7 research outputs found
On Completeness of Groups of Diffeomorphisms
We study completeness properties of the Sobolev diffeomorphism groups endowed with strong right-invariant Riemannian metrics when the underlying manifold is or compact without boundary. The main result is that for , the group is geodesically and metrically complete with a surjective exponential map. We also extend the result to its closed subgroups, in particular the group of volume preserving diffeomorphisms and the group of symplectomorphisms. We then present the connection between the Sobolev diffeomorphism group and the large deformation matching framework in order to apply our results to diffeomorphic image matching
Fast Predictive Image Registration
We present a method to predict image deformations based on patch-wise image
appearance. Specifically, we design a patch-based deep encoder-decoder network
which learns the pixel/voxel-wise mapping between image appearance and
registration parameters. Our approach can predict general deformation
parameterizations, however, we focus on the large deformation diffeomorphic
metric mapping (LDDMM) registration model. By predicting the LDDMM
momentum-parameterization we retain the desirable theoretical properties of
LDDMM, while reducing computation time by orders of magnitude: combined with
patch pruning, we achieve a 1500x/66x speed up compared to GPU-based
optimization for 2D/3D image registration. Our approach has better prediction
accuracy than predicting deformation or velocity fields and results in
diffeomorphic transformations. Additionally, we create a Bayesian probabilistic
version of our network, which allows evaluation of deformation field
uncertainty through Monte Carlo sampling using dropout at test time. We show
that deformation uncertainty highlights areas of ambiguous deformations. We
test our method on the OASIS brain image dataset in 2D and 3D
Automated 3D Lumbar Intervertebral Disc Segmentation from MRI Data Sets
This paper proposed an automated 3D lumbar intervertebral disc (IVD)
segmentation strategy from MRI data. Starting from two user supplied landmarks,
the geometrical parameters of all lumbar vertebral bodies and intervertebral discs
are automatically extracted from a mid-sagittal slice using a graphical model based
approach. After that, a three-dimensional (3D) variable-radius soft tube model of the
lumbar spine column is built to guide the 3D disc segmentation. The disc segmentation
is achieved as a multi-kernel diffeomorphic registration between a 3D template
of the disc and the observed MRI data. Experiments on 15 patient data sets showed
the robustness and the accuracy of the proposed algorithm
Efficient Laplace Approximation for Bayesian Registration Uncertainty Quantification
© Springer Nature Switzerland AG 2018. This paper presents a novel approach to modeling the posterior distribution in image registration that is computationally efficient for large deformation diffeomorphic metric mapping (LDDMM). We develop a Laplace approximation of Bayesian registration models entirely in a bandlimited space that fully describes the properties of diffeomorphic transformations. In contrast to current methods, we compute the inverse Hessian at the mode of the posterior distribution of diffeomorphisms directly in the low dimensional frequency domain. This dramatically reduces the computational complexity of approximating posterior marginals in the high dimensional imaging space. Experimental results show that our method is significantly faster than the state-of-the-art diffeomorphic image registration uncertainty quantification algorithms, while producing comparable results. The efficiency of our method strengthens the feasibility in prospective clinical applications, e.g., real-time image-guided navigation for brain surgery