Total Variation Regularization of Displacements in Parametric Image Registration

One-Shot Learning for Deformable Medical Image Registration and Periodic Motion Tracking

Deformable image registration is a very important field of research in medical imaging. Recently multiple deep learning approaches were published in this area showing promising results. However, drawbacks of deep learning methods are the need for a large amount of training datasets and their inability to register unseen images different from the training datasets. One shot learning comes without the need of large training datasets and has already been proven to be applicable to 3D data. In this work we present a one shot registration approach for periodic motion tracking in 3D and 4D datasets. When applied to a 3D dataset the algorithm calculates the inverse of the registration vector field simultaneously. For registration we employed a U-Net combined with a coarse to fine approach and a differential spatial transformer module. The algorithm was thoroughly tested with multiple 4D and 3D datasets publicly available. The results show that the presented approach is able to track periodic motion and to yield a competitive registration accuracy. Possible applications are the use as a stand-alone algorithm for 3D and 4D motion tracking or in the beginning of studies until enough datasets for a separate training phase are available.

Towards CNN-Based Registration of Craniocaudal and Mediolateral Oblique 2-D X-ray Mammographic Images

We investigate methodologies for the automated registration of pairs of 2-D X-ray mammographic images, taken from the two standard mammographic angles. We present two exploratory techniques, based on Convolutional Neural Networks, to examine their potential for co-registration of findings on the two standard mammographic views. To test algorithm performance, our analysis uses a synthetic, surrogate data set for performing controlled experiments, as well as real 2-D X-ray mammogram imagery. The preliminary results are promising, and provide insights into how the proposed techniques may support multi-view X-ray mammography image registration currently and as technology evolves in the future.

Deformable Image Registration Using Functions of Bounded Deformation

Deformable image registration is a widely used technique in the field of computer vision and medical image processing. Basically, the task of deformable image registration is to find the displacement field between the moving image and the fixed image. Many variational models are proposed for deformable image registration, under the assumption that the displacement field is continuous and smooth. However, displacement fields may be discontinuous, especially for medical images with intensity inhomogeneity, pathological tissues, or heavy noises. In the mathematical theory of elastoplasticity, when the displacement fields are possibly discontinuous, a suitable framework for describing the displacement fields is the space of functions of bounded deformation (BD). Inspired by this, we propose a novel deformable registration model, called the BD model, which allows discontinuities of displacement fields in images. The BD model is formulated in a variational framework by supposing the displacement field to be a function of BD. The existence of solutions of this model is proven. Numerical experiments on 2D images show that the BD model outperforms the classical demons model, the log-domain diffeomorphic demons model, and the state-of-the-art vectorial total variation model. Numerical experiments on two public 3D databases show that the target registration error of the BD model is competitive compared with more than ten other models.

Quadratic penalty method for intensity-based deformable image registration and 4DCT lung motion recovery

Intensity-based deformable image registration (DIR) requires minimizing an image dissimilarity metric. Imaged anatomy, such as bones and vasculature, as well as the resolution of the digital grid, can often cause discontinuities in the corresponding objective function. Consequently, the application of a gradient-based optimization algorithm requires a preprocessing image smoothing to ensure the existence of necessary image derivatives. Simple block matching (exhaustive search) methods do not require image derivative approximations, but their general effectiveness is often hindered by erroneous solutions (outliers). Block match methods are therefore often coupled with a statistical outlier detection method to improve results.

PURPOSE

The purpose of this work is to present a spatially accurate, intensity-based DIR optimization formulation that can be solved with a straightforward gradient-free quadratic penalty algorithm and is suitable for 4D thoracic computed tomography (4DCT) registration. Additionally, a novel regularization strategy based on the well-known leave-one-out robust statistical model cross-validation method is introduced.

METHODS

The proposed Quadratic Penalty DIR (QPDIR) method minimizes both an image dissimilarity term, which is separable with respect to individual voxel displacements, and a regularization term derived from the classical leave-one-out cross-validation statistical method. The resulting DIR problem lends itself to a quadratic penalty function optimization approach, where each subproblem can be solved by straightforward block coordinate descent iteration.

RESULTS

The spatial accuracy of the method was assessed using expert-determined landmarks on ten 4DCT datasets available on www.dir-lab.com. The QPDIR algorithm achieved average millimeter spatial errors between 0.69 (0.91) and 1.19 (1.26) on the ten test cases. On all ten 4DCT test cases, the QPDIR method produced spatial accuracies that are superior or equivalent to those produced by current state-of-the-art methods. Moreover, QPDIR achieved accuracies at the resolution of the landmark error assessment (i.e., the interobserver error) on six of the ten cases.

CONCLUSION

The QPDIR algorithm is based on a simple quadratic penalty function formulation and a regularization term inspired by leave-one-out cross validation. The formulation lends itself to a parallelizable, gradient-free, block coordinate descent numerical optimization method. Numerical results indicate that the method achieves a high spatial accuracy on 4DCT inhale/exhale phases.

Isotropic Total Variation Regularization of Displacements in Parametric Image Registration

Spatial regularization is essential in image registration, which is an ill-posed problem. Regularization can help to avoid both physically implausible displacement fields and local minima during optimization. Tikhonov regularization (squared l₂ -norm) is unable to correctly represent non-smooth displacement fields, that can, for example, occur at sliding interfaces in the thorax and abdomen in image time-series during respiration. In this paper, isotropic Total Variation (TV) regularization is used to enable accurate registration near such interfaces. We further develop the TV-regularization for parametric displacement fields and provide an efficient numerical solution scheme using the Alternating Directions Method of Multipliers (ADMM). The proposed method was successfully applied to four clinical databases which capture breathing motion, including CT lung and MR liver images. It provided accurate registration results for the whole volume. A key strength of our proposed method is that it does not depend on organ masks that are conventionally required by many algorithms to avoid errors at sliding interfaces. Furthermore, our method is robust to parameter selection, allowing the use of the same parameters for all tested databases. The average target registration error (TRE) of our method is superior (10% to 40%) to other techniques in the literature. It provides precise motion quantification and sliding detection with sub-pixel accuracy on the publicly available breathing motion databases (mean TREs of 0.95 mm for DIR 4D CT, 0.96 mm for DIR COPDgene, 0.91 mm for POPI databases).

4D respiratory motion-compensated image reconstruction of free-breathing radial MR data with very high undersampling

PURPOSE

To develop four-dimensional (4D) respiratory time-resolved MRI based on free-breathing acquisition of radial MR data with very high undersampling.

METHODS

We propose the 4D joint motion-compensated high-dimensional total variation (4D joint MoCo-HDTV) algorithm, which alternates between motion-compensated image reconstruction and artifact-robust motion estimation at multiple resolution levels. The algorithm is applied to radial MR data of the thorax and upper abdomen of 12 free-breathing subjects with acquisition times between 37 and 41 s and undersampling factors of 16.8. Resulting images are compared with compressed sensing-based 4D motion-adaptive spatio-temporal regularization (MASTeR) and 4D high-dimensional total variation (HDTV) reconstructions.

RESULTS

For all subjects, 4D joint MoCo-HDTV achieves higher similarity in terms of normalized mutual information and cross-correlation than 4D MASTeR and 4D HDTV when compared with reference 4D gated gridding reconstructions with 8.4 ± 1.1 times longer acquisition times. In a qualitative assessment of artifact level and image sharpness by two radiologists, 4D joint MoCo-HDTV reveals higher scores (P < 0.05) than 4D HDTV and 4D MASTeR at the same undersampling factor and the reference 4D gated gridding reconstructions, respectively.

CONCLUSIONS

4D joint MoCo-HDTV enables time-resolved image reconstruction of free-breathing radial MR data with undersampling factors of 16.8 while achieving low-streak artifact levels and high image sharpness. Magn Reson Med 77:1170-1183, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

A Novel Diagnostic Aid for Detection of Intra-Abdominal Adhesions to the Anterior Abdominal Wall Using Dynamic Magnetic Resonance Imaging

Introduction. Abdominal adhesions can cause serious morbidity and complicate subsequent operations. Their diagnosis is often one of exclusion due to a lack of a reliable, non-invasive diagnostic technique. Development and testing of a candidate technique are described below. Method. During respiration, smooth visceral sliding motion occurs between the abdominal contents and the walls of the abdominal cavity. We describe a technique involving image segmentation and registration to calculate shear as an analogue for visceral slide based on the tracking of structures throughout the respiratory cycle. The presence of an adhesion is attributed to a resistance to visceral slide resulting in a discernible reduction in shear. The abdominal movement due to respiration is captured in sagittal dynamic MR images. Results. Clinical images were selected for analysis, including a patient with a surgically confirmed adhesion. Discernible reduction in shear was observed at the location of the adhesion while a consistent, gradually changing shear was observed in the healthy volunteers. Conclusion. The technique and its validation show encouraging results for adhesion detection but a larger study is now required to confirm its potential.