Indirect Image Registration with Large Diffeomorphic Deformations

The paper adapts the large deformation diffeomorphic metric mapping framework for image registration to the indirect setting where a template is registered against a target that is given through indirect noisy observations. The registration uses diffeomorphisms that transform the template through a (group) action. These diffeomorphisms are generated by solving a flow equation that is defined by a velocity field with certain regularity. The theoretical analysis includes a proof that indirect image registration has solutions (existence) that are stable and that converge as the data error tends so zero, so it becomes a well-defined regularization method. The paper concludes with examples of indirect image registration in 2D tomography with very sparse and/or highly noisy data.Comment: 43 pages, 4 figures, 1 table; revise

Optimized imaging using non-rigid registration

The extraordinary improvements of modern imaging devices offer access to data with unprecedented information content. However, widely used image processing methodologies fall far short of exploiting the full breadth of information offered by numerous types of scanning probe, optical, and electron microscopies. In many applications, it is necessary to keep measurement intensities below a desired threshold. We propose a methodology for extracting an increased level of information by processing a series of data sets suffering, in particular, from high degree of spatial uncertainty caused by complex multiscale motion during the acquisition process. An important role is played by a nonrigid pixel-wise registration method that can cope with low signal-to-noise ratios. This is accompanied by formulating objective quality measures which replace human intervention and visual inspection in the processing chain. Scanning transmission electron microscopy of siliceous zeolite material exhibits the above-mentioned obstructions and therefore serves as orientation and a test of our procedures

Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach

This paper introduces Quicksilver, a fast deformable image registration method. Quicksilver registration for image-pairs works by patch-wise prediction of a deformation model based directly on image appearance. A deep encoder-decoder network is used as the prediction model. While the prediction strategy is general, we focus on predictions for the Large Deformation Diffeomorphic Metric Mapping (LDDMM) model. Specifically, we predict the momentum-parameterization of LDDMM, which facilitates a patch-wise prediction strategy while maintaining the theoretical properties of LDDMM, such as guaranteed diffeomorphic mappings for sufficiently strong regularization. We also provide a probabilistic version of our prediction network which can be sampled during the testing time to calculate uncertainties in the predicted deformations. Finally, we introduce a new correction network which greatly increases the prediction accuracy of an already existing prediction network. We show experimental results for uni-modal atlas-to-image as well as uni- / multi- modal image-to-image registrations. These experiments demonstrate that our method accurately predicts registrations obtained by numerical optimization, is very fast, achieves state-of-the-art registration results on four standard validation datasets, and can jointly learn an image similarity measure. Quicksilver is freely available as an open-source software.Comment: Add new discussion

Multiframe Scene Flow with Piecewise Rigid Motion

We introduce a novel multiframe scene flow approach that jointly optimizes the consistency of the patch appearances and their local rigid motions from RGB-D image sequences. In contrast to the competing methods, we take advantage of an oversegmentation of the reference frame and robust optimization techniques. We formulate scene flow recovery as a global non-linear least squares problem which is iteratively solved by a damped Gauss-Newton approach. As a result, we obtain a qualitatively new level of accuracy in RGB-D based scene flow estimation which can potentially run in real-time. Our method can handle challenging cases with rigid, piecewise rigid, articulated and moderate non-rigid motion, and does not rely on prior knowledge about the types of motions and deformations. Extensive experiments on synthetic and real data show that our method outperforms state-of-the-art.Comment: International Conference on 3D Vision (3DV), Qingdao, China, October 201

Multiframe Scene Flow with Piecewise Rigid Motion

We introduce a novel multiframe scene flow approach that jointly optimizes the consistency of the patch appearances and their local rigid motions from RGB-D image sequences. In contrast to the competing methods, we take advantage of an oversegmentation of the reference frame and robust optimization techniques. We formulate scene flow recovery as a global non-linear least squares problem which is iteratively solved by a damped Gauss-Newton approach. As a result, we obtain a qualitatively new level of accuracy in RGB-D based scene flow estimation which can potentially run in real-time. Our method can handle challenging cases with rigid, piecewise rigid, articulated and moderate non-rigid motion, and does not rely on prior knowledge about the types of motions and deformations. Extensive experiments on synthetic and real data show that our method outperforms state-of-the-art.Comment: International Conference on 3D Vision (3DV), Qingdao, China, October 201

Variational image registration by a total fractional-order variation model

In this paper, a new framework of nonlocal deformation in non-rigid image registration is presented. It is well known that many non-rigid image registration techniques may lead to unsteady deformation (e.g. not one to one) if the dissimilarity between the reference and template images is too large. We present a novel variational framework of the total fractional-order variation to derive the underlying fractional Euler-Lagrange equations and a numerical implementation combining the semi-implicit update and conjugate gradients (CG) solution to solve the nonlinear systems. Numerical experiments show that the new registration not only produces accurate and smooth solutions but also allows for a large rigid alignment, the evaluations of the new model demonstrate substantial improvements in accuracy and robustness over the conventional image registration approaches

Finite element surface registration incorporating curvature, volume preservation, and statistical model information

We present a novel method for nonrigid registration of 3D surfaces and images. The method can be used to register surfaces by means of their distance images, or to register medical images directly. It is formulated as a minimization problem of a sum of several terms representing the desired properties of a registration result: smoothness, volume preservation, matching of the surface, its curvature, and possible other feature images, as well as consistency with previous registration results of similar objects, represented by a statistical deformation model. While most of these concepts are already known, we present a coherent continuous formulation of these constraints, including the statistical deformation model. This continuous formulation renders the registration method independent of its discretization. The finite element discretization we present is, while independent of the registration functional, the second main contribution of this paper. The local discontinuous Galerkin method has not previously been used in image registration, and it provides an efficient and general framework to discretize each of the terms of our functional. Computational efficiency and modest memory consumption are achieved thanks to parallelization and locally adaptive mesh refinement. This allows for the first time the use of otherwise prohibitively large 3D statistical deformation models