SCIENTIFIC COMPUTING AND IMAGING INSTITUTE
at the University of Utah

We develop a novel supervised learning/classification method, called disjunctive normal random forest (DNRF). A DNRF is an ensemble of randomly trained disjunctive normal decision trees (DNDT). To construct a DNDT, we formulate each decision tree in the random forest as a disjunction of rules, which are conjunctions of Boolean functions. We then approximate this disjunction of conjunctions with a differentiable function and approach the learning process as a risk minimization problem that incorporates the classification error into a single global objective function. The minimization problem is solved using gradient descent. DNRFs are able to learn complex decision boundaries and achieve low generalization error. We present experimental results demonstrating the improved performance of DNDTs and DNRFs over conventional decision trees and random forests. We also show the superior performance of DNRFs over state-of-the-art classification methods on benchmark datasets.

Keywords: Random forest, Decision tree, Classifier, Supervised learning, Disjunctive normal form

Scene labeling is the problem of assigning an object label to each pixel. It unifies the image segmentation and object recognition problems. The importance of using contextual information in scene labeling frameworks has been widely realized in the field. We propose a contextual framework, called contextual hierarchical model (CHM), which learns contextual information in a hierarchical framework for scene labeling. At each level of the hierarchy, a classifier is trained based on downsampled input images and outputs of previous levels. Our model then incorporates the resulting multi-resolution contextual information into a classifier to segment the input image at original resolution. This training strategy allows for optimization of a joint posterior probability at multiple resolutions through the hierarchy. Contextual hierarchical model is purely based on the input image patches and does not make use of any fragments or shape examples. Hence, it is applicable to a variety of problems such as object segmentation and edge detection. We demonstrate that CHM outperforms state-of-the-art on Stanford background and Weizmann horse datasets. It also outperforms state-of-the-art edge detection methods on NYU depth dataset and achieves state-of-the-art on Berkeley segmentation dataset (BSDS 500).

Temporal modeling frameworks often operate on scalar variables by summarizing data at initial stages as statistical summaries of the underlying distributions. For instance, DTI analysis often employs summary statistics, like mean, for regions of interest and properties along fiber tracts for population studies and hypothesis testing. This reduction via discarding of variability information may introduce significant errors which propagate through the procedures. We propose a novel framework which uses distribution-valued variables to retain and utilize the local variability information. Classic linear regression is adapted to employ these variables for model estimation. The increased stability and reliability of our proposed method when compared with regression using single-valued statistical summaries, is demonstrated in a validation experiment with synthetic data. Our driving application is the modeling of age-related changes along DTI white matter tracts. Results are shown for the spatiotemporal population trajectory of genu tract estimated from 45 healthy infants and compared with a Krabbe's patient.

Keywords: linear regression, distribution-valued data, spatiotemporal growth trajectory, DTI, early neurodevelopment

We present a novel algorithm for computing hierarchical geodesic models (HGMs) for diffeomorphic longitudinal shape analysis. The proposed algorithm exploits the inherent parallelism arising out of the independence in the contributions of individual geodesics to the group geodesic. The previous serial implementation severely limits the use of HGMs to very small population sizes due to computation time and massive memory requirements. The conventional method makes it impossible to estimate the parameters of HGMs on large datasets due to limited memory available onboard current GPU computing devices. The proposed parallel algorithm easily scales to solve HGMs on a large collection of 3D images of several individuals. We demonstrate its effectiveness on longitudinal datasets of synthetically generated shapes and 3D magnetic resonance brain images (MRI).

Keywords: LDDMM, HGM, Vector Momentum, Diffeomorphisms, Longitudinal Analysis

Vector field simplification aims to reduce the complexity of the flow by removing features in order of their relevance and importance, to reveal prominent behavior and obtain a compact representation for interpretation. Most existing simplification techniques based on the topological skeleton successively remove pairs of critical points connected by separatrices, using distance or area-based relevance measures. These methods rely on the stable extraction of the topological skeleton, which can be difficult due to instability in numerical integration, especially when processing highly rotational flows. These geometric metrics do not consider the flow magnitude, an important physical property of the flow. In this paper, we propose a novel simplification scheme derived from the recently introduced topological notion of robustness, which provides a complementary view on flow structure compared to the traditional topological-skeleton-based approaches. Robustness enables the pruning of sets of critical points according to a quantitative measure of their stability, that is, the minimum amount of vector field perturbation required to remove them. This leads to a hierarchical simplification scheme that encodes flow magnitude in its perturbation metric. Our novel simplification algorithm is based on degree theory, has fewer boundary restrictions, and so can handle more general cases. Finally, we provide an implementation under the piecewise-linear setting and apply it to both synthetic and real-world datasets.

Keywords: vector field, topology-based techniques, flow visualization

A key challenge in the study of a time-varying vector fields is to resolve the correspondences between features in successive time steps and to analyze the dynamic behaviors of such features, so-called feature tracking. Commonly tracked features, such as volumes, areas, contours, boundaries, vortices, shock waves and critical points, represent interesting properties or structures of the data. Recently, the topological notion of robustness, a relative of persistent homology, has been introduced to quantify the stability of critical points. Intuitively, the robustness of a critical point is the minimum amount of perturbation necessary to cancel it. In this chapter, we offer a fresh interpretation of the notion of feature tracking, in particular, critical point tracking, through the lens of robustness.We infer correspondences between critical points based on their closeness in stability, measured by robustness, instead of just distance proximities within the domain. We prove formally that robustness helps us understand the sampling conditions under which we can resolve the correspondence problem based on region overlap techniques, and the uniqueness and uncertainty associated with such techniques. These conditions also give a theoretical basis for visualizing the piecewise linear realizations of critical point trajectories over time.

Recently, multi-scale notions of local homology (a variant of persistent homology) have been used to study the local structure of spaces around a given point from a point cloud sample. Current reconstruction guarantees rely on constructing embedded complexes which become diffcult to construct in higher dimensions. We show that the persistence diagrams used for estimating local homology can be approximated using families of Vietoris-Rips complexes, whose simpler construction are robust in any dimension. To the best of our knowledge, our results, for the first time make applications based on local homology, such as stratification learning, feasible in high dimensions.

Image boundaries are a fundamental component of many interactive digital photography techniques, enabling applications such as segmentation, panoramas, and seamless image composition. Interactions for image boundaries often rely on two complimentary but separate approaches: editing via painting or clicking constraints. In this work, we provide a novel, unified approach for interactive editing of pairwise image boundaries that combines the ease of painting with the direct control of constraints. Rather than a sequential coupling, this new formulation allows full use of both interactions simultaneously, giving users unprecedented flexibility for fast boundary editing. To enable this new approach, we provide technical advancements. In particular, we detail a reformulation of image boundaries as a problem of finding cycles, expanding and correcting limitations of the previous work. Our new formulation provides boundary solutions for painted regions with performance on par with state-of-the-art specialized, paint-only techniques. In addition, we provide instantaneous exploration of the boundary solution space with user constraints. Furthermore, we show how to increase performance and decrease memory consumption through novel strategies and/or optional approximations. Finally, we provide examples of common graphics applications impacted by our new approach.

Reconstruction of neural circuits at the microscopic scale of individual neurons and synapses, also known as connectomics, is an important challenge for neuroscience. While an important motivation of connectomics is providing anatomical ground truth for neural circuit models, the ability to decipher neural wiring maps at the individual cell level is also important in studies of many neurodegenerative diseases. Reconstruction of a neural circuit at the individual neuron level requires the use of electron microscopy images due to their extremely high resolution. Computational challenges include pixel-by-pixel annotation of these images into classes such as cell membrane, mitochondria and synaptic vesicles and the segmentation of individual neurons. State-of-the-art image analysis solutions are still far from the accuracy and robustness of human vision and biologists are still limited to studying small neural circuits using mostly manual analysis. In this chapter, we describe our image analysis pipeline that makes use of novel supervised machine learning techniques to tackle this problem.

Dual analysis uses statistics to describe both the dimensions and rows of a high-dimensional dataset. Researchers have integrated it into StratomeX, a Caleydo view for cancer subtype analysis. In addition, significant-difference plots show the elements of a candidate subtype that differ significantly from other subtypes, thus letting analysts characterize subtypes. Analysts can also investigate how data samples relate to their assigned subtype and other groups. This approach lets them create well-defined subtypes based on statistical properties. Three case studies demonstrate the approach's utility, showing how it reproduced findings from a published subtype characterization.

The details of the mechanical factors that modulate angiogenesis remain poorly understood. Previous in vitro studies of angiogenesis using microvessel fragments cultured within collagen constructs demonstrated that neovessel alignment can be induced via mechanical constraint of the boundaries (i.e., boundary conditions). The objective of this study was to investigate the role of mechanical boundary conditions in the regulation of angiogenic alignment and growth in an in vitro model of angiogenesis. Angiogenic microvessels within three-dimensional constructs were subjected to different boundary conditions, thus producing different stress and strain fields during growth. Neovessel outgrowth and orientation were quantified from confocal image data after 6 days. Vascularity and branching decreased as the amount of constraint imposed on the culture increased. In long-axis constrained hexahedral constructs, microvessels aligned parallel to the constrained axis. In contrast, constructs that were constrained along the short axis had random microvessel orientation. Finite element models were used to simulate the contraction of gels under the various boundary conditions and to predict the local strain field experienced by microvessels. Results from the experiments and simulations demonstrated that microvessels aligned perpendicular to directions of compressive strain. Alignment was due to anisotropic deformation of the matrix from cell-generated traction forces interacting with the mechanical boundary conditions. These findings demonstrate that boundary conditions and thus the effective stiffness of the matrix regulate angiogenesis. This study offers a potential explanation for the oriented vascular beds that occur in native tissues and provides the basis for improved control of tissue vascularization in both native tissues and tissue-engineered constructs.

Keywords: angiogenesis, deformation, image analysis, morphometry, orientation, strain

Modeling of early brain growth trajectories from longitudinal MRI will provide new insight into neurodevelopmental characteristics, timing and type of changes in neurological disorders from controls. In addition to an ongoing large-scale infant autism neuroimaging study 1, we recruited 4 infants with Down’s syndrome (DS) in order to evaluate newly developed methods for 4D segmentation from longitudinal infant MRI, and for temporal modeling of brain growth trajectories. Specifically to Down's, a comparison of patterns of full brain and lobar tissue growth may lead to better insight into the observed variability of cognitive development and neurological effects, and may help with development of disease-modifying therapeutic intervention.

Understanding the growth patterns of the early brain is crucial to the study of neuro-development. In the early stages of brain growth, a rapid sequence of biophysical and chemical processes take place. A crucial component of these processes, known as myelination, consists of the formation of a myelin sheath around a nerve fiber, enabling the effective transmission of neural impulses. As the brain undergoes myelination, there is a subsequent change in the contrast between gray matter and white matter as observed in MR scans. In this work, graywhite matter contrast is proposed as an effective measure of appearance which is relatively invariant to location, scanner type, and scanning conditions. To validate this, contrast is computed over various cortical regions for an adult human phantom. MR (Magnetic Resonance) images of the phantom were repeatedly generated using different scanners, and at different locations. Contrast displays less variability over changing conditions of scan compared to intensity-based measures, demonstrating that it is less dependent than intensity on external factors. Additionally, contrast is used to analyze longitudinal MR scans of the early brain, belonging to healthy controls and Down's Syndrome (DS) patients. Kernel regression is used to model subject-specific trajectories of contrast changing with time. Trajectories of contrast changing with time, as well as time-based biomarkers extracted from contrast modeling, show large differences between groups. The preliminary applications of contrast based analysis indicate its future potential to reveal new information not covered by conventional volumetric or deformation-based analysis, particularly for distinguishing between normal and abnormal growth patterns.

Early brain maturational processes such as myelination manifest as changes in the relative appearance of white-gray matter tissue classes in MR images. Imaging modalities such as T1W (T1-Weighted) and T2W (T2-Weighted) MRI each display specific patterns of appearance change associated with distinct neurobiological components of these maturational processes. In this paper we present a framework to jointly model multimodal appearance changes across time for a longitudinal imaging dataset, resulting in quantitative assessment of the patterns of early brain maturation not yet available to clinicians. We measure appearance by quantifying contrast between white and gray matter in terms of the distance between their intensity distributions, a method demonstrated to be relatively stable to interscan variability. A multivariate nonlinear mixed effects (NLME) model is used for joint statistical modeling of this contrast measure across multiple imaging modalities. The multivariate NLME procedure considers correlations between modalities in addition to intra-modal variability. The parameters of the logistic growth function used in NLME modeling provide useful quantitative information about the timing and progression of contrast change in multimodal datasets. Inverted patterns of relative white-gray matter intensity gradient that are observable in T1W scans with respect to T2W scans are characterized by the SIR (Signal Intensity Ratio). The CONTDIR (Contrast Direction) which measures the direction of the gradient at each time point relative to that in the adult-like scan adds a directional attribute to contrast. The major contribution of this paper is a framework for joint multimodal temporal modeling of white-gray matter MRI contrast change and estimation of subject-specific and population growth trajectories. Results confirm qualitative descriptions of growth patterns in pediatric radiology studies and our new quantitative modeling scheme has the potential to advance understanding of variability of brain tissue maturation and to eventually differentiate normal from abnormal growth for early diagnosis of pathology.

Diffusion tensor imaging has become an important modality in the field of neuroimaging to capture changes in micro-organization and to assess white matter integrity or development. While there exists a number of tractography toolsets, these usually lack tools for preprocessing or to analyze diffusion properties along the fiber tracts. Currently, the field is in critical need of a coherent end-to-end toolset for performing an along-fiber tract analysis, accessible to non-technical neuroimaging researchers. The UNC-Utah NA-MIC DTI framework represents a coherent, open source, end-to-end toolset for atlas fiber tract based DTI analysis encompassing DICOM data conversion, quality control, atlas building, fiber tractography, fiber parameterization, and statistical analysis of diffusion properties. Most steps utilize graphical user interfaces (GUI) to simplify interaction and provide an extensive DTI analysis framework for non-technical researchers/investigators. We illustrate the use of our framework on a small sample, cross sectional neuroimaging study of eight healthy 1-year-old children from the Infant Brain Imaging Study (IBIS) Network. In this limited test study, we illustrate the power of our method by quantifying the diffusion properties at 1 year of age on the genu and splenium fiber tracts.

Keywords: neonatal neuroimaging, white matter pathways, magnetic resonance imaging, diffusion tensor imaging, diffusion imaging quality control, DTI atlas building

4D pathological anatomy modeling is key to understanding complex pathological brain images. It is a challenging problem due to the difficulties in detecting multiple appearing and disappearing lesions across time points and estimating dynamic changes and deformations between them. We propose a novel semi-supervised method, called 4D active cut, for lesion recognition and deformation estimation. Existing interactive segmentation methods passively wait for user to refine the segmentations which is a difficult task in 3D images that change over time. 4D active cut instead actively selects candidate regions for querying the user, and obtains the most informative user feedback. A user simply answers 'yes' or 'no' to a candidate object without having to refine the segmentation slice by slice. Compared to single-object detection of the existing methods, our method also detects multiple lesions with spatial coherence using Markov random fields constraints. Results show improvement on the lesion detection, which subsequently improves deformation estimation.

Keywords: Active learning, graph cuts, longitudinal MRI, Markov Random Fields, semi-supervised learning

Automated segmenting and labeling of individual brain anatomical regions, in MRI are challenging, due to the issue of individual structural variability. Although atlas-based segmentation has shown its potential for both tissue and structure segmentation, due to the inherent natural variability as well as disease-related changes in MR appearance, a single atlas image is often inappropriate to represent the full population of datasets processed in a given neuroimaging study. As an alternative for the case of single atlas segmentation, the use of multiple atlases alongside label fusion techniques has been introduced using a set of individual “atlases” that encompasses the expected variability in the studied population. In our study, we proposed a multi-atlas segmentation scheme with a novel graph-based atlas selection technique. We first paired and co-registered all atlases and the subject MR scans. A directed graph with edge weights based on intensity and shape similarity between all MR scans is then computed. The set of neighboring templates is selected via clustering of the graph. Finally, weighted majority voting is employed to create the final segmentation over the selected atlases. This multi-atlas segmentation scheme is used to extend a single-atlas-based segmentation toolkit entitled AutoSeg, which is an open-source, extensible C++ based software pipeline employing BatchMake for its pipeline scripting, developed at the Neuro Image Research and Analysis Laboratories of the University of North Carolina at Chapel Hill. AutoSeg performs N4 intensity inhomogeneity correction, rigid registration to a common template space, automated brain tissue classification based skull-stripping, and the multi-atlas segmentation. The multi-atlas-based AutoSeg has been evaluated on subcortical structure segmentation with a testing dataset of 20 adult brain MRI scans and 15 atlas MRI scans. The AutoSeg achieved mean Dice coefficients of 81.73% for the subcortical structures.

Keywords: segmentation, Registration, MRI, Atlas, Brain, Insight Toolkit

Selecting structures from volume data using direct over-the-visualization interactions, such as a paint brush, is perhaps the most intuitive method in a variety of application scenarios. Unfortunately, it seems difficult to design a universal tool that is effective for all different structures in biology research. In [WOCH12b], an interactive technique was proposed for extracting neural structures from confocal microscopy data. It uses a dual-stroke paint brush to select desired structures directly from volume visualizations. However, the technique breaks down when it was applied to selecting densely packed structures with condensed shapes, such as nuclei from zebrafish eye development research. We collaborated with biologists studying zebrafish eye development and adapted the paint brush tool for real-time nucleus selection from volume data. The morphological diffusion algorithm used in the previous paint brush is restricted to gradient descending directions for improved nucleus boundary definition. Occluded seeds are removed using backward ray-casting. The adapted paint brush is then used in tracking cell movements in a time sequence dataset of a developing zebrafish eye.