The Generalized Log-Ratio Transformation: Learning Shape and Adjacency Priors for Simultaneous Thigh Muscle Segmentation.

We present a novel probabilistic shape representation that implicitly includes prior anatomical volume and adjacency information, termed the generalized log-ratio (GLR) representation. We demonstrate the usefulness of this representation in the task of thigh muscle segmentation. Analysis of the shapes and sizes of thigh muscles can lead to a better understanding of the effects of chronic obstructive pulmonary disease (COPD), which often results in skeletal muscle weakness in lower limbs. However, segmenting these muscles from one another is difficult due to a lack of distinctive features and inter-muscular boundaries that are difficult to detect. We overcome these difficulties by building a shape model in the space of GLR representations. We remove pose variability from the model by employing a presegmentation-based alignment scheme. We also design a rotationally invariant random forest boundary detector that learns common appearances of the interface between muscles from training data. We combine the shape model and the boundary detector into a fully automatic globally optimal segmentation technique. Our segmentation technique produces a probabilistic segmentation that can be used to generate uncertainty information, which can be used to aid subsequent analysis. Our experiments on challenging 3D magnetic resonance imaging data sets show that the use of the GLR representation improves the segmentation accuracy, and yields an average Dice similarity coefficient of 0.808 ±0.074, comparable to other state-of-the-art thigh segmentation techniques.

Topology preservation and anatomical feasibility in random walker image registration.

The random walker image registration (RWIR) method is a powerful tool for aligning medical images that also provides useful uncertainty information. However, it is difficult to ensure topology preservation in RWIR, which is an important property in medical image registration as it is often necessary for the anatomical feasibility of an alignment. In this paper, we introduce a technique for determining spatially adaptive regularization weights for RWIR that ensure an anatomically feasible transformation. This technique only increases the run time of the RWIR algorithm by about 10%, and avoids over-smoothing by only increasing regularization in specific image regions. Our results show that our technique ensures topology preservation and improves registration accuracy.

Structural network analysis of brain development in young preterm neonates.

Preterm infants develop differently than those born at term and are at higher risk of brain pathology. Thus, an understanding of their development is of particular importance. Diffusion tensor imaging (DTI) of preterm infants offers a window into brain development at a very early age, an age at which that development is not yet fully understood. Recent works have used DTI to analyze structural connectome of the brain scans using network analysis. These studies have shown that, even from infancy, the brain exhibits small-world properties. Here we examine a cohort of 47 normal preterm neonates (i.e., without brain injury and with normal neurodevelopment at 18 months of age) scanned between 27 and 45 weeks post-menstrual age to further the understanding of how the structural connectome develops. We use full-brain tractography to find white matter tracts between the 90 cortical and sub-cortical regions defined in the University of North Carolina Chapel Hill neonatal atlas. We then analyze the resulting connectomes and explore the differences between weighting edges by tract count versus fractional anisotropy. We observe that the brain networks in preterm infants, much like infants born at term, show high efficiency and clustering measures across a range of network scales. Further, the development of many individual region-pair connections, particularly in the frontal and occipital lobes, is significantly correlated with age. Finally, we observe that the preterm infant connectome remains highly efficient yet becomes more clustered across this age range, leading to a significant increase in its small-world structure.

The isometric log-ratio transform for probabilistic multi-label anatomical shape representation.

Sources of uncertainty in the boundaries of structures in medical images have motivated the use of probabilistic labels in segmentation applications. An important component in many medical image segmentation tasks is the use of a shape model, often generated by applying statistical techniques to training data. Standard statistical techniques (e.g., principal component analysis) often assume data lies in an unconstrained vector space, but probabilistic labels are constrained to the unit simplex. If these statistical techniques are used directly on probabilistic labels, relative uncertainty information can be sacrificed. A standard method for facilitating analysis of probabilistic labels is to map them to a vector space using the LogOdds transform. However, the LogOdds transform is asymmetric in one of the labels, which skews results in some applications. The isometric log-ratio (ILR) transform is a symmetrized version of the LogOdds transform, and is so named as it is an isometry between the Aitchison geometry, the inherent geometry of the simplex, and standard Euclidean geometry. We explore how to interpret the Aitchison geometry when applied to probabilistic labels in medical image segmentation applications. We demonstrate the differences when applying the LogOdds transform or the ILR transform to probabilistic labels prior to statistical analysis. Specifically, we show that statistical analysis of ILR transformed data better captures the variability of anatomical shapes in cases where multiple different foreground regions share boundaries (as opposed to foreground-background boundaries).

Probabilistic multi-shape segmentation of knee extensor and flexor muscles.

Patients with chronic obstructive pulmonary disease (COPD) often exhibit skeletal muscle weakness in lower limbs. Analysis of the shapes and sizes of these muscles can lead to more effective therapy. Unfortunately, segmenting these muscles from one another is a challenging task due to a lack of image information in many areas. We present a fully automatic segmentation method that overcomes the inherent difficulties of this problem to accurately segment the different muscles. Our method enforces a multi-region shape prior on the segmentation to ensure feasibility and provides an energy minimizing probabilistic segmentation that indicates areas of uncertainty. Our experiments on 3D MRI datasets yield an average Dice similarity coefficient of 0.92 +/- 0.03 with the ground truth.

Fast random walker with priors using precomputation for interactive medical image segmentation.

Updating segmentation results in real-time based on repeated user input is a reliable way to guarantee accuracy, paramount in medical imaging applications, while making efficient use of an expert's time. The random walker algorithm with priors is a robust method able to find a globally optimal probabilistic segmentation with an intuitive method for user input. However, like many other segmentation algorithms, it can be too slow for real-time user interaction. We propose a speedup to this popular algorithm based on offline precomputation, taking advantage of the time images are stored on servers prior to an analysis session. Our results demonstrate the benefits of our approach. For example, the segmentations found by the original random walker and by our new precomputation method for a given 3D image have a Dice's similarity coefficient of 0.975, yet our method runs in 1/25th of the time.

Monte Carlo study of degenerate ground states and residual entropy in a frustrated honeycomb lattice Ising model.

We study a classical fully frustrated honeycomb lattice Ising model using Markov-chain Monte Carlo methods and exact calculations. The Hamiltonian realizes a degenerate ground-state manifold of equal-energy states, where each hexagonal plaquette of the lattice has one and only one unsatisfied bond, with an extensive residual entropy that grows as the number of spins N. Traditional single-spin-flip Monte Carlo methods fail to sample all possible spin configurations in this ground state efficiently, due to their separation by large energy barriers. We develop a nonlocal "chain-flip" algorithm that solves this problem, and demonstrate its effectiveness on the Ising Hamiltonian with and without perturbative interactions. The two perturbations considered are a slightly weakened bond and an external magnetic field h. For some cases, the chain-flip move is necessary for the simulation to find an ordered ground state. In the case of the magnetic field, two magnetized ground states with nonextensive entropy are found, and two special values of h exist where the residual entropy again becomes extensive, scaling proportionally to N ln phi, where phi is the golden ratio.