We are interested in unsupervised reconstruction of complex near-capillary vasculature with thousands of bifurcations where supervision and learning are infeasible. Unsupervised methods can use many structural constraints, e.g. topology, geometry, physics. Common techniques use variants of MST on geodesic tubular graphs minimizing symmetric pairwise costs, i.e. distances. We show limitations of such standard undirected tubular graphs producing typical errors at bifurcations where flow "directedness" is critical. We introduce a new general concept of confluence for continuous oriented curves forming vessel trees and show how to enforce it on discrete tubular graphs. While confluence is a high-order property, we present an efficient practical algorithm for reconstructing confluent vessel trees using minimum arborescence on a directed graph enforcing confluence via simple flow-extrapolating arc construction. Empirical tests on large near-capillary sub-voxel vasculature volumes demonstrate significantly improved reconstruction accuracy at bifurcations. Our code has also been made publicly available1.

We propose a new geometric regularization principle for reconstructing vector fields based on prior knowledge about their divergence. As one important example of this general idea, we focus on vector fields modelling blood flow pattern that should be divergent in arteries and convergent in veins. We show that this previously ignored regularization constraint can significantly improve the quality of vessel tree reconstruction particularly around bifurcations where non-zero divergence is concentrated. Our divergence prior is critical for resolving (binary) sign ambiguity in flow orientations produced by standard vessel filters, \eg Frangi. Our vessel tree centerline reconstruction combines divergence constraints with robust curvature regularization. Our unsupervised method can reconstruct complete vessel trees with near-capillary details on synthetic and real 3D volumes.

Structural changes to the wall of the left atrium are known to occur with conditions that predispose to Atrial fibrillation. Imaging studies have demonstrated that these changes may be detected non-invasively. An important indicator of this structural change is the wall's thickness. Present studies have commonly measured the wall thickness at few discrete locations. Dense measurements with computer algorithms may be possible on cardiac scans of Computed Tomography (CT) and Magnetic Resonance Imaging (MRI). The task is challenging as the atrial wall is a thin tissue and the imaging resolution is a limiting factor. It is unclear how accurate algorithms may get and how they compare in this new emerging area. We approached this problem of comparability with the Segmentation of Left Atrial Wall for Thickness (SLAWT) challenge organised in conjunction with MICCAI 2016 conference. This manuscript presents the algorithms that had participated and evaluation strategies for comparing them on the challenge image database that is now open-source. The image database consisted of cardiac CT (n=10) and MRI (n=10) of healthy and diseased subjects. A total of 6 algorithms were evaluated with different metrics, with 3 algorithms in each modality. Segmentation of the wall with algorithms was found to be feasible in both modalities. There was generally a lack of accuracy in the algorithms and inter-rater differences showed that algorithms could do better. Benchmarks were determined and algorithms were ranked to allow future algorithms to be ranked alongside the state-of-the-art techniques presented in this work. A mean atlas was also constructed from both modalities to illustrate the variation in thickness within this small cohort.

Sensitivity to phase deviations in MRI forms the basis of a variety of techniques, including magnetic susceptibility weighted imaging and chemical shift imaging. Current phase processing techniques fall into two families: those which process the complex image data with magnitude and phase coupled, and phase unwrapping-based techniques that first linearize the phase topology across the image. However, issues, such as low signal and the existence of phase poles, can lead both methods to experience error. Cyclic continuous max-flow (CCMF) phase processing uses primal-dual-variational optimization over a cylindrical manifold, which represent the inherent topology of phase images, increasing its robustness to these issues. CCMF represents a third distinct paradigm in phase processing, being the only technique equipped with the inherent topology of phase. CCMF is robust and efficient with at least comparable accuracy as the prior paradigms.

Many applications in vision require estimation of thin structures such as boundary edges, surfaces, roads, blood vessels, neurons, etc. Unlike most previous approaches, we simultaneously detect and delineate thin structures with sub-pixel localization and real-valued orientation estimation. This is an ill-posed problem that requires regularization. We propose an objective function combining detection likelihoods with a prior minimizing curvature of the center-lines or surfaces. Unlike simple block-coordinate descent, we develop a novel algorithm that is able to perform joint optimization of location and detection variables more effectively. Our lower bound optimization algorithm applies to quadratic or absolute curvature. The proposed early vision framework is sufficiently general and it can be used in many higher-level applications. We illustrate the advantage of our approach on a range of 2D and 3D examples.

Phase contrast magnetic resonance imaging (MRI) can provide in vivo myocardial velocity field measurements. These data allow densely spaced material points to be tracked throughout the whole heart cycle using, for example, the Fourier tracking algorithm. To process the tracking results for myocardial deformation and strain quantification, we developed a method that is based on fitting the tracking results to an appropriate local deformation model. We further analyzed the accuracy and precision of the method and provided performance predictions for several local models. In order to validate the method and the theoretical performance analysis, we conducted controlled computer simulations and a phantom study. The results agreed well with expectations. Human heart data were also acquired and analyzed, and provided encouraging results. At the signal-to-noise ratio (SNR) level and spatial resolution expected in clinical settings, the study predicts strain quantification accuracy and precision that may allow the technique to become a practical and powerful noninvasive approach for the study of cardiac function, although clinically acceptable data acquisition strategies for three-dimensional (3-D) data are still a challenge.