34 research outputs found
PDE-constrained LDDMM via geodesic shooting and inexact Gauss-Newton-Krylov optimization using the incremental adjoint Jacobi equations
The class of non-rigid registration methods proposed in the framework of
PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a
particularly interesting family of physically meaningful diffeomorphic
registration methods. Inexact Newton-Krylov optimization has shown an excellent
numerical accuracy and an extraordinarily fast convergence rate in this
framework. However, the Galerkin representation of the non-stationary velocity
fields does not provide proper geodesic paths. In this work, we propose a
method for PDE-constrained LDDMM parameterized in the space of initial velocity
fields under the EPDiff equation. The derivation of the gradient and the
Hessian-vector products are performed on the final velocity field and
transported backward using the adjoint and the incremental adjoint Jacobi
equations. This way, we avoid the complex dependence on the initial velocity
field in the derivations and the computation of the adjoint equation and its
incremental counterpart. The proposed method provides geodesics in the
framework of PDE-constrained LDDMM, and it shows performance competitive to
benchmark PDE-constrained LDDMM and EPDiff-LDDMM methods
Diffeomorphic density registration
In this book chapter we study the Riemannian Geometry of the density
registration problem: Given two densities (not necessarily probability
densities) defined on a smooth finite dimensional manifold find a
diffeomorphism which transforms one to the other. This problem is motivated by
the medical imaging application of tracking organ motion due to respiration in
Thoracic CT imaging where the fundamental physical property of conservation of
mass naturally leads to modeling CT attenuation as a density. We will study the
intimate link between the Riemannian metrics on the space of diffeomorphisms
and those on the space of densities. We finally develop novel computationally
efficient algorithms and demonstrate there applicability for registering RCCT
thoracic imaging.Comment: 23 pages, 6 Figures, Chapter for a Book on Medical Image Analysi
Contrastive Registration for Unsupervised Medical Image Segmentation
Medical image segmentation is a relevant task as it serves as the first step
for several diagnosis processes, thus it is indispensable in clinical usage.
Whilst major success has been reported using supervised techniques, they assume
a large and well-representative labelled set. This is a strong assumption in
the medical domain where annotations are expensive, time-consuming, and
inherent to human bias. To address this problem, unsupervised techniques have
been proposed in the literature yet it is still an open problem due to the
difficulty of learning any transformation pattern. In this work, we present a
novel optimisation model framed into a new CNN-based contrastive registration
architecture for unsupervised medical image segmentation. The core of our
approach is to exploit image-level registration and feature-level from a
contrastive learning mechanism, to perform registration-based segmentation.
Firstly, we propose an architecture to capture the image-to-image
transformation pattern via registration for unsupervised medical image
segmentation. Secondly, we embed a contrastive learning mechanism into the
registration architecture to enhance the discriminating capacity of the network
in the feature-level. We show that our proposed technique mitigates the major
drawbacks of existing unsupervised techniques. We demonstrate, through
numerical and visual experiments, that our technique substantially outperforms
the current state-of-the-art unsupervised segmentation methods on two major
medical image datasets.Comment: 11 pages, 3 figure
Large deformation diffeomorphic registration of diffusion-weighted imaging data
Registration plays an important role in group analysis of diffusion-weighted imaging (DWI) data. It can be used to build a reference anatomy for investigating structural variation or tracking changes in white matter. Unlike traditional scalar image registration where spatial alignment is the only focus, registration of DWI data requires both spatial alignment of structures and reorientation of local signal profiles. As such, DWI registration is much more complex and challenging than scalar image registration. Although a variety of algorithms has been proposed to tackle the problem, most of them are restricted by the zdiffusion model used for registration, making it difficult to fit to the registered data a different model. In this paper we describe a method that allows any diffusion model to be fitted after registration for subsequent multifaceted analysis. This is achieved by directly aligning DWI data using a large deformation diffeomorphic registration framework. Our algorithm seeks the optimal coordinate mapping by simultaneously considering structural alignment, local signal profile reorientation, and deformation regularization. Our algorithm also incorporates a multi-kernel strategy to concurrently register anatomical structures at different scales. We demonstrate the efficacy of our approach using in vivo data and report detailed qualitative and quantitative results in comparison with several different registration strategies
Multiple Shape Registration using Constrained Optimal Control
Lagrangian particle formulations of the large deformation diffeomorphic
metric mapping algorithm (LDDMM) only allow for the study of a single shape. In
this paper, we introduce and discuss both a theoretical and practical setting
for the simultaneous study of multiple shapes that are either stitched to one
another or slide along a submanifold. The method is described within the
optimal control formalism, and optimality conditions are given, together with
the equations that are needed to implement augmented Lagrangian methods.
Experimental results are provided for stitched and sliding surfaces