Density ridge manifold traversal

The density ridge framework for estimating principal curves and surfaces has in a number of recent works been shown to capture manifold structure in data in an intuitive and effective manner. However, to date there exists no efficient way to traverse these manifolds as defined by density ridges. This is unfortunate, as manifold traversal is an important problem for example for shape estimation in medical imaging, or in general for being able to characterize and understand state transitions or local variability over the data manifold. In this paper, we remedy this situation by introducing a novel manifold traversal algorithm based on geodesics within the density ridge approach. The traversal is executed in a subspace capturing the intrinsic dimensionality of the data using dimensionality reduction techniques such as principal component analysis or kernel entropy component analysis. A mapping back to the ambient space is obtained by training a neural network. We compare against maximum mean discrepancy traversal, a recent approach, and obtain promising results

Cartography of high-dimensional flows: A visual guide to sections and slices

Symmetry reduction by the method of slices quotients the continuous symmetries of chaotic flows by replacing the original state space by a set of charts, each covering a neighborhood of a dynamically important class of solutions, qualitatively captured by a `template'. Together these charts provide an atlas of the symmetry-reduced `slice' of state space, charting the regions of the manifold explored by the trajectories of interest. Within the slice, relative equilibria reduce to equilibria and relative periodic orbits reduce to periodic orbits. Visualizations of these solutions and their unstable manifolds reveal their interrelations and the role they play in organizing turbulence/chaos.Comment: 12 Pages, 12 figure

Multiscale medial shape-based analysis of image objects

pre-printMedial representation of a three-dimensional (3-D) object or an ensemble of 3-D objects involves capturing the object interior as a locus of medial atoms, each atom being two vectors of equal length joined at the tail at the medial point. Medial representation has a variety of beneficial properties, among the most important of which are 1) its inherent geometry, provides an object-intrinsic coordinate system and thus provides correspondence between instances of the object in and near the object(s); 2) it captures the object interior and is, thus, very suitable for deformation; and 3) it provides the basis for an intuitive object-based multiscale sequence leading to efficiency of segmentation algorithms and trainability of statistical characterizations with limited training sets. As a result of these properties, medial representation is particularly suitable for the following image analysis tasks; how each operates will be described and will be illustrated by results: 1) segmentation of objects and object complexes via deformable models; 2) segmentation of tubular trees, e.g., of blood vessels, by following height ridges of measures of fit of medial atoms to target images; 3) object-based image registration via medial loci of such blood vessel trees; 4) statistical characterization of shape differences between control and pathological classes of structures. These analysis tasks are made possible by a new form of medial representation called m-reps, which is described

Geometry-Driven Detection, Tracking and Visual Analysis of Viscous and Gravitational Fingers

Viscous and gravitational flow instabilities cause a displacement front to break up into finger-like fluids. The detection and evolutionary analysis of these fingering instabilities are critical in multiple scientific disciplines such as fluid mechanics and hydrogeology. However, previous detection methods of the viscous and gravitational fingers are based on density thresholding, which provides limited geometric information of the fingers. The geometric structures of fingers and their evolution are important yet little studied in the literature. In this work, we explore the geometric detection and evolution of the fingers in detail to elucidate the dynamics of the instability. We propose a ridge voxel detection method to guide the extraction of finger cores from three-dimensional (3D) scalar fields. After skeletonizing finger cores into skeletons, we design a spanning tree based approach to capture how fingers branch spatially from the finger skeletons. Finally, we devise a novel geometric-glyph augmented tracking graph to study how the fingers and their branches grow, merge, and split over time. Feedback from earth scientists demonstrates the usefulness of our approach to performing spatio-temporal geometric analyses of fingers.Comment: Published at IEEE Transactions on Visualization and Computer Graphic

Surface Shape Perception in Volumetric Stereo Displays

In complex volume visualization applications, understanding the displayed objects and their spatial relationships is challenging for several reasons. One of the most important obstacles is that these objects can be translucent and can overlap spatially, making it difficult to understand their spatial structures. However, in many applications, for example medical visualization, it is crucial to have an accurate understanding of the spatial relationships among objects. The addition of visual cues has the potential to help human perception in these visualization tasks. Descriptive line elements, in particular, have been found to be effective in conveying shape information in surface-based graphics as they sparsely cover a geometrical surface, consistently following the geometry. We present two approaches to apply such line elements to a volume rendering process and to verify their effectiveness in volume-based graphics. This thesis reviews our progress to date in this area and discusses its effects and limitations. Specifically, it examines the volume renderer implementation that formed the foundation of this research, the design of the pilot study conducted to investigate the effectiveness of this technique, the results obtained. It further discusses improvements designed to address the issues revealed by the statistical analysis. The improved approach is able to handle visualization targets with general shapes, thus making it more appropriate to real visualization applications involving complex objects

Computerized Analysis of Magnetic Resonance Images to Study Cerebral Anatomy in Developing Neonates

The study of cerebral anatomy in developing neonates is of great importance for the understanding of brain development during the early period of life. This dissertation therefore focuses on three challenges in the modelling of cerebral anatomy in neonates during brain development. The methods that have been developed all use Magnetic Resonance Images (MRI) as source data. To facilitate study of vascular development in the neonatal period, a set of image analysis algorithms are developed to automatically extract and model cerebral vessel trees. The whole process consists of cerebral vessel tracking from automatically placed seed points, vessel tree generation, and vasculature registration and matching. These algorithms have been tested on clinical Time-of- Flight (TOF) MR angiographic datasets. To facilitate study of the neonatal cortex a complete cerebral cortex segmentation and reconstruction pipeline has been developed. Segmentation of the neonatal cortex is not effectively done by existing algorithms designed for the adult brain because the contrast between grey and white matter is reversed. This causes pixels containing tissue mixtures to be incorrectly labelled by conventional methods. The neonatal cortical segmentation method that has been developed is based on a novel expectation-maximization (EM) method with explicit correction for mislabelled partial volume voxels. Based on the resulting cortical segmentation, an implicit surface evolution technique is adopted for the reconstruction of the cortex in neonates. The performance of the method is investigated by performing a detailed landmark study. To facilitate study of cortical development, a cortical surface registration algorithm for aligning the cortical surface is developed. The method first inflates extracted cortical surfaces and then performs a non-rigid surface registration using free-form deformations (FFDs) to remove residual alignment. Validation experiments using data labelled by an expert observer demonstrate that the method can capture local changes and follow the growth of specific sulcus