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.     

Oui! Outlier Interpretation on Multi‐dimensional Data via Visual Analytics

Outliers, the data instances that do not conform with normal patterns in a dataset, are widely studied in various domains, such as cybersecurity, social analysis, and public health. By detecting and analyzing outliers, users can either gain insights into abnormal patterns or purge the data of errors. However, different domains usually have different considerations with respect to outliers. Understanding the defining characteristics of outliers is essential for users to select and filter appropriate outliers based on their domain requirements. Unfortunately, most existing work focuses on the efficiency and accuracy of outlier detection, neglecting the importance of outlier interpretation. To address these issues, we propose Oui, a visual analytic system that helps users understand, interpret, and select the outliers detected by various algorithms. We also present a usage scenario on a real dataset and a qualitative user study to demonstrate the effectiveness and usefulness of our system.     

Visual Analysis of Trajectories in Multi‐Dimensional State Spaces

Multi‐dimensional data originate from many different sources and are relevant for many applications. One specific sub‐type of such data is continuous trajectory data in multi‐dimensional state spaces of complex systems. We adapt the concept of spatially continuous scatterplots and spatially continuous parallel coordinate plots to such trajectory data, leading to continuous‐time scatterplots and continuous‐time parallel coordinates. Together with a temporal heat map representation, we design coordinated views for visual analysis and interactive exploration. We demonstrate the usefulness of our visualization approach for three case studies that cover examples of complex dynamic systems: cyber‐physical systems consisting of heterogeneous sensors and actuators networks (the collection of time‐dependent sensor network data of an exemplary smart home environment), the dynamics of robot arm movement and motion characteristics of humanoids.     

Projected Field Similarity for Comparative Visualization of Multi‐Run Multi‐Field Time‐Varying Spatial Data

The purpose of multi‐run simulations is often to capture the variability of the output with respect to different initial settings. Comparative analysis of multi‐run spatio‐temporal simulation data requires us to investigate the differences in the dynamics of the simulations' changes over time. To capture the changes and differences, aggregated statistical information may often be insufficient, and it is desirable to capture the local differences between spatial data fields at different times and between different runs. To calculate the pairwise similarity between data fields, we generalize the concept of isosurface similarity from individual surfaces to entire fields and propose efficient computation strategies. The described approach can be applied considering a single scalar field for all simulation runs or can be generalized to a similarity measure capturing all data fields of a multi‐field data set simultaneously. Given the field similarity, we use multi‐dimensional scaling approaches to visualize the similarity in two‐dimensional or three‐dimensional projected views as well as plotting one‐dimensional similarity projections over time. Each simulation run is depicted as a polyline within the similarity maps. The overall visual analysis concept can be applied using our proposed field similarity or any other existing measure for field similarity. We evaluate our measure in comparison to popular existing measures for different configurations and discuss their advantages and limitations. We apply them to generate similarity maps for real‐world data sets within the overall concept for comparative visualization of multi‐run spatio‐temporal data and discuss the results.     

Graph‐Based Wavelet Representation of Multi‐Variate Terrain Data

Terrain data can be processed from the double perspective of computer graphics and graph theory. We propose a hybrid method that uses geometrical and vertex attribute information to construct a weighted graph reflecting the variability of the vertex data. As a planar graph, a generic terrain data set is subjected to a geometry‐sensitive vertex partitioning procedure. Through the use of a combined, thin‐plate energy and multi‐dimensional quadric metric error, feature estimation heuristic, we construct ‘even’ and ‘odd’ node subsets. Using an invertible lifting scheme, adapted from generic weighted graphs, detail vectors are extracted and used to recover or filter the node information. The design of the prediction and update filters improves the root mean squared error of the signal over general graph‐based approaches. As a key property of this design, preserving the mean of the graph signal becomes essential for decreasing the error measure and conserving the salient shape features.     

Stochastic Volume Rendering of Multi‐Phase SPH Data

In this paper, we present a novel method for the direct volume rendering of large smoothed‐particle hydrodynamics (SPH) simulation data without transforming the unstructured data to an intermediate representation. By directly visualizing the unstructured particle data, we avoid long preprocessing times and large storage requirements. This enables the visualization of large, time‐dependent, and multivariate data both as a post‐process and in situ. To address the computational complexity, we introduce stochastic volume rendering that considers only a subset of particles at each step during ray marching. The sample probabilities for selecting this subset at each step are thereby determined both in a view‐dependent manner and based on the spatial complexity of the data. Our stochastic volume rendering enables us to scale continuously from a fast, interactive preview to a more accurate volume rendering at higher cost. Lastly, we discuss the visualization of free‐surface and multi‐phase flows by including a multi‐material model with volumetric and surface shading into the stochastic volume rendering.     

InSpectr: Multi‐Modal Exploration,Visualization, and Analysis of Spectral Data

This paper addresses the increasing demand in industry for methods to analyze and visualize multimodal data involving a spectral modality. Two data modalities are used: high‐resolution X‐ray computed tomography (XCT) for structural characterization and low‐resolution X‐ray fluorescence (XRF) spectral data for elemental decomposition. We present InSpectr, an integrated tool for the interactive exploration and visual analysis of multimodal, multiscalar data. The tool has been designed around a set of tasks identified by domain experts in the fields of XCT and XRF. It supports registered single scalar and spectral datasets optionally coupled with element maps and reference spectra. InSpectr is instantiating various linked views for the integration of spatial and non‐spatial information to provide insight into an industrial component's structural and material composition: views with volume renderings of composite and individual 3D element maps visualize global material composition; transfer functions defined directly on the spectral data and overlaid pie‐chart glyphs show elemental composition in 2D slice‐views; a representative aggregated spectrum and spectra density histograms are introduced to provide a global overview in the spectral view. Spectral magic lenses, spectrum probing and elemental composition probing of points using a pie‐chart view and a periodic table view aid the local material composition analysis. Two datasets are investigated to outline the usefulness of the presented techniques: a 3D virtually created phantom with a brass metal alloy and a real‐world 2D water phantom with insertions of gold, barium, and gadolinium. Additionally a detailed user evaluation of the results is provided.     

Discrete Multi‐Material Interface Reconstruction for Volume Fraction Data

Material interface reconstruction (MIR) is the task of constructing boundary interfaces between regions of homogeneous material, while satisfying volume constraints, over a structured or unstructured spatial domain. In this paper, we present a discrete approach to MIR based upon optimizing the labeling of fractional volume elements within a discretization of the problem's original domain. We detail how to construct and initially label a discretization, and introduce a volume conservative swap move for optimization. Furthermore, we discuss methods for extracting and visualizing material interfaces from the discretization. Our technique has significant advantages over previous methods: we produce interfaces between multiple materials that are continuous across cell boundaries for time‐varying and static data in arbitrary dimension with bounded error.     

Visual Analysis of Spatio‐Temporal Data: Applications in Weather Forecasting

Weather conditions affect multiple aspects of human life such as economy, safety, security, and social activities. For this reason, weather forecast plays a major role in society. Currently weather forecasts are based on Numerical Weather Prediction (NWP) models that generate a representation of the atmospheric flow. Interactive visualization of geo‐spatial data has been widely used in order to facilitate the analysis of NWP models. This paper presents a visualization system for the analysis of spatio‐temporal patterns in short‐term weather forecasts. For this purpose, we provide an interactive visualization interface that guides users from simple visual overviews to more advanced visualization techniques. Our solution presents multiple views that include a timeline with geo‐referenced maps, an integrated webmap view, a forecast operation tool, a curve‐pattern selector, spatial filters, and a linked meteogram. Two key contributions of this work are the timeline with geo‐referenced maps and the curve‐pattern selector. The latter provides novel functionality that allows users to specify and search for meaningful patterns in the data. The visual interface of our solution allows users to detect both possible weather trends and errors in the weather forecast model. We illustrate the usage of our solution with a series of case studies that were designed and validated in collaboration with domain experts.     

On Near Optimal Lattice Quantization of Multi‐Dimensional Data Points

One of the most elementary application of a lattice is the quantization of real‐valued s‐dimensional vectors into finite bit precision to make them representable by a digital computer. Most often, the simple s‐dimensional regular grid is used for this task where each component of the vector is quantized individually. However, it is known that other lattices perform better regarding the average quantization error. A rank‐1 lattices is a special type of lattice, where the lattice points can be described by a single s‐dimensional generator vector. Further, the number of points inside the unit cube [0, 1)^s is arbitrary and can be directly enumerated by a single one‐dimensional integer value. By choosing a suitable generator vector the minimum distance between the lattice points can be maximized which, as we show, leads to a nearly optimal mean quantization error. We present methods for finding parameters for s‐dimensional maximized minimum distance rank‐1 lattices and further show their practical use in computer graphics applications.     

Multi‐Tracking of First Order Multi‐Agent Networks Via Self‐Triggered Control

A multi‐tracking problem of multi‐agent networks is investigated in this paper where multi‐tracking refers to that the states of multiple agents in each subnetwork asymptotically converge to the same desired trajectory in the presence of information exchanges among subnetworks. The multi‐tracking of first order multi‐agent networks with directed topologies was studied. Self‐triggered protocols were proposed along with triggering functions to solve the stationary multi‐tracking and bounded dynamic multi‐tracking. The self‐triggered scheduling is obtained, and the system does not exhibit Zeno behavior. Numerical examples are provided to illustrate the effectiveness of the obtained criteria.     

Interactive Fusion and Tracking For Multi‐Modal Spatial Data Visualization

Scientific data acquired through sensors which monitor natural phenomena, as well as simulation data that imitate time‐identified events, have fueled the need for interactive techniques to successfully analyze and understand trends and patterns across space and time. We present a novel interactive visualization technique that fuses ground truth measurements with simulation results in real‐time to support the continuous tracking and analysis of spatiotemporal patterns. We start by constructing a reference model which densely represents the expected temporal behavior, and then use GPU parallelism to advect measurements on the model and track their location at any given point in time. Our results show that users can interactively fill the spatio‐temporal gaps in real world observations, and generate animations that accurately describe physical phenomena.     

Visual Exploration of High‐Dimensional Data through Subspace Analysis and Dynamic Projections

We introduce a novel interactive framework for visualizing and exploring high‐dimensional datasets based on subspace analysis and dynamic projections. We assume the high‐dimensional dataset can be represented by a mixture of low‐dimensional linear subspaces with mixed dimensions, and provide a method to reliably estimate the intrinsic dimension and linear basis of each subspace extracted from the subspace clustering. Subsequently, we use these bases to define unique 2D linear projections as viewpoints from which to visualize the data. To understand the relationships among the different projections and to discover hidden patterns, we connect these projections through dynamic projections that create smooth animated transitions between pairs of projections. We introduce the view transition graph, which provides flexible navigation among these projections to facilitate an intuitive exploration. Finally, we provide detailed comparisons with related systems, and use real‐world examples to demonstrate the novelty and usability of our proposed framework.     

Visualizing Probabilistic Multi‐Phase Fluid Simulation Data using a Sampling Approach

Eulerian Method of Moment (MoM) solvers are gaining popularity for multi‐phase CFD simulation involving bubbles or droplets in process engineering. Because the actual positions of bubbles are uncertain, the spatial distribution of bubbles is described by scalar fields of moments, which can be interpreted as probability density functions. Visualizing these simulation results and comparing them to physical experiments is challenging, because neither the shape nor the distribution of bubbles described by the moments lend themselves to visual interpretation. In this work, we describe a visualization approach that provides explicit instances of the bubble distribution and produces bubble geometry based on local flow properties. To facilitate animation, the instancing of the bubble distribution provides coherence over time by advancing bubbles between time steps and updating the distribution. Our approach provides an intuitive visualization and enables direct visual comparison of simulation results to physical experiments.     

Variance Analysis of Multi‐sample and One‐sample Multiple Importance Sampling

We reexamine in this paper the variance for the Multiple Importance Sampling (MIS) estimator for multi‐sample and one‐sample model. As a result of our analysis we can obtain the optimal estimator for the multi‐sample model for the case where the weights do not depend on the count of samples. We extend the analysis to include the cost of sampling. With these results in hand we find a better estimator than balance heuristic with equal count of samples. Further, we show that the variance for the one‐sample model is larger or equal than for the multi‐sample model, and that there are only two cases where the variance is the same. Finally, we study on four examples the difference of variances for equal count as used by Veach, our new estimator, and a recently introduced heuristic.     

Multi‐planar plenoptic displays

Multi‐planar plenoptic displays consist of multiple spatially varying light‐emitting and light‐modulating planes. In this work, we introduce a framework to display light field data on this new type of display device. First, we present a mathematical notation that describes each of the layers in terms of the corresponding light transport operators. Next, we explain an algorithm that renders a light field with depth into a given multi‐planar plenoptic display and analyze the approximation error. We show two different physical prototypes that we have designed and built: The first design uses a dynamic parallax barrier and a number of bi‐state (translucent/opaque) screens. The second design uses a beam splitter to co‐locate two pairs of parallax barriers and static image projection screens. We evaluate both designs on a number of different 3D scenes. Finally, we present simulated and real results for different display configurations.     

Multi‐Resolution Cloth Simulation

We propose a novel, multi‐resolution method to efficiently perform large‐scale cloth simulation. Our cloth simulation method is based on a triangle‐based energy model constructed from a cloth mesh. We identify that solutions of the linear system of cloth simulation are smooth in certain regions of the cloth mesh and solve the linear system on those regions in a reduced solution space. Then we reconstruct the original solutions by performing a simple interpolation from solutions computed in the reduced space. In order to identify regions where solutions are smooth, we propose simplification metrics that consider stretching, shear, and bending forces, as well as geometric collisions. Our multi‐resolution method can be applied to many existing cloth simulation methods, since our method works on a general linear system. In order to demonstrate benefits of our method, we apply our method into four large‐scale cloth benchmarks that consist of tens or hundreds of thousands of triangles. Because of the reduced computations, we achieve a performance improvement by a factor of up to one order of magnitude, with a little loss of simulation quality.     

Scalable Multi‐view Registration for Multi‐Projector Displays on Vertically Extruded Surfaces

Recent work have shown that it is possible to register multiple projectors on non‐planar surfaces using a single uncalibrated camera instead of a calibrated stereo pair when dealing with a special class of non‐planar surfaces, vertically extruded surfaces. However, this requires the camera view to contain the entire display surface. This is often an impossible scenario for large displays, especially common in visualization, edutainment, training and simulation applications. In this paper we present a new method that can achieve an accurate geometric registration even when the field‐of‐view of the uncalibrated camera can cover only a part of the vertically extruded display at a time. We pan and tilt the camera from a single point and employ a multi‐view approach to register the projectors on the display. This allows the method to scale easily both in terms of camera resolution and display size. To the best of our knowledge, our method is the first to achieve a scalable multi‐view geometric registration of large vertically extruded displays with a single uncalibrated camera. This method can also handle a different situation of having multiple similarly oriented cameras in different locations, if the camera focal length is known.     

Multi‐contextuality in boundary‐spanning practices

The capability to establish boundary‐spanning practices within and across organizations has for long been recognized as a key strategic resource. As organizations are becoming distributed and dynamic, they will be increasingly populated by multiple functional, geographical, hierarchical and professional boundaries. The inherent complexity of such settings makes it difficult for organizations to leverage their boundary‐spanning practices. Information technology (IT) systems have been hailed as a critical enabler of boundary spanning. However, there is little knowledge on how organizations are affected by the introduction of different types of IT systems. Building on an interpretive case study of Swedish transport organizations, this paper explores consequences of sensor technology for boundary spanning. The paper contributes with an understanding of what coexisting use contexts mean for boundary‐spanning practices. A theoretical implication is that such multi‐contextuality requires an integrative view on boundary spanning that combines insights from the organizational innovation and work practice literatures.     

Multi‐Scale Geometry Interpolation

Interpolating vertex positions among triangle meshes with identical vertex‐edge graphs is a fundamental part of many geometric modelling systems. Linear vertex interpolation is robust but fails to preserve local shape. Most recent approaches identify local affine transformations for parts of the mesh, model desired interpolations of the affine transformations, and then optimize vertex positions to conform with the desired transformations. However, the local interpolation of the rotational part is non‐trivial for more than two input configurations and ambiguous if the meshes are deformed significantly. We propose a solution to the vertex interpolation problem that starts from interpolating the local metric (edge lengths) and mean curvature (dihedral angles) and makes consistent choices of local affine transformations using shape matching applied to successively larger parts of the mesh. The local interpolation can be applied to any number of input vertex configurations and due to the hierarchical scheme for generating consolidated vertex positions, the approach is fast and can be applied to very large meshes.