In this state-of-the-art report we discuss relevant research works related to the visualization of complex, multivariate data. We discuss how different techniques take effect at specific stages of the visualization pipeline and how they apply to multi-variate data sets being composed of scalars, vectors and tensors. We also provide a categorization of these techniques with the aim for a better overview of related approaches. Based on this classification we highlight combinable and hybrid approaches and focus on techniques that potentially lead towards new directions in visualization research. In the second part of this paper we take a look at recent techniques that are useful for the visualization of complex data sets either because they are general purpose or because they can be adapted to specific problems.

Abstract — In this paper we describe a novel method to integrate interactive visual analysis and machine learning to support the insight generation of the user. The suggested approach combines the vast search and processing power of the computer with the superior reasoning and pattern recognition capabilities of the human user. An evolutionary search algorithm has been adapted to assist in the fuzzy logic formalization of hypotheses that aim at explaining features inside multivariate, volumetric data. Up to now, users solely rely on their knowledge and expertise when looking for explanatory theories. However, it often remains unclear whether the selected attribute ranges represent the real explanation for the feature of interest. Other selections hidden in the large number of data variables could potentially lead to similar features. Moreover, as simulation complexity grows, users are confronted with huge multidimensional data sets making it almost impossible to find meaningful hypotheses at all. We propose an interactive cycle of knowledge-based analysis and automatic hypothesis generation. Starting from initial hypotheses, created with linking and brushing, the user steers a heuristic search algorithm to look for alternative or related hypotheses. The results are analyzed in information visualization views that are linked to the volume rendering. Individual properties as well as global aggregates are visually presented to provide insight into the most relevant aspects of the generated hypotheses. This novel approach becomes computationally feasible due to a GPU implementation of the time-critical parts in the algorithm. A thorough evaluation of search times and noise sensitivity as well as a case study on data from the automotive domain substantiate the usefulness of the suggested approach.

Abstract—Uncertainty is ubiquitous in science, engineering and medicine. Drawing conclusions from uncertain data is the normal case, not an exception. While the field of statistical graphics is well established, only a few 2D and 3D visualization and feature extraction methods have been devised that consider uncertainty. We present mathematical formulations for uncertain equivalents of isocontours based on standard probability theory and statistics and employ them in interactive visualization methods. As input data we consider discretized uncertain scalar fields and model these as random fields. To create a continuous representation suitable for visualization we introduce interpolated probability density functions. Furthermore, we introduce numerical condition as a general means in featurebased visualization. The condition number – which potentially diverges in the isocontour problem – describes how errors in the input data are amplified in feature computation. We show how the average numerical condition of isocontours aids the selection of thresholds that correspond to robust isocontours. Additionally, we introduce the isocontour density and the level crossing probability field; these two measures for the spatial distribution of uncertain isocontours are directly based on the probabilistic model of the input data. Finally, we adapt interactive visualization methods to evaluate and display these measures and apply them to 2D and 3D data sets.

In this work we present a point classification algorithm for multi-variate data. Our method is based on the concept of attribute subspaces, which are derived from a set of user specified attribute target values. Our classification approach enables users to visually distinguish regions of saliency through concurrent viewing of these subspaces in single images. We also allow a user to threshold the data according to a specified distance from attribute target values. Based on the degree of thresholding, the remaining data points are assigned radii of influence that are used for the final coloring. This limits the view to only those points that are most relevant, while maintaining a similar visual context. Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Display Algorithms 1.

Abstract—Feature detection and display are the essential goals of the visualization process. Most visualization software achieves these goals by mapping properties of sampled intensity values and their derivatives to color and opacity. In this work, we propose to explicitly study the local frequency distribution of intensity values in broader neighborhoods centered around each voxel. We have found frequency distributions to contain meaningful and quantitative information that is relevant for many kinds of feature queries. Our approach allows users to enter predicate-based hypotheses about relational patterns in local distributions and render visualizations that show how neighborhoods match the predicates. Distributions are a familiar concept to non-expert users, and we have built a simple graphical user interface for forming and testing queries interactively. The query framework readily applies to arbitrary spatial datasets and supports queries on time variant and multifield data. Users can directly query for classes of features previously inaccessible in general feature detection tools. Using several well-known datasets, we show new quantitative features that enhance our understanding of familiar visualization results. Index Terms—Volume visualization, volume rendering, multivariate data, features in volume data 1

Statistical complexity is a measure of complexity of discrete-time stationary stochastic processes, which has many applications. We investigate its more abstract properties as a non-linear functional on the space of processes and show its close relation to Knight’s prediction process. We prove lower semicontinuity, concavity, and a formula for the ergodic decomposition of statistical complexity. On the way, we show that the discrete version of the prediction process has a continuous Markov transition. We also prove that, given the past output of a partially deterministic hidden Markov model (HMM), the uncertainty of the internal state is constant over time and knowledge of the internal state gives no additional information on the future output. Using this fact, we show that the causal state distribution is

Vector fields are a common concept for the representation of many different kinds of flow phenomena in science and engineering. Topology-based methods have shown their convenience for visualizing and analyzing steady flow but a counterpart for unsteady flow is still missing. However, a lot of good and relevant work has been done aiming at such a solution. We give an overview of the research done on the way towards topology-based visualization of unsteady flow, pointing out the different approaches and methodologies involved as well as their relation to each other, taking classical (i.e. steady) vector field topology as our starting point. Particularly, we focus on Lagrangian Methods, Space-Time Domain Approaches, Local Methods, and Stochastic and Multi-Field Approaches. Furthermore, we illustrated our review with practical examples for the different approaches.

Volumetric data offer considerably more low-level information than the density and gradient values traditionally employed in transfer function-guided volume visualization. We propose the use of a richer set of low-level feature descriptors to allow a more sensitive and refined characterization of the data. The ensemble of these feature descriptors then forms a distinct data signature that can describe, classify, and categorize a dataset at levels of detail. 1

In visualization, data, information and knowledge are three terms used extensively, often in an interrelated context. In many cases, they are used to indicate different levels of abstraction, understanding or truthfulness. For example, ‘visualization is concerned with exploring data and information [5]; ‘the primary objective in data visualization is to gain insight into an information space ’ [6]; and ‘information visualization ’ is for ‘data mining and knowledge discovery ’ [4]. In other cases, these three terms are used to indicate data types, for instances, as adnominals in noun phases, such as data visualization, information visualization and knowledge visualization. These examples suggest that data, information and knowledge could be both the input and output of a visualization process, raising questions about the exact role of data, information and

In visualization, data, information and knowledge are three terms used extensively, often in an interrelated context. In many cases, they are used to indicate different levels of abstraction, understanding or truthfulness. For example, ‘visualization is concerned with exploring data and information [5]; ‘the primary objective in data visualization is to gain insight into an information space ’ [6]; and ‘information visualization ’ is for ‘data mining and knowledge discovery ’ [4]. In other cases, these three terms are used to indicate data types, for instances, as adnominals in noun phases, such as data visualization, information visualization and knowledge visualization. These examples suggest that data, information and knowledge could be both the input and output of a visualization process, raising questions about the exact role of data, information and