Variational Image Registration Using Inhomogeneous Regularization

We present a generalization of the convolution-based variational image registration approach, in which different regularizers can be implemented by conveniently exchanging the convolution kernel, even if it is nonseparable or nonstationary. Nonseparable kernels pose a challenge because they cannot be efficiently implemented by separate 1D convolutions. We propose to use a low-rank tensor decomposition to efficiently approximate nonseparable convolution. Nonstationary kernels pose an even greater challenge because the convolution kernel depends on, and needs to be evaluated for, every point in the image. We propose to pre-compute the local kernels and efficiently store them in memory using the Tucker tensor decomposition model. In our experiments we use the nonseparable exponential kernel and a nonstationary landmark kernel. The exponential kernel replicates desirable properties of elastic image registration, while the landmark kernel incorporates local prior knowledge about corresponding points in the images. We examine the trade-off between the computational resources needed and the approximation accuracy of the tensor decomposition methods. Furthermore, we obtain very smooth displacement fields even in the presence of large landmark displacements

An improved discontinuity-preserving image registration model and its fast algorithm

Recently, Chumchob–Chen(2010) proposed a discontinuity-preserving image registration model which was more flexible than those common techniques such as the diffusion and total variation based regularization techniques. However, each component of displacement field is regularized separately in this model and then the nonlinear diffusion processes resulting from the first variation of the discontinuity-preserving regularization do not enforce coupling between the primary components of the displacement field. Thus the discontinuity-preserving model may prevent to obtain a good registration in some situations, for example non-smooth registration problems with non-axis-aligned discontinuities. To utilize interdependence between the primary components of the deformation field for smooth and non-smooth registration problems, we propose an improved discontinuity-preserving image registration model in this paper, second we propose an idea of relaxed fixed point combining with Gauss–Newton scheme with Armijo's line search for solving the new model and further to combine with a multilevel method to achieve fast convergence. Numerical experiments not only confirm that our proposed method is efficient and stable, but also it can give more satisfying registration results according to image quality

Consistent Discretizations for Vanishing Regularization Solutions to Image Processing Problems

A model problem is used to represent a typical image processing problem of reconstructing an unknown in the face of incomplete data. A consistent discretization for a vanishing regularization solution is defined so that, in the absence of noise, limits first with respect to regularization and then with respect to grid refinement agree with a continuum counterpart defined in terms of a saddle point formulation. It is proved and demonstrated computationally for an artificial example and for a realistic example with magnetic resonance images that a mixed finite element discretization is consistent in the sense defined here. On the other hand, it is demonstrated computationally that a standard finite element discretization is not consistent, and the reason for the inconsistency is suggested in terms of theoretical and computational evidence

Joint denoising and distortion correction of atomic scale scanning transmission electron microscopy images

Nowadays, modern electron microscopes deliver images at atomic scale. The precise atomic structure encodes information about material properties. Thus, an important ingredient in the image analysis is to locate the centers of the atoms shown in micrographs as precisely as possible. Here, we consider scanning transmission electron microscopy (STEM), which acquires data in a rastering pattern, pixel by pixel. Due to this rastering combined with the magnification to atomic scale, movements of the specimen even at the nanometer scale lead to random image distortions that make precise atom localization difficult. Given a series of STEM images, we derive a Bayesian method that jointly estimates the distortion in each image and reconstructs the underlying atomic grid of the material by fitting the atom bumps with suitable bump functions. The resulting highly non-convex minimization problems are solved numerically with a trust region approach. Well-posedness of the reconstruction method and the model behavior for faster and faster rastering are investigated using variational techniques. The performance of the method is finally evaluated on both synthetic and real experimental data