Indirect Image Registration with Large Diffeomorphic Deformations

Chen, Chong; Öktem, Ozan

doi:10.1137/17m1134627

Cited by 31 publications

(80 citation statements)

References 54 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This group action yields a deformation that merely moves the position of the pixel/voxel but does not change its intensity. An alternative group action is the one that corresponds to mass-preserving deformations [17,60]:…”

Section: Spatiotemporal Inverse Problem Based On Shape Theorymentioning

confidence: 99%

“…On the other hand, with given template I, the remaining goal is to estimate the evolution parameter "φ t " from noisy measured data. We call it sequentially indirect image registration, which is a generalization of indirect image registration [17]. The inverse problem in (3) is ill-posed due to a variety of reasons.…”

Section: A General Framework Of Joint Image Reconstruction and Motionmentioning

confidence: 99%

“…Then V is an admissible Hilbert space [11]. In the rest of the paper, the space of vector fields is selected as an admissible RKHS for the advantages of sufficient smoothness and fast computability [17]. Furthermore, a flow of diffeomorphisms can be generated via an admissible velocity field, which is stated as the following theorem.…”

Section: The Lddmm Frameworkmentioning

confidence: 99%

See 2 more Smart Citations

A New Variational Model for Joint Image Reconstruction and Motion Estimation in Spatiotemporal Imaging

Chen¹,

Gris²,

Öktem³

2019

SIAM J. Imaging Sci.

Self Cite

View full text Add to dashboard Cite

We propose a new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging, which is investigated along a general framework that we present with shape theory. This model consists of two components, one for conducting modified static image reconstruction, and the other performs sequentially indirect image registration. For the latter, we generalize the large deformation diffeomorphic metric mapping framework into the sequentially indirect registration setting. The proposed model is compared theoretically against alternative approaches (optical flow based model and diffeomorphic motion models), and we demonstrate that the proposed model has desirable properties in terms of the optimal solution. The theoretical derivations and efficient algorithms are also presented for a time-discretized scenario of the proposed model, which show that the optimal solution of the time-discretized version is consistent with that of the time-continuous one, and most of the computational components is the easy-implemented linearized deformation. The complexity of the algorithm is analyzed as well. This work is concluded by some numerical examples in 2D space + time tomography with very sparse and/or highly noisy data.

show abstract

Section: Spatiotemporal Inverse Problem Based On Shape Theorymentioning

confidence: 99%

Section: A General Framework Of Joint Image Reconstruction and Motionmentioning

confidence: 99%

Section: The Lddmm Frameworkmentioning

confidence: 99%

See 1 more Smart Citation

A New Variational Model for Joint Image Reconstruction and Motion Estimation in Spatiotemporal Imaging

Chen¹,

Gris²,

Öktem³

2019

SIAM J. Imaging Sci.

Self Cite

View full text Add to dashboard Cite

show abstract

“…In image registration, the goal is to find a reasonable deformation of a given template image so that it matches a given target image as closely as possible according to a predefined similarity measure, see [40,39] for an introduction. When the target image is unknown and only given through indirect measurements, it is referred to as indirect image registration and has been explored only recently [12,24,31,45]. As a result, a deformation together with a transformed template can be computed from tomographic data.…”

Section: Introductionmentioning

confidence: 99%

“…In comparison to abovementioned existing methods for indirect image registration, such as [12,24,31,45], our method is conceptually different in several ways. The first difference concerns the discretisation.…”

Section: Introductionmentioning

confidence: 99%

Template-Based Image Reconstruction from Sparse Tomographic Data

et al. 2019

Self Cite

View full text Add to dashboard Cite

We propose a variational regularisation approach for the problem of template-based image reconstruction from indirect, noisy measurements as given, for instance, in X-ray computed tomography. An image is reconstructed from such measurements by deforming a given template image. The image registration is directly incorporated into the variational regularisation approach in the form of a partial differential equation that models the registration as either mass-or intensity-preserving transport from the template to the unknown reconstruction. We provide theoretical results for the proposed variational regularisation for both cases. In particular, we prove existence of a minimiser, stability with respect to the data, and convergence for vanishing noise when either of the abovementioned equations is imposed and more general distance functions are used. Numerically, we solve the problem by extending existing Lagrangian methods and propose a multilevel approach that is applicable whenever a suitable downsampling procedure for the operator and the measured data can be provided. Finally, we demonstrate the performance of our method for template-based image reconstruction from highly undersampled and noisy Radon transform data. We compare results for massand intensity-preserving image registration, various regularisation functionals, and different distance functions. Our results show that very reasonable reconstructions can be obtained when only few measurements are available and demonstrate that the use of a normalised cross correlation-based distance is advantageous when the image intensities between the template and the unknown image differ substantially.

show abstract