Third AGM Meeting on Symmetry and Shape Analysis 2017-2018
15 June 2018, Imperial College London
This one-day meeting will cover various disciplines related to symmetry and shape analysis. Specific topics will include:
-- data structure and fusion,
-- multiple resolutions and dynamic images,
-- changes in image topology.
[IMPORTANT! -- All non-speaker attendees are requested to register by writing to Alexis Arnaudon by Monday, 4 June]
Timetable (tentative):
12:00 – 13:00 Lunch buffet
13:00 – 13:45 Stefan Sommer (University of Copenhagen)
13:45 – 14:30 Wenjia Bai (Imperial College London)
14:30 – 15:00 Coffee break
15:00 – 15:45 Line Kühnel (University of Copenhagen)
15:45 – 16:30 Yaël Balbastre (University College London)
Titles and Abstracts
Yaël Balbastre
Shape and appearance modelling*
The large deformation diffeomorphic metric mapping [1] framework has been used extensively to study brain anatomy by assuming that individual brains can be represented by a mean shape---or template---and a topology-preserving transformation. Under this assumption, the underlying diffeomorphisms capture all of the inter-individual variability and their covariance structure carries anatomical information. This covariance structure can be inferred by relying on a probabilistic principal component analysis adapted to the smooth structure of diffeomorphisms. Following Zhang's and Fletcher’s [2] seminal work, we propose a Bayesian model in which initial velocity fields are represented by a linear combination of smooth principal components plus an additional field aimed at modelling residual anatomical variability. We show that the inferred latent representation allows extracting meaningful anatomical features such as brain size or `brain age'. However, the assumption that all inter-individual differences can be modelled by deformations alone is quite strong. We further extend the model to allow changes to the template along modes of appearance variability captured from the images. The combined model is able to capture both appearance (i.e., topological) and shape (i.e., topology-preserving) variability.
*This is joint work with John Ashburner.
[1] Beg, M.F., Miller, M.I., Trouvé, A., Younes, L., 2005. Computing large deformation metric mappings via geodesic flows of diffeomorphisms. Int. J. Comput. Vis. 61, 139-157.
[2] Zhang, M., Fletcher, P.T., 2015. Bayesian principal geodesic analysis for estimating intrinsic diffeomorphic image variability. Medical Image Analysis 25, 37-44.
Wenjia Bai
Machine learning for cardiac MR image analysis
Machine learning applies statistical techniques to learning models from data. In this talk, we will present two approaches which use machine learning for cardiac MR imageanalysis. The first approach is atlas-based, which encodes the anatomical prior knowledgeinto pairs of atlas images and label maps and maps this knowledge onto the image undersegmentation. The second approach is based on convolutional neural networks, which learnsmulti-scale image features for inferring the segmentation. Both approaches have achieved ahigh accuracy on the task of cardiac MR image segmentation. At the end, we will alsobriefly present a statistical shape model of heart learnt from cardiac MR images.
Line Kühnel
Parameter estimation for image distributions based on stochastic registration
We introduce a stochastic method for parameter inference for data distributions of images. Several deterministic methods have considered estimation of the mean template of the data distribution, while few tackle the problem of modelling the noise structure of data. The presented procedure makes inference of both template and noise structure by matching moments of the data distribution with a transition distribution of the diffusion process given by the stochastic Euler-Poincaré equation. The stochastic Euler- Poincaré equation defines perturbed geodesics on manifolds based on a predefined class of noise fields modelling the covariance structure of the transition distribution. We discuss how the initial point (the template) and parameters for the chosen noise fields can be estimated for high-dimensional image data. Due to the high-dimensionality of data the moment matching in full dimensions is computationally infeasible. To solve the problem of high-dimensions, we apply the FLASH procedure developed for deterministic template estimation. FLASH uses truncated Fourier transformations to decrease the dimensionality of data making the optimization problem computationally feasible in order to get reasonable estimates for the parameters for the data distribution.
Stefan Sommer
Strings and bridges
Likelihood based inference and Bayesian analysis of nonlinear data, for example shape data in computational anatomy and data with major modes of variation restricted to learned nonlinear subspaces, rely on parametric families of probability distributions. Such distributions can be constructed intrinsically from the nonlinear geometry using geometric stochastic processes. Evaluating data likelihoods can then be approached by simulation of data conditioned stochastic bridges. In the talk we will consider different approaches to the conditioned bridges simulation problem in Euclidean and nonlinear domains. Bridge sampling can be compared to stochastic strings used for rate event sampling in physics. We contrast shape string with bridges, and use strings to derive a stochastic version of the Beg shape matching algorithm.
Directions:
Lecture Room 402 in the EPSRC Centres for Doctoral Training suite is located on the 4th floor of the ICSM building with access via the SHERFIELD Level 2 Lift lobby:
Map to EPSRC Centres for Doctoral Training Suite
SHERFIELD is building 20 on the campus map:
Map of South Kensington Campus
Contacts: