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We introduce an approach for the interactive visual analysis of weighted, dynamic networks. These networks arise in areas such as computational neuroscience, sociology, and biology. Network analysis remains challenging due to complex time-varying network behavior. For example, edges disappear/reappear, communities grow/vanish, or overall network topology changes. Our technique, TimeSum, detects the important topological changes in graph data to abstract the dynamic network and visualize one summary representation for each temporal phase, a state. We define a network state as a graph with similar topology over a specific time interval. To enable a holistic comparison of networks, we use a difference network to depict edge and community changes. We present case studies to demonstrate that our methods are effective and useful for extracting and exploring complex dynamic behavior of networks.

This paper studies the influence of the definition of neighborhoods and methods used for creating point connectivity on topological analysis of scalar functions. It is assumed that a scalar function is known only at a finite set of points with associated function values. In order to utilize topological approaches to analyze the scalar-valued point set, it is necessary to choose point neighborhoods and, usually, point connectivity to meaningfully determine critical-point behavior for the point set. Two distances are used to measure the difference in topology when different point neighborhoods and means to define connectivity are used: (i) the bottleneck distance for persistence diagrams and (ii) the distance between merge trees. Usually, these distances define how different scalar functions are with respect to their topology. These measures, when properly adapted to point sets coupled with a definition of neighborhood and connectivity, make it possible to understand how topological characteristics depend on connectivity. Noise is another aspect considered. Five types of neighborhoods and connectivity are discussed: (i) the Delaunay triangulation; (ii) the relative neighborhood graph; (iii) the Gabriel graph; (iv) the k-nearest-neighbor (KNN) neighborhood; and (v) the Vietoris-Rips complex. It is discussed in detail how topological characterizations depend on the chosen connectivity.

We present ECoG ClusterFlow, a novel interactive visual analysis tool for the exploration of high-resolution Electrocorticography (ECoG) data. Our system detects and visualizes dynamic high-level structures, such as communities, using the time-varying spatial connectivity network derived from the high-resolution ECoG data. ECoG ClusterFlow provides a multi-scale visualization of the spatio-temporal patterns underlying the time-varying communities using two views: 1) an overview summarizing the evolution of clusters over time and 2) a hierarchical glyph-based technique that uses data aggregation and small multiples techniques to visualize the propagation of clusters in their spatial domain. ECoG ClusterFlow makes it possible 1) to compare the spatio-temporal evolution patterns across various time intervals, 2) to compare the temporal information at varying levels of granularity, and 3) to investigate the evolution of spatial patterns without occluding the spatial context information. We present case studies done in collaboration with neuroscientists on our team for both simulated and real epileptic seizure data aimed at evaluating the effectiveness of our approach.

Scattered data interpolation and approximation techniques allow for the reconstruction of a scalar field based upon a finite number of scattered samples of the field. In general, the fidelity of the reconstruction with respect to the original scalar field tends to deteriorate as the number of samples decreases. For the situation of very sparse sampling, the results may not be acceptable at all. However, if it is known that the scalar field of interest is correlated with a known flow field - as is the case when the scalar field represents the value of an oceanographic tracer that propagates under the influence of the ocean's flow - then this knowledge can be exploited to enhance the scattered data reconstruction method. One way to exploit flow field information is to use it to construct a modified notion of distance between points. Replacing the standard Euclidean distance metric with a flow-field-aware notion of distance provides a method for extending standard scattered data interpolation methods into flow-based methods that produce superior results for very sparse data. The resulting reconstructions typically have lower root-mean-square errors than reconstructions that do not use the flow information, and qualitatively they often appear physically more realistic.

The visualization and analysis of complex fields often requires identifying and extracting domain specific features. Through a collaboration with geophysicists we extend previous work on crease surfaces with a new and complimentary definition: extremas in principal surface curvature rather than scalar value. Using this definition, we visualize the resulting surfaces which correspond to individual wave fronts. As these wave fronts propagate through a control structure (medium), they undergo changes in intensity, shape and topology due to reflection, refraction and interference. We demonstrate our ability to effectively visualize these phenomena in complex data sets including a large-scale simulation of a hypothetical earthquake along the San Andreas fault in Southern California.

Recent progress in retinal image acquisition techniques, including optical coherence tomography (OCT) and scanning laser ophthalmoscopy (SLO), combined with improved performance of adaptive optics (AO) instrumentation, has resulted in improvement in the quality of in vivo images of cellular structures in the outer layers of the human retina. Despite the significant progress in imaging cone and rod photoreceptor mosaics, visualization of cellular structures in the inner retina has been achieved only with extrinsic contrast agents that have not been approved for use with humans. In this paper we describe the main limiting factors in visualizing inner retinal cells and the methods we implemented to reduce their effects on images acquired with AO-OCT. These include improving the system point spread function (AO performance), monitoring of motion artifacts (retinal motion tracking), and speckle pattern reduction (temporal and spatial averaging). Results of imaging inner retinal morphology and the improvement offered by the new UC Davis AOOCT system with spatio-temporal image averaging are presented. © 2012 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).

Eye movements present during acquisition of a retinal image with optical coherence tomography (OCT) introduce motion artifacts into the image, complicating analysis and registration. This effect is especially pronounced in highresolution data sets acquired with adaptive optics (AO)-OCT instruments. Several retinal tracking systems have been introduced to correct retinal motion during data acquisition. We present a method for correcting motion artifacts in AOOCT volume data after acquisition using simultaneously captured adaptive optics-scanning laser ophthalmoscope (AOSLO) images. We extract transverse eye motion data from the AO-SLO images, assign a motion adjustment vector to each AO-OCT A-scan, and re-sample from the scattered data back onto a regular grid. The corrected volume data improve the accuracy of quantitative analyses of microscopic structures. © 2011 Copyright Society of Photo-Optical Instrumentation Engineers (SPIE).

An accurate solid eye model (with volumetric retinal morphology) has many applications in the field of ophthalmology, including evaluation of ophthalmic instruments and optometry/ophthalmology training. We present a method that uses volumetric OCT retinal data sets to produce an anatomically correct representation of three-dimensional (3D) retinal layers. This information is exported to a laser scan system to re-create it within solid eye retinal morphology of the eye used in OCT testing. The solid optical model eye is constructed from PMMA acrylic, with equivalent optical power to that of the human eye (∼58D). Additionally we tested a water bath eye model from Eyetech Ltd. with a customized retina consisting of five layers of ∼60 μm thick biaxial polypropylene film and hot melt rubber adhesive. © 2010 SPIE.

Topology-based methods have been successfully used for the analysis and visualization of piecewise-linear functions defined on triangle meshes. This paper describes a mechanism for extending these methods to piecewise-quadratic functions defined on triangulations of surfaces. Each triangular patch is tessellated into monotone regions, so that existing algorithms for computing topological representations of piecewise-linear functions may be applied directly to the piecewise-quadratic function. In particular, the tessellation is used for computing the Reeb graph, a topological data structure that provides a succinct representation of level sets of the function. © 2009 World Scientific Publishing Company.

One of the central challenges in modern science is the need to quickly derive knowledge and understanding from large, complex collections of data. We present a new approach that deals with this challenge by combining and extending techniques from high performance visual data analysis and scientific data management. This approach is demonstrated within the context of gaining insight from complex, time-varying datasets produced by a laser wakefield accelerator simulation. Our approach leverages histogram-based parallel coordinates for both visual information display as well as a vehicle for guiding a data mining operation. Data extraction and subsetting are implemented with state-of-the-art index/query technology. This approach, while applied here to accelerator science, is generally applicable to a broad set of science applications, and is implemented in a production-quality visual data analysis infrastructure. We conduct a detailed performance analysis and demonstrate good scalability on a distributed memory Cray XT4 system. © 2008 IEEE.

Topology-based methods have been successfully used for the analysis and visualization of piecewise-linear functions defined on triangle meshes. This paper describes a mechanism for extending these methods to piecewise-quadratic functions defined on triangulations of surfaces. Each triangular patch is tessellated into monotone regions, so that existing algorithms for computing topological representations of piecewise-linear functions may be applied directly to piecewise-quadratic functions. In particular, the tessellation is used for computing the Reeb graph, which provides a succinct representation of level sets of the function. © 2006 Springer-Verlag Berlin/Heidelberg.

The acquisition speed of current FD-OCT (Fourier Domain - Optical Coherence Tomography) instruments allows rapid screening of three-dimensional (3D) volumes of human retinas in clinical settings. To take advantage of this ability requires software used by physicians to be capable of displaying and accessing volumetric data as well as supporting post processing in order to access important quantitative information such as thickness maps and segmented volumes. We describe our clinical FD-OCT system used to acquire 3D data from the human retina over the macula and optic nerve head. B-scans are registered to remove motion artifacts and post-processed with customized 3D visualization and analysis software. Our analysis software includes standard 3D visualization techniques along with a machine learning support vector machine (SVM) algorithm that allows a user to semi-automatically segment different retinal structures and layers. Our program makes possible measurements of the retinal layer thickness as well as volumes of structures of interest, despite the presence of noise and structural deformations associated with retinal pathology. Our software has been tested successfully in clinical settings for its efficacy in assessing 3D retinal structures in healthy as well as diseased cases. Our tool facilitates diagnosis and treatment monitoring of retinal diseases.

Adaptive mesh refinement (AMR) is a technique used in numerical simulations to automatically refine (or de-refine) certain regions of the physical domain in a finite difference calculation. AMR data consists of nested hierarchies of data grids. As AMR visualization is still a relatively unexplored topic, our work is motivated by the need to perform efficient visualization of large AMR data sets. We present a software algorithm for parallel direct volume rendering of AMR data using a cell-projection technique on several different parallel platforms. Our algorithm can use one of several different distribution methods, and we present performance results for each of these alternative approaches. By partitioning an AMR data set into blocks of constant resolution and estimating rendering costs of individual blocks using an application specific benchmark, it is possible to achieve even load balancing.

We present a method for the hierarchical representation of vector fields. Our approach is based on iterative refinement using clustering and principal component analysis. The input to our algorithm is a discrete set of points with associated vectors. The algorithm generates a top-down segmentation of the discrete field by splitting clusters of points. We measure the error of the various approximation levels by measuring the discrepancy between streamlines generated by the original discrete field and its approximations based on much smaller discrete data sets. Our method assumes no particular structure of the field, nor does it require any topological connectivity information. It is possible to generate multiresolution representations of vector fields using this approach.

Although the geometry and kinematics of the first-order structures accommodating Arabia-Eurasia convergence are relatively well known in Turkey and Iran, major shortening structures remain poorly understood within the central portion of the collision zone, in eastern Anatolia and the Caucasus. New remotely sensed neotectonic mapping, synthesis of regional geologic and stratigraphic data, and balanced cross sections suggest that the Kura fold-thrust belt has accommodated the majority of Arabia-Eurasia convergence since the early Pliocene between the longitudes of ~45[degrees]E and ~49[degrees]E. This belt lies southeast of the N80[degrees]W-striking Greater Caucasus Mountains and forms an eastward-narrowing band of elevated topography that roughly parallels the range front for ~400 km along strike. The belt is separated from the Greater Caucasus to the north by the 10- to 25-kin-wide Alazani Basin and comprises a series of predominantly south-verging folds deforming Eocene--Quaternary flysch and molasse. To document structural geometries within the Kura fold-thrust belt, we have used the Real-time Interactive Mapping System (RIMS) software to analyze Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER), visible to near-infrared (VNIR), and digital elevation model (DEM) data. This neotectonic mapping indicates an along-strike, eastward decrease in both structural complexity and the degree to which deformed geomorphic surfaces are dissected. Existing geologic maps indicate a corresponding eastward decrease in the depth of exposure. By integrating the structural geometries determined in our analysis of remote-sensing data with existing geologic data, we have constructed two balanced cross sections, which suggest these systematic along-strike variations result from a west-to-east decrease in total shortening within the Kura fold-thrust belt. We interpret this variable shortening to stem from eastward propagation of the Kura fold-thrust belt. Comparison of our preliminary total shortening estimates with those predicted by current plate motions suggest that the Kura fold-thrust belt has accommodated ~30%-40% (~25 km) of total Arabia-Eurasia convergence since 5 Ma, and thus forms a first-order structural system within the central portion of the collision zone. doi: 10.1130/B26464.1