Topology‐based Visualization of Transformation Pathways in Complex Chemical Systems

Studying transformation in a chemical system by considering its energy as a function of coordinates of the system's components provides insight and changes our understanding of this process. Currently, a lack of effective visualization techniques for high‐dimensional energy functions limits chemists to plot energy with respect to one or two coordinates at a time. In some complex systems, developing a comprehensive understanding requires new visualization techniques that show relationships between all coordinates at the same time. We propose a new visualization technique that combines concepts from topological analysis, multi‐dimensional scaling, and graph layout to enable the analysis of energy functions for a wide range of molecular structures. We demonstrate our technique by studying the energy function of a dimer of formic and acetic acids and a LTA zeolite structure, in which we consider diffusion of methane.     

Abstractive Representation and Exploration of Hierarchically Clustered Diffusion Tensor Fiber Tracts

Diffusion tensor imaging (DTI) has been used to generate fibrous structures in both brain white matter and muscles. Fiber clustering groups the DTI fibers into spatially and anatomically related tracts. As an increasing number of fiber clustering methods have been recently developed, it is important to display, compare, and explore the clustering results efficiently and effectively. In this paper, we present an anatomical visualization technique that reduces the geometric complexity of the fiber tracts and emphasizes the high‐level structures. Beginning with a volumetric diffusion tensor image, we first construct a hierarchical clustering representation of the fiber bundles. These bundles are then reformulated into a 3D multi‐valued volume data. We then build a set of geometric hulls and principal fibers to approximate the shape and orientation of each fiber bundle. By simultaneously visualizing the geometric hulls, individual fibers, and other data sets such as fractional anisotropy, the overall shape of the fiber tracts are highlighted, while preserving the fibrous details. A rater with expert knowledge of white matter structure has evaluated the resulting interactive illustration and confirmed the improvement over straightforward DTI fiber tract visualization.     

Visualizing Strain Anisotropy in Mantle Flow Fields

The evolution of strain and development of material anisotropy in models of the Earth’s mantle flow convey important information about how to interpret the geometric relationship between observation of seismic anisotropy and the actual mantle flow field. By combining feature extraction techniques such as path line integration and tensor accumulation, we compute time‐varying strain vector fields that build the foundation for a number of feature extraction and visualization techniques. The proposed field segmentation, clustering, histograms and multi‐volume visualization techniques facilitate an intuitive understanding of three‐dimensional strain in such flow fields, overcoming limitations of previous methods such as 2‐D line plots and slicing. We present applications of our approach to an artificial time varying flow data set and a real world example of stationary flow in a subduction zone and discuss the challenges of processing these geophysical data sets as well as the insights gained.     

Illustrative Hybrid Visualization and Exploration of Anatomical and Functional Brain Data

Common practice in brain research and brain surgery involves the multi‐modal acquisition of brain anatomy and brain activation data. These highly complex three‐dimensional data have to be displayed simultaneously in order to convey spatial relationships. Unique challenges in information and interaction design have to be solved in order to keep the visualization sufficiently complete and uncluttered at the same time. The visualization method presented in this paper addresses these issues by using a hybrid combination of polygonal rendering of brain structures and direct volume rendering of activation data. Advanced rendering techniques including illustrative display styles and ambient occlusion calculations enhance the clarity of the visual output. The presented rendering pipeline produces real‐time frame rates and offers a high degree of configurability. Newly designed interaction and measurement tools are provided, which enable the user to explore the data at large, but also to inspect specific features closely. We demonstrate the system in the context of a cognitive neurosciences dataset. An initial informal evaluation shows that our visualization method is deemed useful for clinical research.     

Visual Analysis of Confocal Raman Spectroscopy Data using Cascaded Transfer Function Design

2D Confocal Raman Microscopy (CRM) data consist of high dimensional per‐pixel spectral data of 1000 bands and allows for complex spectral and spatial‐spectral analysis tasks, i.e., in material discrimination, material thickness, and spatial material distributions. Currently, simple integral methods are commonly applied as visual analysis solutions to CRM data which exhibit restricted discrimination power in various regards. In this paper we present a novel approach for the visual analysis of 2D multispectral CRM data using multi‐variate visualization techniques. Due to the large amount of data and the demand of an explorative approach without a‐priori restriction, our system allows for arbitrary interactive (de)selection of varaibles w/o limitation and an unrestricted online definition/construction of new, combined properties. Our approach integrates CRM specific quantitative measures and handles material‐related features for mixed materials in a quantitative manner. Technically, we realize the online definition/construction of new, combined properties as semi‐automatic, cascaded, 1D and 2D multidimensional transfer functions (MD‐TFs). By interactively incorporating new (raw or derived) properties, the dimensionality of the MD‐TF space grows during the exploration procedure and is virtually unlimited. The final visualization is achieved by an enhanced color mixing step which improves saturation and contrast.     

Visualizing High‐Dimensional Structures by Dimension Ordering and Filtering using Subspace Analysis

High‐dimensional data visualization is receiving increasing interest because of the growing abundance of high‐dimensional datasets. To understand such datasets, visualization of the structures present in the data, such as clusters, can be an invaluable tool. Structures may be present in the full high‐dimensional space, as well as in its subspaces. Two widely used methods to visualize high‐dimensional data are the scatter plot matrix (SPM) and the parallel coordinate plot (PCP). SPM allows a quick overview of the structures present in pairwise combinations of dimensions. On the other hand, PCP has the potential to visualize not only bi‐dimensional structures but also higher dimensional ones. A problem with SPM is that it suffers from crowding and clutter which makes interpretation hard. Approaches to reduce clutter are available in the literature, based on changing the order of the dimensions. However, usually this reordering has a high computational complexity. For effective visualization of high‐dimensional structures, also PCP requires a proper ordering of the dimensions. In this paper, we propose methods for reordering dimensions in PCP in such a way that high‐dimensional structures (if present) become easier to perceive. We also present a method for dimension reordering in SPM which yields results that are comparable to those of existing approaches, but at a much lower computational cost. Our approach is based on finding relevant subspaces for clustering using a quality criterion and cluster information. The quality computation and cluster detection are done in image space, using connected morphological operators. We demonstrate the potential of our approach for synthetic and astronomical datasets, and show that our method compares favorably with a number of existing approaches.     

Visual Analysis of Multi‐Dimensional Categorical Data Sets

We present a set of interactive techniques for the visual analysis of multi‐dimensional categorical data. Our approach is based on multiple correspondence analysis (MCA), which allows one to analyse relationships, patterns, trends and outliers among dependent categorical variables. We use MCA as a dimensionality reduction technique to project both observations and their attributes in the same 2D space. We use a treeview to show attributes and their domains, a histogram of their representativity in the data set and as a compact overview of attribute‐related facts. A second view shows both attributes and observations. We use a Voronoi diagram whose cells can be interactively merged to discover salient attributes, cluster values and bin categories. Bar chart legends help assigning meaning to the 2D view axes and 2D point clusters. We illustrate our techniques with real‐world application data.     

Piece wise Laplacian‐based Projection for Interactive Data Exploration and Organization

Multidimensional projection has emerged as an important visualization tool in applications involving the visual analysis of high‐dimensional data. However, high precision projection methods are either computationally expensive or not flexible enough to enable feedback from user interaction into the projection process. A built‐in mechanism that dynamically adapts the projection based on direct user intervention would make the technique more useful for a larger range of applications and data sets. In this paper we propose the Piecewise Laplacian‐based Projection (PLP), a novel multidimensional projection technique, that, due to the local nature of its formulation, enables a versatile mechanism to interact with projected data and to allow interactive changes to alter the projection map dynamically, a capability unique of this technique. We exploit the flexibility provided by PLP in two interactive projection‐based applications, one designed to organize pictures visually and another to build music playlists. These applications illustrate the usefulness of PLP in handling high‐dimensional data in a flexible and highly visual way. We also compare PLP with the currently most promising projections in terms of precision and speed, showing that it performs very well also according to these quality criteria.     

Visualization of Particle‐based Data with Transparency and Ambient Occlusion

Particle‐based simulation techniques, like the discrete element method or molecular dynamics, are widely used in many research fields. In real‐time explorative visualization it is common to render the resulting data using opaque spherical glyphs with local lighting only. Due to massive overlaps, however, inner structures of the data are often occluded rendering visual analysis impossible. Furthermore, local lighting is not sufficient as several important features like complex shapes, holes, rifts or filaments cannot be perceived well. To address both problems we present a new technique that jointly supports transparency and ambient occlusion in a consistent illumination model. Our approach is based on the emission‐absorption model of volume rendering. We provide analytic solutions to the volume rendering integral for several density distributions within a spherical glyph. Compared to constant transparency our approach preserves the three‐dimensional impression of the glyphs much better. We approximate ambient illumination with a fast hierarchical voxel cone‐tracing approach, which builds on a new real‐time voxelization of the particle data. Our implementation achieves interactive frame rates for millions of static or dynamic particles without any preprocessing. We illustrate the merits of our method on real‐world data sets gaining several new insights.     

Automatic Registration of Multi‐Projector Domes Using a Single Uncalibrated Camera

In this paper we present a novel technique for easily calibrating multiple casually aligned projectors on spherical domes using a single uncalibrated camera. Using the prior knowledge of the display surface being a dome, we can estimate the camera intrinsic and extrinsic parameters and the projector to display surface correspondences automatically using a set of images. These images include the image of the dome itself and a projected pattern from each projector. Using these correspondences we can register images from the multiple projectors on the dome. Further, we can register displays which are not entirely visible in a single camera view using multiple pan and tilted views of an uncalibrated camera making our method suitable for displays of different size and resolution. We can register images from any arbitrary viewpoint making it appropriate for a single head‐tracked user in a 3D visualization system. Also, we can use several cartographic mapping techniques to register images in a manner that is appropriate for multi‐user visualization. Domes are known to produce a tremendous sense of immersion and presence in visualization systems. Yet, till date, there exists no easy way to register multiple projectors on a dome to create a high‐resolution realistic visualizations. To the best of our knowledge, this is the first method that can achieve accurate geometric registration of multiple projectors on a dome simply and automatically using a single uncalibrated camera.     

Time‐Series Plots Integrated in Parallel‐Coordinates Displays

We present a natural extension of two‐dimensional parallel‐coordinates plots for revealing relationships in time‐dependent multi‐attribute data by building on the idea that time can be considered as the third dimension. A time slice through the visualization represents a certain point in time and can be viewed as a regular parallel‐coordinates display. A vertical slice through one of the axes of the parallel‐coordinates display would show a time‐series plot. For a focus‐and‐context Integration of both views, we embed time‐series plots between two adjacent axes of the parallel‐coordinates plot. Both time‐series plots are drawn using a pseudo three‐dimensional perspective with a single vanishing point. An independent parallel‐coordinates panel that connects the two perspectively displayed time‐series plots can move forward and backward in time to reveal changes in the relationship between the time‐dependent attributes. The visualization of time‐series plots in the context of the parallel‐coordinates plot facilitates the exploration of time‐related aspects of the data without the need to switch to a separate display. We provide a consistent set of tools for selecting and contrasting subsets of the data, which are important for various application domains.     

SoundRiver: Semantically‐Rich Sound Illustration

Sound is an integral part of most movies and videos. In many situations, viewers of a video are unable to hear the sound track, for example, when watching it in a fast forward mode, viewing it by hearing‐impaired viewers or when the plot is given as a storyboard. In this paper, we present an automated visualization solution to such problems. The system first detects the common components (such as music, speech, rain, explosions, and so on) from a sound track, then maps them to a collection of programmable visual metaphors, and generates a composite visualization. This form of sound visualization, which is referred to as SoundRiver, can be also used to augment various forms of video abstraction and annotated key frames and to enhance graphical user interfaces for video handling software. The SoundRiver conveys more semantic information to the viewer than traditional graphical representations of sound illustration, such as phonoautographs, spectrograms or artistic audiovisual animations.     

State‐of‐the‐Art in GPU‐Based Large‐Scale Volume Visualization

This survey gives an overview of the current state of the art in GPU techniques for interactive large‐scale volume visualization. Modern techniques in this field have brought about a sea change in how interactive visualization and analysis of giga‐, tera‐ and petabytes of volume data can be enabled on GPUs. In addition to combining the parallel processing power of GPUs with out‐of‐core methods and data streaming, a major enabler for interactivity is making both the computational and the visualization effort proportional to the amount and resolution of data that is actually visible on screen, i.e. ‘output‐sensitive’ algorithms and system designs. This leads to recent output‐sensitive approaches that are ‘ray‐guided’, ‘visualization‐driven’ or ‘display‐aware’. In this survey, we focus on these characteristics and propose a new categorization of GPU‐based large‐scale volume visualization techniques based on the notions of actual output‐resolution visibility and the current working set of volume bricks—the current subset of data that is minimally required to produce an output image of the desired display resolution. Furthermore, we discuss the differences and similarities of different rendering and data traversal strategies in volume rendering by putting them into a common context—the notion of address translation. For our purposes here, we view parallel (distributed) visualization using clusters as an orthogonal set of techniques that we do not discuss in detail but that can be used in conjunction with what we present in this survey.     

Improving Performance and Accuracy of Local PCA

Local Principal Component Analysis (LPCA) is one of the popular techniques for dimensionality reduction and data compression of large data sets encountered in computer graphics. The LPCA algorithm is a variant of k‐means clustering where the repetitive classification of high dimensional data points to their nearest cluster leads to long execution times. The focus of this paper is on improving the efficiency and accuracy of LPCA. We propose a novel SortCluster LPCA algorithm that significantly reduces the cost of the point‐cluster classification stage, achieving a speed‐up of up to 20. To improve the approximation accuracy, we investigate different initialization schemes for LPCA and find that the k‐means++ algorithm [ [AV07] ] yields best results, however at a high computation cost. We show that similar ideas that lead to the efficiency of our SortCluster LPCA algorithm can be used to accelerate k‐means++. The resulting initialization algorithm is faster than purely random seeding while producing substantially more accurate data approximation.     

State‐of‐the‐Art in Compressed GPU‐Based Direct Volume Rendering

Great advancements in commodity graphics hardware have favoured graphics processing unit (GPU)‐based volume rendering as the main adopted solution for interactive exploration of rectilinear scalar volumes on commodity platforms. Nevertheless, long data transfer times and GPU memory size limitations are often the main limiting factors, especially for massive, time‐varying or multi‐volume visualization, as well as for networked visualization on the emerging mobile devices. To address this issue, a variety of level‐of‐detail (LOD) data representations and compression techniques have been introduced. In order to improve capabilities and performance over the entire storage, distribution and rendering pipeline, the encoding/decoding process is typically highly asymmetric, and systems should ideally compress at data production time and decompress on demand at rendering time. Compression and LOD pre‐computation does not have to adhere to real‐time constraints and can be performed off‐line for high‐quality results. In contrast, adaptive real‐time rendering from compressed representations requires fast, transient and spatially independent decompression. In this report, we review the existing compressed GPU volume rendering approaches, covering sampling grid layouts, compact representation models, compression techniques, GPU rendering architectures and fast decoding techniques.     

Matrix Trees

We propose a new data representation for octrees and kd‐trees that improves upon memory size and algorithm speed of existing techniques. While pointerless approaches exploit the regular structure of the tree to facilitate efficient data access, their memory footprint becomes prohibitively large as the height of the tree increases. Pointerbased trees require memory consumption proportional to the number of tree nodes, thus exploiting the typical sparsity of large trees. Yet, their traversal is slowed by the need to follow explicit pointers across the different levels. Our solution is a pointerless approach that represents each tree level with its own matrix, as opposed to traditional pointerless trees that use only a single vector. This novel data organization allows us to fully exploit the tree's regular structure and improve the performance of tree operations. By using a sparse matrix data structure we obtain a representation that is suited for sparse and dense trees alike. In particular, it uses less total memory than pointer‐based trees even when the data set is extremely sparse. We show how our approach is easily implemented on the GPU and illustrate its performance in typical visualization scenarios.     

A Maximum Enhancing Higher‐Order Tensor Glyph

Glyphs are a fundamental tool in tensor visualization, since they provide an intuitive geometric representation of the full tensor information. The Higher‐Order Maximum Enhancing (HOME) glyph, a generalization of the second‐order tensor ellipsoid, was recently shown to emphasize the orientational information in the tensor through a pointed shape around maxima. This paper states and formally proves several important properties of this novel glyph, presents its first three‐dimensional implementation, and proposes a new coloring scheme that reflects peak direction and sharpness. Application to data from High Angular Resolution Diffusion Imaging (HARDI) shows that the method allows for interactive data exploration and confirms that the HOME glyph conveys fiber spread and crossings more effectively than the conventional polar plot.     

Interactive Visualization of Multimodal Volume Data for Neurosurgical Tumor Treatment

We present novel interactive methods for the visualization of multimodal volume data as used in neurosurgical therapy planning. These methods allow surgeons to explore multimodal volumes and focus on functional data and lesions. Computer graphics techniques are proposed to create expressive visualizations at interactive frame rates to reduce time‐consuming and complex interaction with the medical data. Contributions of our work are the distance‐based enhancements of functional data and lesions which allows the surgeon to perceive functional and anatomical structures at once and relate them directly to the intervention. In addition we propose methods for the visual exploration of the path to the structures of interest, to enhance anatomical landmarks, and to provide additional depth indicators. These techniques have been integrated in a visualization prototype that provides interaction capabilities for finding the optimal therapeutic strategy for the neurosurgeon.     

Social Network Clustering and Visualization using Hierarchical Edge Bundles

The hierarchical edge bundle (HEB) method generates useful visualizations of dense graphs, such as social networks, but requires a predefined clustering hierarchy, and does not easily benefit from existing straight‐line visualization improvements. This paper proposes a new clustering approach that extracts the community structure of a network and organizes it into a hierarchy that is flatter than existing community‐based clustering approaches and maps better to HEB visualization. Our method not only discovers communities and generates clusters with better modularization qualities, but also creates a balanced hierarchy that allows HEB visualization of unstructured social networks without predefined hierarchies. Results on several data sets demonstrate that this approach clarifies real‐world communication, collaboration and competition network structure and reveals information missed in previous visualizations. We further implemented our techniques into a social network visualization application on facebook.com and let users explore the visualization and community clustering of their own social networks.