Sparse deformation prediction using Markove Decision Processes (MDP) for Non-rigid registration of MR image

Divergence-Free Fitting-Based Incompressible Deformation Quantification of Liver

Liver is an incompressible organ that maintains its volume during the respiration-induced deformation. Quantifying this deformation with the incompressible constraint is significant for liver tracking. The constraint can be accomplished with retaining the divergence-free field obtained by the deformation decomposition. However, the decomposition process is time-consuming, and the removal of non-divergence-free field weakens the deformation. In this study, a divergence-free fitting-based registration method is proposed to quantify the incompressible deformation rapidly and accurately. First, the deformation to be estimated is mapped to the velocity in a diffeomorphic space. Then, this velocity is decomposed by a fast Fourier-based Hodge-Helmholtz decomposition to obtain the divergence-free, curl-free, and harmonic fields. The curl-free field is replaced and fitted by the obtained harmonic field with a translation field to generate a new divergence-free velocity. By optimizing this velocity, the final incompressible deformation is obtained. Moreover, a deep learning framework (DLF) is constructed to accelerate the incompressible deformation quantification. An incompressible respiratory motion model is built for the DLF by using the proposed registration method and is then used to augment the training data. An encoder-decoder network is introduced to learn appearance-velocity correlation at patch scale. In the experiment, we compare the proposed registration with three state-of-the-art methods. The results show that the proposed method can accurately achieve the incompressible registration of liver with a mean liver overlap ratio of 95.33%. Moreover, the time consumed by DLF is nearly 15 times shorter than that by other methods.

Balanced multi-image demons for non-rigid registration of magnetic resonance images

A new approach is introduced for non-rigid registration of a pair of magnetic resonance images (MRI). It is a generalization of the demons algorithm with low computational cost, based on local information augmentation (by integrating multiple images) and balanced implementation. Specifically, a single deformation that best registers more pairs of images is estimated. All these images are extracted by applying different operators to the two original ones, processing local neighbors of each pixel. The following five images were found to be appropriate for MRI registration: the raw image and those obtained by contrast-limited adaptive histogram equalization, local median, local entropy and phase symmetry. Thus, each local point in the images is supplemented by augmented information coming by processing its neighbor. Moreover, image pairs are processed in alternation for each iteration of the algorithm (in a balanced way), computing both a forward and a backward registration. The new method (called balanced multi-image demons) is tested on sagittal MRIs from 10 patients, both in simulated and experimental conditions, improving the performances over the classical demons approach with minimal increase of the computational cost (processing time around twice that of standard demons). Specifically, a simulated deformation was applied to the MRIs (either original or corrupted by additive Gaussian or speckle noises). In all tested cases, the new algorithm improved the estimation of the simulated deformation (squared estimation error decreased by about 65% in the average). Moreover, statistically significant improvements were obtained in experimental tests, in which different brain regions (i.e., brain, posterior fossa and cerebellum) were identified by the atlas approach and compared to those manually delineated (in the average, Dice coefficient increased of about 6%). The conclusion is that a balanced method applied to multiple information extracted from neighboring pixels is a low cost approach to improve registration of MRIs.

Groupwise registration with global-local graph shrinkage in atlas construction

Graph-based groupwise registration methods are widely used in atlas construction. Given a group of images, a graph is built whose nodes represent the images, and whose edges represent a geodesic path between two nodes. The distribution of images on an image manifold is explored through edge traversal in a graph. The final atlas is a mean image at the population center of the distribution on the manifold. The procedure of warping all images to the mean image turns to dynamic graph shrinkage in which nodes become closer to each other. Most conventional groupwise registration frameworks construct and shrink a graph without considering the local distribution of images on the dataset manifold and the local structure variations between image pairs. Neglecting the local information fundamentally decrease the accuracy and efficiency when population atlases are built for organs with large inter-subject anatomical variabilities. To overcome the problem, this paper proposes a global-local graph shrinkage approach that can generate accurate atlas. A connected graph is constructed automatically based on global similarities across the images to explore the global distribution. A local image distribution obtained by image clustering is used to simplify the edges of the constructed graph. Subsequently, local image similarities refine the deformation estimated through global image similarity for each image warping along the graph edges. Through the image warping, the overall simplified graph shrinks gradually to yield the atlas with respecting both global and local features. The proposed method is evaluated on 61 synthetic and 20 clinical liver datasets, and the results are compared with those of six state-of-the-art groupwise registration methods. The experimental results show that the proposed method outperforms non-global-local method approaches in terms of accuracy.