1 code implementation • 13 Feb 2023 • Francesco Santini, Jakob Wasserthal, Abramo Agosti, Xeni Deligianni, Kevin R. Keene, Hermien E. Kan, Stefan Sommer, Christoph Stuprich, Fengdan Wang, Claudia Weidensteiner, Giulia Manco, Matteo Paoletti, Valentina Mazzoli, Arjun Desai, Anna Pichiecchio
Semantic segmentation is a crucial step to extract quantitative information from medical (and, specifically, radiological) images to aid the diagnostic process, clinical follow-up.
1 code implementation • 11 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
2 code implementations • 22 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
2 code implementations • 15 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
1 code implementation • 3 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
1 code implementation • 10 Feb 2023 • Elizabeth Baker, Thomas Besnier, Stefan Sommer
Modelling randomness in shape data, for example, the evolution of shapes of organisms in biology, requires stochastic models of shapes.
no code implementations • 15 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.
no code implementations • 19 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.
1 code implementation • 29 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.
no code implementations • 31 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.
no code implementations • 20 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.
no code implementations • 31 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.
no code implementations • 1 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.
no code implementations • 18 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.
no code implementations • 16 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.
no code implementations • 23 Dec 2014 • Henry O. Jacobs, Stefan Sommer
We discretize a cost functional for image registration problems by deriving Taylor expansions for the matching term.
no code implementations • 23 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.
no code implementations • 3 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.
no code implementations • 9 Nov 2018 • Sune Darkner, Stefan Sommer, Andreas Schuhmacher, Henrik Ingerslev Anders O. Baandrup, Carsten Thomsen, Søren Jønsson
This is however not the case for the part of the ear canal that is embedded in the skull, until the typanic membrane.
no code implementations • 13 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.
no code implementations • 13 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.
no code implementations • 30 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.
no code implementations • 7 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.
no code implementations • 27 Jan 2023 • Gefan Yang, Stefan Sommer
We propose a novel denoising diffusion generative model for predicting nonlinear fluid fields named FluidDiff.
no code implementations • 14 Mar 2023 • Lili Bao, Jiahao Lu, Shihui Ying, Stefan Sommer
In this paper, we propose a new approach to deformable image registration that captures sliding motions.
no code implementations • 6 Jul 2023 • Morten Akhøj, James Benn, Erlend Grong, Stefan Sommer, Xavier Pennec
In this paper we demonstrate how sub-Riemannian geometry can be used for manifold learning and surface reconstruction by combining local linear approximations of a point cloud to obtain lower dimensional bundles.
no code implementations • 22 Dec 2023 • Liwei Hu, Wenyong Wang, Yu Xiang, Stefan Sommer
The aerodynamic coefficients of aircrafts are significantly impacted by its geometry, especially when the angle of attack (AoA) is large.
no code implementations • 2 Feb 2024 • Elizabeth Louise Baker, Gefan Yang, Michael L. Severinsen, Christy Anna Hipsley, Stefan Sommer
Generative diffusion models and many stochastic models in science and engineering naturally live in infinite dimensions before discretisation.