1 code implementation • 6 Apr 2023 • Adam Gosztolai, Robert L. Peach, Alexis Arnaudon, Mauricio Barahona, Pierre Vandergheynst
The dynamics of neuron populations during many behavioural tasks evolve on low-dimensional manifolds.
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 • 6 May 2021 • Alessandro Barp, So Takao, Michael Betancourt, Alexis Arnaudon, Mark Girolami
A complete recipe of measure-preserving diffusions in Euclidean space was recently derived unifying several MCMC algorithms into a single framework.
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 • 24 Sep 2019 • Robert L. Peach, Alexis Arnaudon, Mauricio Barahona
Classification tasks based on feature vectors can be significantly improved by including within deep learning a graph that summarises pairwise relationships between the samples.
no code implementations • 8 Jan 2019 • Andreas Bock, Alexis Arnaudon, Colin Cotter
We present a framework for shape matching in computational anatomy allowing users control of the degree to which the matching is diffeomorphic.
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 • 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.
3 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
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.
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 • 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.