Manifolds

no code implementations31 May 2017 Stefan Sommer, Alexis Arnaudon, Line Kuhnel, Sarang Joshi

We present an inference algorithm and connected Monte Carlo based estimation procedures for metric estimation from landmark configurations distributed according to the transition distribution of a Riemannian Brownian motion arising from the Large Deformation Diffeomorphic Metric Mapping (LDDMM) metric.

A Statistical Model for Simultaneous Template Estimation, Bias Correction, and Registration of 3D Brain Images

no code implementations1 May 2017 Akshay Pai, Stefan Sommer, Lars Lau Raket, Line Kühnel, Sune Darkner, Lauge Sørensen, Mads Nielsen

Template estimation plays a crucial role in computational anatomy since it provides reference frames for performing statistical analysis of the underlying anatomical population variability.

Image Registration

A Geometric Framework for Stochastic Shape Analysis

1 code implementation29 Mar 2017 Alexis Arnaudon, Darryl D. Holm, Stefan Sommer

We introduce a stochastic model of diffeomorphisms, whose action on a variety of data types descends to stochastic evolution of shapes, images and landmarks.

Image Registration

A Stochastic Large Deformation Model for Computational Anatomy

no code implementations16 Dec 2016 Alexis Arnaudon, Darryl D. Holm, Akshay Pai, Stefan Sommer

In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise.

Most Likely Separation of Intensity and Warping Effects in Image Registration

no code implementations18 Apr 2016 Line Kühnel, Stefan Sommer, Akshay Pai, Lars Lau Raket

This paper introduces a class of mixed-effects models for joint modeling of spatially correlated intensity variation and warping variation in 2D images.

Image Registration

Higher-order Spatial Accuracy in Diffeomorphic Image Registration

no code implementations23 Dec 2014 Henry O. Jacobs, Stefan Sommer

We discretize a cost functional for image registration problems by deriving Taylor expansions for the matching term.

Image Registration

Symmetry in Image Registration and Deformation Modeling

no code implementations23 Dec 2014 Stefan Sommer, Henry O. Jacobs

We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data.

Image Registration

Optimization over Geodesics for Exact Principal Geodesic Analysis

1 code implementation11 Aug 2010 Stefan Sommer, François Lauze, Mads Nielsen

In fields ranging from computer vision to signal processing and statistics, increasing computational power allows a move from classical linear models to models that incorporate non-linear phenomena.

Computational Geometry

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