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

BInGo: Bayesian Intrinsic Groupwise Registration via Explicit Hierarchical Disentanglement

Multimodal groupwise registration aligns internal structures in a group of medical images. Current approaches to this problem involve developing similarity measures over the joint intensity profile of all images, which may be computationally prohibitive for large image groups and unstable under various conditions. To tackle these issues, we propose BInGo, a general unsupervised hierarchical Bayesian framework based on deep learning, to learn intrinsic structural representations to measure the similarity of multimodal images. Particularly, a variational auto-encoder with a novel posterior is proposed, which facilitates the disentanglement learning of structural representations and spatial transformations, and characterizes the imaging process from the common structure with shape transition and appearance variation. Notably, BInGo is scalable to learn from small groups, whereas being tested for large-scale groupwise registration, thus significantly reducing computational costs. We compared BInGo with five iterative or deep learning methods on three public intrasubject and intersubject datasets, i.e. BraTS, MS-CMR of the heart, and Learn2Reg abdomen MR-CT, and demonstrated its superior accuracy and computational efficiency, even for very large group sizes (e.g., over 1300 2D images from MS-CMR in each group)

Infant Brain Atlases from Neonates to 1- and 2-Year-Olds

Background: Studies for infants are usually hindered by the insufficient image contrast, especially for neonates. Prior knowledge, in the form of atlas, can provide additional guidance for the data processing such as spatial normalization, label propagation, and tissue segmentation. Although it is highly desired, there is currently no such infant atlas which caters for all these applications. The reason may be largely due to the dramatic early brain development, image processing difficulties, and the need of a large sample size. Methodology: To this end, after several years of subject recruitment and data acquisition, we have collected a unique longitudinal dataset, involving 95 normal infants (56 males and 39 females) with MRI scanned at 3 ages, i.e., neonate, 1-yearold, and 2-year-old. State-of-the-art MR image segmentation and registration techniques were employed, to construct which include the templates (grayscale average images), tissue probability maps (TPMs), and brain parcellation maps (i.e., meaningful anatomical regions of interest) for each age group. In addition, the longitudinal correspondences between agespecific atlases were also obtained. Experiments of typical infant applications validated that the proposed atlas outperformed other atlases and is hence very useful for infant-related studies. Conclusions: We expect that the proposed infant 0–1–2 brain atlases would be significantly conducive to structural and functional studies of the infant brains. These atlases are publicly available in our website

Video Interpolation using Optical Flow and Laplacian Smoothness

Non-rigid video interpolation is a common computer vision task. In this paper we present an optical flow approach which adopts a Laplacian Cotangent Mesh constraint to enhance the local smoothness. Similar to Li et al., our approach adopts a mesh to the image with a resolution up to one vertex per pixel and uses angle constraints to ensure sensible local deformations between image pairs. The Laplacian Mesh constraints are expressed wholly inside the optical flow optimization, and can be applied in a straightforward manner to a wide range of image tracking and registration problems. We evaluate our approach by testing on several benchmark datasets, including the Middlebury and Garg et al. datasets. In addition, we show application of our method for constructing 3D Morphable Facial Models from dynamic 3D data

Detailing patient specific modelling to aid clinical decision-making

The anatomy of the craniofacial skeleton has been described through the aid of dissection identifying hard and soft tissue structures. Although the macro and microscopic investigation of internal facial tissues have provided invaluable information on constitution of the tissues it is important to inspect and model facial tissues in the living individual. Detailing the form and function of facial tissues will be invaluable in clinical diagnoses and planned corrective surgical interventions such as management of facial palsies and craniofacial disharmony/anomalies. Recent advances in lower-cost, non-invasive imaging and computing power (surface scanning, Cone Beam Computerized Tomography (CBCT) and Magnetic Resonance (MRI)) has enabled the ability to capture and process surface and internal structures to a high resolution. The three-dimensional surface facial capture has enabled characterization of facial features all of which will influence subtleties in facial movement and surgical planning. This chapter will describe the factors that influence facial morphology in terms of gender and age differences, facial movement—surface and underlying structures, modeling based on average structures, orientation of facial muscle fibers, biomechanics of movement—proof of principle and surgical intervention

Segmentation of image ensembles via latent atlases

Spatial priors, such as probabilistic atlases, play an important role in MRI segmentation. However, the availability of comprehensive, reliable and suitable manual segmentations for atlas construction is limited. We therefore propose a method for joint segmentation of corresponding regions of interest in a collection of aligned images that does not require labeled training data. Instead, a latent atlas, initialized by at most a single manual segmentation, is inferred from the evolving segmentations of the ensemble. The algorithm is based on probabilistic principles but is solved using partial differential equations (PDEs) and energy minimization criteria. We evaluate the method on two datasets, segmenting subcortical and cortical structures in a multi-subject study and extracting brain tumors in a single-subject multi-modal longitudinal experiment. We compare the segmentation results to manual segmentations, when those exist, and to the results of a state-of-the-art atlas-based segmentation method. The quality of the results supports the latent atlas as a promising alternative when existing atlases are not compatible with the images to be segmented.National Institutes of Health (U.S.) (National Institute for Biomedical Imaging and Bioengineering (U.S.)/National Alliance for Medical Image Computing (U.S.) U54-EB005149)National Institutes of Health (U.S.) (National Center for Research Resources (U.S.)/Neuroimaging Analysis Center (U.S.) P41-RR13218)National Institutes of Health (U.S.) (National Institute of Neurological Disorders and Stroke (U.S.) R01-NS051826)National Institutes of Health (U.S.) (National Center for Research Resources (U.S.)/Biomedical Informatics Research Network U24-RR021382)National Science Foundation (U.S.) (CAREER Award 0642971)German Academy of Sciences Leopoldina (Fellowship LPDS 2009-10)Academy of Finland (Grant 133611

Tracking, Detection and Registration in Microscopy Material Images

Fast and accurate characterization of fiber micro-structures plays a central role for material scientists to analyze physical properties of continuous fiber reinforced composite materials. In materials science, this is usually achieved by continuously crosssectioning a 3D material sample for a sequence of 2D microscopic images, followed by a fiber detection/tracking algorithm through the obtained image sequence. To speed up this process and be able to handle larger-size material samples, we propose sparse sampling with larger inter-slice distance in cross sectioning and develop a new algorithm that can robustly track large-scale fibers from such a sparsely sampled image sequence. In particular, the problem is formulated as multi-target tracking and Kalman filters are applied to track each fiber along the image sequence. One main challenge in this tracking process is to correctly associate each fiber to its observation given that 1) fiber observations are of large scale, crowded and show very similar appearances in a 2D slice, and 2) there may be a large gap between the predicted location of a fiber and its observation in the sparse sampling. To address this challenge, a novel group-wise association algorithm is developed by leveraging the fact that fibers are implanted in bundles and the fibers in the same bundle are highly correlated through the image sequence. Tracking-by-detection algorithms rely heavily on detection accuracy, especially the recall performance. The state-of-the-art fiber detection algorithms perform well under ideal conditions, but are not accurate where there are local degradations of image quality, due to contaminants on the material surface and/or defocus blur. Convolutional Neural Networks (CNN) could be used for this problem, but would require a large number of manual annotated fibers, which are not available. We propose an unsupervised learning method to accurately detect fibers on the large scale, which is robust against local degradations of image quality. The proposed method does not require manual annotations, but uses fiber shape/size priors and spatio-temporal consistency in tracking to simulate the supervision in the training of the CNN. Due to the significant microscope movement during the data acquisition, the sampled microscopy images might be not well aligned, which increases the difficulties for further large-scale fiber tracking. In this dissertation, we design an object tracking system which could accurately track large-scale fibers and simultaneously perform satisfactory image registration. Large-scale fiber tracking task is accomplished by Kalman filters based tracking methods. With the assistance of fiber tracking, the image registration is performed in a coarse-to-fine way. To evaluate the proposed methods, a dataset was collected by Air Force Research Laboratories (AFRL). The material scientists in AFRL used a serial sectioning instrument to cross-section the 3D material samples. During sample preparation, the samples are ground, cleaned, and then imaged. Experimental results on this collected dataset have demonstrated that the proposed methods yield significant improvements in large-scale fiber tracking and detection, together with satisfactory image registration

Externalities in the Matching of Workers and Firms in Britain

We provide empirical evidence on the nature of spatial externalities in a matching model for the UK. We use a monthly panel of outflows, unemployment and vacancy stocks data from the registers at Jobcentres in the UK; these are mapped on to travel-to-work areas. We find evidence of significant spill-over effects that are generally in line with the predictions of theory. For example, we find that conditional on local labour market conditions, high unemployment levels in neighbouring areas raise the number of local filled vacancies but lower the local outflow from unemployment.matching model, externalities, spatial dependence, unemployment outflows