A Geometric Approach to Pairwise Bayesian Alignment of Functional Data Using Importance Sampling

We present a Bayesian model for pairwise nonlinear registration of functional data. We use the Riemannian geometry of the space of warping functions to define appropriate prior distributions and sample from the posterior using importance sampling. A simple square-root transformation is used to simplify the geometry of the space of warping functions, which allows for computation of sample statistics, such as the mean and median, and a fast implementation of a $k$-means clustering algorithm. These tools allow for efficient posterior inference, where multiple modes of the posterior distribution corresponding to multiple plausible alignments of the given functions are found. We also show pointwise $95\%$ credible intervals to assess the uncertainty of the alignment in different clusters. We validate this model using simulations and present multiple examples on real data from different application domains including biometrics and medicine

Brain atlas fusion from high-thickness diagnostic magnetic resonance images by learning-based super-resolution

It is fundamentally important to fuse the brain atlas from magnetic resonance (MR) images for many imaging-based studies. Most existing works focus on fusing the atlases from high-quality MR images. However, for low-quality diagnostic images (i.e., with high inter-slice thickness), the problem of atlas fusion has not been addressed yet. In this paper, we intend to fuse the brain atlas from the high-thickness diagnostic MR images that are prevalent for clinical routines. The main idea of our works is to extend the conventional groupwise registration by incorporating a novel super-resolution strategy. The contribution of the proposed super-resolution framework is two-fold. First, each high-thickness subject image is reconstructed to be isotropic by the patch-based sparsity learning. Then, the reconstructed isotropic image is enhanced for better quality through the random-forest-based regression model. In this way, the images obtained by the super-resolution strategy can be fused together by applying the groupwise registration method to construct the required atlas. Our experiments have shown that the proposed framework can effectively solve the problem of atlas fusion from the low-quality brain MR images

Joint Segmentation and Groupwise Registration of Cardiac Perfusion Images Using Temporal Information

We propose a joint segmentation and groupwise registration method for dynamic cardiac perfusion images that uses temporal information. The nature of perfusion images makes groupwise registration especially attractive as the temporal information from the entire image sequence can be used. Registration aims to maximize the smoothness of the intensity signal while segmentation minimizes a pixel's dissimilarity with other pixels having the same segmentation label. The cost function is optimized in an iterative fashion using B-splines. Tests on real patient datasets show that compared with two other methods, our method shows lower registration error and higher segmentation accuracy. This is attributed to the use of temporal information for groupwise registration and mutual complementary registration and segmentation information in one framework while other methods solve the two problems separatel

Intrasubject multimodal groupwise registration with the conditional template entropy

Image registration is an important task in medical image analysis. Whereas most methods are designed for the registration of two images (pairwise registration), there is an increasing interest in simultaneously aligning more than two images using groupwise registration. Multimodal registration in a groupwise setting remains difficult, due to the lack of generally applicable similarity metrics. In this work, a novel similarity metric for such groupwise registration problems is proposed. The metric calculates the sum of the conditional entropy between each image in the group and a representative template image constructed iteratively using principal component analysis. The proposed metric is validated in extensive experiments on synthetic and intrasubject clinical image data. These experiments showed equivalent or improved registration accuracy compared to other state-of-the-art (dis)similarity metrics and improved transformation consistency compared to pairwise mutual information

Affine Registration of label maps in Label Space

Two key aspects of coupled multi-object shape\ud analysis and atlas generation are the choice of representation\ud and subsequent registration methods used to align the sample\ud set. For example, a typical brain image can be labeled into\ud three structures: grey matter, white matter and cerebrospinal\ud fluid. Many manipulations such as interpolation, transformation,\ud smoothing, or registration need to be performed on these images\ud before they can be used in further analysis. Current techniques\ud for such analysis tend to trade off performance between the two\ud tasks, performing well for one task but developing problems when\ud used for the other.\ud This article proposes to use a representation that is both\ud flexible and well suited for both tasks. We propose to map object\ud labels to vertices of a regular simplex, e.g. the unit interval for\ud two labels, a triangle for three labels, a tetrahedron for four\ud labels, etc. This representation, which is routinely used in fuzzy\ud classification, is ideally suited for representing and registering\ud multiple shapes. On closer examination, this representation\ud reveals several desirable properties: algebraic operations may\ud be done directly, label uncertainty is expressed as a weighted\ud mixture of labels (probabilistic interpretation), interpolation is\ud unbiased toward any label or the background, and registration\ud may be performed directly.\ud We demonstrate these properties by using label space in a gradient\ud descent based registration scheme to obtain a probabilistic\ud atlas. While straightforward, this iterative method is very slow,\ud could get stuck in local minima, and depends heavily on the initial\ud conditions. To address these issues, two fast methods are proposed\ud which serve as coarse registration schemes following which the\ud iterative descent method can be used to refine the results. Further,\ud we derive an analytical formulation for direct computation of the\ud "group mean" from the parameters of pairwise registration of all\ud the images in the sample set. We show results on richly labeled\ud 2D and 3D data sets

Atlas construction and spatial normalisation to facilitate radiation-induced late effects research in childhood cancer

Reducing radiation-induced side effects is one of the most important challenges in paediatric cancer treatment. Recently, there has been growing interest in using spatial normalisation to enable voxel-based analysis of radiation-induced toxicities in a variety of patient groups. The need to consider three-dimensional distribution of doses, rather than dose-volume histograms, is desirable but not yet explored in paediatric populations. In this paper, we investigate the feasibility of atlas construction and spatial normalisation in paediatric radiotherapy. We used planning computed tomography (CT) scans from twenty paediatric patients historically treated with craniospinal irradiation to generate a template CT that is suitable for spatial normalisation. This childhood cancer population representative template was constructed using groupwise image registration. An independent set of 53 subjects from a variety of childhood malignancies was then used to assess the quality of the propagation of new subjects to this common reference space using deformable image registration (i.e., spatial normalisation). The method was evaluated in terms of overall image similarity metrics, contour similarity and preservation of dose-volume properties. After spatial normalisation, we report a dice similarity coefficient of 0.95±0.05, 0.85±0.04, 0.96±0.01, 0.91±0.03, 0.83±0.06 and 0.65±0.16 for brain and spinal canal, ocular globes, lungs, liver, kidneys and bladder. We then demonstrated the potential advantages of an atlas-based approach to study the risk of second malignant neoplasms after radiotherapy. Our findings indicate satisfactory mapping between a heterogeneous group of patients and the template CT. The poorest performance was for organs in the abdominal and pelvic region, likely due to respiratory and physiological motion and to the highly deformable nature of abdominal organs. More specialised algorithms should be explored in the future to improve mapping in these regions. This study is the first step toward voxel-based analysis in radiation-induced toxicities following paediatric radiotherapy