Visual summary statistics

technical reportTraditionally, statistical summaries of categorical data often have been visualized using graphical plots of central moments (e.g., mean and standard deviation), or cumulants (e.g., median and quartiles) by box plots. In this work we reexamine the box plot and its relatives and develop a new hybrid summary plot that combines moment, cumulant, and density information. In view of the important role of plots in decision making, our work focuses on incorporating additional descriptive parameters while simultaneously improving the comprehensibility of the summary plots using advanced visual techniques. In many complex situations providing a comprehensive view of the data requires additional summary characteristics, therefore, we submit that these additional parameters, like higher-order central moments can be valuable elements of multi-dimensional summary displays

Closed-form approximations to the volume rendering integral with Gaussian transfer functions

technical reportIn direct volume rendering, transfer functions map data points to optical properties such as color and opacity. We have found transfer functions based on the Gaussian primitive to be particularly useful for multivariate volumes, because they are simple and rely on a limited number of free parameters. We show how this class of transfer function primitives can be analytically integrated over a line segment under the assumption that data values vary linearly between two sampled points. Analytically integrated segment can then be composited using standard techniques

Interactive volume rendering using multi-dimensional transfer functions and direct manipulation widgets

Journal ArticleMost direct volume renderings produced today employ one-dimensional transfer functions, which assign color and opacity to the volume based solely on the single scalar quantity which comprises the dataset. Though they have not received widespread attention, multi-dimensional transfer functions are a very effective way to extract specific material boundaries and convey subtle surface properties

Interactive volume rendering using multi-dimensional transfer functions and direct manipulation widgets

Journal ArticleMost direct volume renderings produced today employ onedimensional transfer functions, which assign color and opacity to the volume based solely on the single scalar quantity which comprises the dataset. Though they have not received widespread attention, multi-dimensional transfer functions are a very effective way to extract specific material boundaries and convey subtle surface properties. However, identifying good transfer functions is difficult enough in one dimension, let alone two or three dimensions. This paper demonstrates an important class of three-dimensional transfer functions for scalar data (based on data value, gradient magnitude, and a second directional derivative), and describes a set of direct manipulation widgets which make specifying such transfer functions intuitive and convenient. We also describe how to use modern graphics hardware to interactively render with multi-dimensional transfer functions. The transfer functions, widgets, and hardware combine to form a powerful system for interactive volume exploration

Model for volume lighting and modeling

Journal ArticleAbstract-Direct volume rendering is a commonly used technique in visualization applications. Many of these applications require sophisticated shading models to capture subtle lighting effects and characteristics of volumetric data and materials. For many volumes, homogeneous regions pose problems for typical gradient-based surface shading. Many common objects and natural phenomena exhibit visual quality that cannot be captured using simple lighting models or cannot be solved at interactive rates using more sophisticated methods. We present a simple yet effective interactive shading model which captures volumetric light attenuation effects that incorporates volumetric shadows, an approximation to phase functions, an approximation to forward scattering, and chromatic attenuation that provides the subtle appearance of translucency. We also present a technique for volume displacement or perturbation that allows realistic interactive modeling of high frequency detail for both real and synthetic volumetric data

Interactive translucent volume rendering and procedural modeling

Journal ArticleDirect volume rendering is a commonly used technique in visualization applications. Many of these applications require sophisticated shading models to capture subtle lighting effects and characteristics of volume metric data and materials. Many common objects and natural phenomena exhibit visual quality that cannot be captured using simple lighting models or cannot be solved at interactive rates using more sophisticated methods. We present a simple yet effective interactive shading model which captures volumetric light attenuation effects to produce volumetric shadows and the subtle appearance of translucency. We also present a technique for volume displacement or perturbation that allows realistic interactive modeling of high frequency detail for real and synthetic volumetric data

Volume rendering multivariate data to visualize meteorological simulations: a case study

Journal ArticleHigh resolution computational weather models are becoming increasing complex. However, the analysis of these models has not benefited from recent advancements in volume visualization. This case study applies the ideas and techniques from multi-dimensional transfer function based volume rendering to the multivariate weather simulations. The specific goal of identifying frontal zones is addressed. By combining temperature and humidity as a multivariate field, the frontal zones are more readily identified thereby assisting the meteorologists in their analysis tasks

Multidimensional transfer functions for interactive volume rendering

Journal ArticleAbstract-Most direct volume renderings produced today employ one-dimensional transfer functions which assign color and opacity to the volume based solely on the single scalar quantity which comprises the data set. Though they have not received widespread attention, multidimensional transfer functions are a very effective way to extract materials and their boundaries for both scalar and multivariate data. However, identifying good transfer functions is difficult enough in one dimension, let alone two or three dimensions. This paper demonstrates an important class of three-dimensional transfer functions for scalar data, and describes the application of multidimensional transfer functions to multivariate data. We present a set of direct manipulation widgets that make specifying such transfer functions intuitive and convenient. We also describe how to use modern graphics hardware to both interactively render with multidimensional transfer functions and to provide interactive shadows for volumes. The transfer functions, widgets, and hardware combine to form a powerful system for interactive volume exploration

Gaussian transfer functions for multi-field volume visualization

Journal ArticleVolume rendering is a flexible technique for visualizing dense 3D volumetric datasets. A central element of volume rendering is the conversion between data values and observable quantities such as color and opacity. This process is usually realized through the use of transfer functions that are precomputed and stored in lookup tables. For multidimensional transfer functions applied to multivariate data, these lookup tables become prohibitively large. We propose the direct evaluation of a particular type of transfer functions based on a sum of Gaussians. Because of their simple form (in terms of number of parameters), these functions and their analytic integrals along line segments can be evaluated efficiently on current graphics hardware, obviating the need for precomputed lookup tables. We have adopted these transfer functions because they are well suited for classification based on a unique combination of multiple data values that localize features in the transfer function domain. We apply this technique to the visualization of several multivariate datasets (CT, cryosection) that are difficult to classify and render accurately at interactive rates using traditional approaches

Statistically quantitative volume visualization

Journal ArticleVisualization users are increasingly in need of techniques for assessing quantitative uncertainty and error in the images produced. Statistical segmentation algorithms compute these quantitative results, yet volume rendering tools typically produce only qualitative imagery via transfer functionbased classification. This paper presents a visualization technique that allows users to nteractively explore the uncertainty, risk, and probabilistic decision of surface boundaries. Our approach makes it possible to directly visualize the combined "fuzzy" classification results from multiple segmentations by combining these data into a unified probabilistic data space. We represent this unified space, the combination of scalar volumes from numerous segmentations, using a novel graph-based dimensionality reduction scheme. The scheme both dramatically reduces the dataset size and is suitable for efficient, high quality, quantitative visualization. Lastly, we show that the statistical risk arising from overlapping segmentations is a robust measure for visualizing features and assigning optical properties