Soil moisture plays important roles in the land-atmosphere interaction, rainfall–runoff process, climate and weather forecast, and crop yield. An accurate estimation of soil moisture creates opportunities to improve the understanding of soil moisture-related processes in atmospheric sciences, hydrology, and agriculture. Traditional methods to measure soil moisture mainly rely on in-situ measurements which are usually costly and reliant on the use of field instrumentation and point data. A robust remote sensing technique is highly needed to frequently monitor the soil moisture content over a large region or landscape. This paper presents a metric learning-based regression algorithm to learn the mapping function from the input hyperspectral data to the output soil moisture. In particular, the proposed soil moisture estimation method employs the Gaussian process to model the joint distribution of spectral bands over functions. It further incorporates the learning of distance function to find feature subspace for improving soil estimation performance. Experimental results on a real dataset show that the proposed metric learning-based soil moisture estimation method can significantly improve the performance compared to the state-of-the-art soil moisture estimation methods using principle component analysis for feature reduction.

Global soil moisture mapping at high spatial and temporal resolution is important for its related meteorological, hydrological, and agricultural applications. Using the L-band signals, several satellite-based microwave sensors are providing global soil moisture retrievals at a spatial resolution of about 40 km and a revisit time of 2–3 days. Recent research shows that the forward scattered Global Navigation Satellite System (GNSS) signals at L-band can convey high-resolution information of land surface conditions, including surface soil moisture. However, these signals are often affected by complex land surface characteristics and the bistatic nature of GNSS-R technique, leading to nonlinear relation between the signals and surface soil moisture. In this work, a machine learning (ML) approach is used to map quasi-global soil moisture from Cyclone GNSS (CYGNSS) observables. Specifically, several land surface parameters are obtained and used in combination with CYGNSS data in the ML model by using the Soil Moisture Active Passive (SMAP) data as reference. A good performance of the ML method is achieved with median ubRMSDs of 0.0426 m3/m3and 0.034 m3/m3for global coverage and regions with vegetation water content less than 4 kg/m2, respectively. Moreover, an independent evaluation of the CYGNSS data against in-situ measurements suggests that the overall accuracy of CYGNSS soil moisture is comparable with SMAP data. With an increased sampling frequency of CYGNSS, the generated products can supplement current global soil moisture database. In addition, the ML-based CYGNSS products are published via a website portal for future users11https://www.gri.msstate.edu/research/ssm/.

High Spatio-temporal soil moisture is essential for many meteorological, hydrological, and agricultural applications and studies. Spaceborne Global Navigation Satellite System Reflectometry (GNSS-R) provides a promising opportunity for high-resolution soil moisture retrievals. NASA's Cyclone Global Navigation Satellite System is a preeminent GNSS-R application that offers high spatial and temporal resolution observations from Earth's surface. However, the quasi-random sampling of land surface by the CYGNSS constellation circumvents obtaining fully observed daily soil moisture predictions. This work investigates multidimensional spatial and temporal interpolation of the CYGNSS soil moisture estimates using methods such as linear, nearest, and natural interpolation. The results indicate that the interpolation error (RMSE) was 0.032$m^{3}/m^{3}$, 0.038$m^{3}/m^{3}$, and 0.030$m^{3}/m^{3}$for linear, nearest, and natural interpolation, respectively. The results also show that interpolated and observed CYGNSS SM values have the similar performance metrics when validated with the SMAP 9-km gridded SM product.

High spatio-temporal soil moisture is critical for the understanding of land-atmosphere interactions and affects meteorological, hydrological and agricultural applications. Currently, most satellite-based microwave sensors provide global soil moisture retrievals at ~40 km spatial and 2-3 days temporal resolution. Using the forward scattered L-band Global Navigation Satellite System (GNSS) signals, surface soil moisture can be estimated at higher spatial and temporal scales. However, due to the complex land surface characteristics and bistatic nature of GNSS signals, the retrieval algorithms for deriving surface soil moisture from GNSS signals are still under development. In this work, a machine learning (ML) algorithm has been used for estimating soil moisture from Cyclone Global Navigation Satellite System (CYGNSS) measurements. The in-situ data from International Soil Moisture Network and global soil moisture data from Soil Moisture Active Passive (SMAP) have been deployed as the reference data in the ML algorithm. In particular, various remote sensing-based land surface parameters have been included and facilitate a robust soil moisture retrieving process. The proposed approach has achieved an ubRMSD of 0.0523 m3/m3between the retrieved soil moisture from CYGNSS and in-situ measurements in a 5-fold cross-validation over 129 ground-based soil moisture sites, suggesting a satisfactory performance of the ML-based approach. Moreover, the global median ubRMSD of 0.042 m3/m3is obtained between SMAP and CYGNSS ML predictions. Surface soil moisture can be retrieved at ~9 km spatial and 1-2 days temporal scales through the presented framework.

The high computational demands of classifying very high-resolution (VHR) imagery calls for efficient implementations such as parallel processing, in particular, for computing on Graphics Processing Units (GPUs). In this work, a problem of classifying invasive Phragmites australis from other vegetation is considered. This study uses VHR imagery with a ground sampling distance of 25 centimeters acquired using a small-unmanned aerial system. We studied the use of Compute Unified Device Architecture for two feature extraction methods with a probabilistic neural network classifier. The texture extraction and parameter optimization on GPUs uses a divide and conquer strategy. The results of the study show the use of GPUs significantly increased speed when compared to a traditional Central Processing Unit based classification setup.

Plant species monitoring in wetland ecosystems is crucial for preservation of water quality and many other ecological functions. Difficulties associated with conducting field work (i.e., hazardous terrain) can affect the ability of resource managers to correctly identify wetland plant species in a timely fashion. Thus, in wetland sites where access can be difficult, differentiation of plant species from aerial imagery can be of use. In this work, we studied laboratory produced hyperspectral data to classify various wetland plants thereby determining optimal multispectral bands that can distinguish these species. We then used an unmanned aerial systems (UAS) mountable 5-band multispectral sensor to classify 11 different wetland plant species to determine effectiveness of the multispectral bands chosen by the preliminary hyperspectral analysis. Classification experiments on the hyperspectral data produced the overall accuracies of 94-97% with 20% training samples. Experiments on the UAS collected multispectral data produced overall accuracy of 75% when considering four classes and 58% overall accuracy when considering 11 classes.

The Deepwater Horizon blowout in the Gulf of Mexico resulted in one of the largest accidental oil disasters in U.S. history. NASA acquired radar and hyperspectral imagery and made them available to the scientific community for analyzing impacts of the oil spill. In this study, we use the L-band quad-polarized radar data acquired by Unmanned Aerial Vehicle Synthetic Aperture Radar (UAVSAR) and Hyperspectral Imagery (HSI) from the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) optical sensor. The main objective of this research is to apply fusion techniques on polarimetric radar and hyperspectral imagery to investigate the benefit of fusion for improved classification of coastal vegetation contaminated by oil. In this approach, fusion is implemented at the pixel level by concatenating the hyperspectral data with the high resolution SAR data and analyze the fused data with Support Vector Machine (SVM) classification algorithm.

Hyperspectral imaging enables detailed ground cover classification with hundreds of spectral bands at each pixel. Rich spectral information can be a drawback since supervised classification of a hyperspectral image requires a balance between the number of training samples and its dimension. Achieving this balance requires a large number of training or ground truth samples, which is generally difficult, expensive and time-consuming. This led researchers to explore the use of semi-supervised learning techniques where new training samples (unlabeled) are obtained from a small set of available labeled samples without significant effort. In this paper, we propose a semi-supervised approach which adapts active learning to a co-training framework in which the algorithm automatically selects new training samples from abundant unlabeled pixels. Efficacy of the proposed approach is validated using a probabilistic support vector machine classifier. Our experimental results with an Indian Pines hyperspectral image collected by the National Aeronautics and Space Administration Jet Propulsion Laboratory's Airborne Visible-Infrared Imaging Spectrometer indicate that the use of this co-training based approach represents promising strategy in the context of hyperspectral image classification.

This paper presents a 2D flow visualization user study that we conducted using new methodologies to increase the objectiveness. We evaluated grid-based variable-size arrows, evenly spaced streamlines, and line integral convolution (LIC) variants (basic, oriented, and enhanced versions) coupled with a colorwheel and/or rainbow color map, which are representative of many geometry-based and texture-based techniques. To reduce data-related bias, template-based explicit flow synthesis was used to create a wide variety of symmetric flows with similar topological complexity. To suppress task-related bias, pattern-based implicit task design was employed, addressing critical point recognition, critical point classification, and symmetric pattern categorization. In addition, variable-duration and fixed-duration measurement schemes were utilized for lightweight precision-critical and heavyweight judgment intensive flow analysis tasks, respectively, to record visualization effectiveness. We eliminated outliers and used the Ryan REGWQ post-hoc homogeneous subset tests in statistical analysis to obtain reliable findings. Our study shows that a texture-based dense representation with accentuated flow streaks, such as enhanced LIC, enables intuitive perception of the flow, while a geometry-based integral representation with uniform density control, such as evenly spaced streamlines, may exploit visual interpolation to facilitate mental reconstruction of the flow. It is also shown that inappropriate color mapping (e.g., colorwheel) may add distractions to a flow representation.

Displaying the abundant information contained in a remotely sensed hyperspectral image is a challenging problem. Currently, no approach can satisfactorily render the desired information at arbitrary levels of detail. In this paper, we present a feature-driven multilayer visualization technique that automatically chooses data visualization techniques based on the spatial distribution and importance of the endmembers. It can simultaneously visualize the overall material distribution, subpixel level details, and target pixels and materials. By incorporating interactive tools, different levels of detail can be presented per users' request. This scheme employs five layers from the bottom to the top: the background layer, data-driven spot layer, pie-chart layer, oriented sliver layer, and anomaly layer. The background layer provides the basic tone of the display; the data-driven spot layer manifests the overall material distribution in an image scene; the pie-chart layer presents the precise abundances of endmember materials in each pixel; the oriented sliver layer emphasizes the distribution of important anomalous materials; and the anomaly layer highlights anomaly pixels (i.e., potential targets). Displays of the airborne AVIRIS data and spaceborne Hyperion data demonstrate that the proposed multilayer visualization scheme can efficiently display more information globally and locally.

Numerical weather prediction ensembles are routinely used for operational weather forecasting. The members of these ensembles are individual simulations with either slightly perturbed initial conditions or different model parameterizations, or occasionally both. Multi-member ensemble output is usually large, multivariate, and challenging to interpret interactively. Forecast meteorologists are interested in understanding the uncertainties associated with numerical weather prediction; specifically variability between the ensemble members. Currently, visualization of ensemble members is mostly accomplished through spaghetti plots of a single mid-troposphere pressure surface height contour. In order to explore new uncertainty visualization methods, the Weather Research and Forecasting (WRF) model was used to create a 48-hour, 18 member parameterization ensemble of the 13 March 1993 "Superstorm". A tool was designed to interactively explore the ensemble uncertainty of three important weather variables: water-vapor mixing ratio, perturbation potential temperature, and perturbation pressure. Uncertainty was quantified using individual ensemble member standard deviation, inter-quartile range, and the width of the 95% confidence interval. Bootstrapping was employed to overcome the dependence on normality in the uncertainty metrics. A coordinated view of ribbon and glyph-based uncertainty visualization, spaghetti plots, iso-pressure colormaps, and data transect plots was provided to two meteorologists for expert evaluation. They found it useful in assessing uncertainty in the data, especially in finding outliers in the ensemble run and therefore avoiding the WRF parameterizations that lead to these outliers. Additionally, the meteorologists could identify spatial regions where the uncertainty was significantly high, allowing for identification of poorly simulated storm environments and physical interpretation of these model issues.

This paper presents a new streamline placement algorithm that produces evenly spaced long streamlines while preserving topological features of a flow field. Singularities and separatrices are extracted to decompose the flow field into topological regions. In each region, a seeding path is selected from a set of streamlines integrated in the orthogonal flow field. The uniform sample points on this path are then used as seeds to generate streamlines in the original flow field. Additional seeds are placed where a large gap between adjacent streamlines occurs. The number of short streamlines is significantly reduced as evenly spaced long streamlines spawned along the seeding paths can fill the topological regions very well. Several metrics for evaluating streamline placement quality are discussed and applied to our method as well as some other approaches. Compared to previous work in uniform streamline placement, our method is more effective in creating evenly spaced long streamlines and preserving topological features. It has the potential to provide both intuitive perception of important flow characteristics and detail reconstruction across visually pleasing streamlines.

Many techniques have been proposed to show uncertainty in data visualizations. However, very little is known about their effectiveness in conveying meaningful information. In this paper, we present a user study that evaluates the perception of uncertainty amongst four of the most commonly used techniques for visualizing uncertainty in one-dimensional and two-dimensional data. The techniques evaluated are traditional errorbars, scaled size of glyphs, color-mapping on glyphs, and color-mapping of uncertainty on the data surface. The study uses generated data that was designed to represent the systematic and random uncertainty components. Twenty-seven users performed two types of search tasks and two types of counting tasks on 1D and 2D datasets. The search tasks involved finding data points that were least or most uncertain. The counting tasks involved counting data features or uncertainty features. A 4x4 full-factorial ANOVA indicated a significant interaction between the techniques used and the type of tasks assigned for both datasets indicating that differences in performance between the four techniques depended on the type of task performed. Several one-way ANOVAs were computed to explore the simple main effects. Bonferronni's correction was used to control for the family-wise error rate for alpha-inflation. Although we did not find a consistent order among the four techniques for all the tasks, there are several findings from the study that we think are useful for uncertainty visualization design. We found a significant difference in user performance between searching for locations of high and searching for locations of low uncertainty. Errorbars consistently underperformed throughout the experiment. Scaling the size of glyphs and color-mapping of the surface performed reasonably well. The efficiency of most of these techniques were highly dependent on the tasks performed. We believe that these findings can be used in future uncertainty visualization design. In addition, the framework developed in this user study presents a structured approach to evaluate uncertainty visualization techniques, as well as provides a basis for future research in uncertainty visualization.

Abstract We present the results from a user study looking at the ability of observers to mentally integrate wind direction and magnitude over a vector field. The data set chosen for the study is an MM5 (PSU/NCAR Mesoscale Model) simulation of Hurricane Lili over the Gulf of Mexico as it approaches the southeastern United States. Nine observers participated in the study. This study investigates the effect of layering on the observer's ability to determine the magnitude and direction of a vector field. We found a tendency for observers to underestimate the magnitude of the vectors and a counter‐clockwise bias when determining the average direction of a vector field. We completed an additional study with two observers to try to uncover the source of the counter‐clockwise bias. These results have direct implications to atmospheric scientists, but may also be able to be applied to other fields that use 2D vector fields.

This paper investigates RGB color composition schemes for hyperspectral imagery display. A three-channel composite inevitably loses a significant amount of information contained in the original high-dimensional data. The objective here is to display the useful information as distinctively as possible for high-class separability. To achieve this objective, it is important to find an effective data processing step prior to color display. A series of supervised and unsupervised data transformation and classification algorithms are reviewed, implemented, and compared for this purpose. The resulting color displays are evaluated in terms of class separability using a statistical detector and perceptual color distance. We demonstrate that the use of the data processing step can significantly improve the quality of color display, whereas data classification generally outperforms data transformation, although the implementation is more complicated. Several instructive suggestions for practitioners are provided.

Visualization of remotely-sensed meteorological data has traditionally consisted of two dimensional maps. However, the technological advancements in recent years have allowed data to be collected in new and unique ways and with greatly increased range and density. In particular, data are now collected at discrete locations within a volume, as opposed to points on a surface. The data volume, as opposed to an image, necessitates a different form of visualization. Unlike common techniques that stick on two dimensional maps, the main focus for the new techniques is showing the precipitation and other meteorological data in a more intuitive manner. This paper will introduce one of several possible ways to visualize a volume dataset. In this particular case rain intensity values gathered by NASA's TRMM satellite deliver a stereotypic volume dataset.

Displaying the abundant information contained in a hyperspectral image is a challenging problem. Almost any visualization approach reduces the information content. However, we want to maximize the amount of object or material information presented. A visualization approach that uses classification as an intermediate step may maximize the information transfer. In our research, we are particularly interested in the display of mixed-pixel classification results, since most pixels in a remotely sensed hyperspectral image are mixed pixels. In this paper, we propose a visualization technique that employs two layers to integrate the mixture information (i.e., endmembers and their abundances) in each pixel. Images can be displayed with any desired level of details.

Remote sensing imagery has relatively low spatial resolution. Since different materials/objects may be present in the area covered by a pixel, the pixel reflectance can be considered as the linear mixture of reflectance of these materials/objects (i.e., endmembers). Thus in remote sensing image processing we deal with mixed pixels instead of pure pixels as in traditional digital image processing. A multi-spectral or hyper-spectral image has tens to hundreds of spectral bands. How to display the plentiful information contained in such a 3D image cube is a challenging problem. In this paper, we will propose a visualization technique that employs two layers to integrate the mixture information (i.e., endmembers and their functional abundances) in each pixel With user-friendly interactive tools, images can be displayed at any desired level of details.

This paper presents an advanced evenly-spaced streamline placement algorithm for fast, high-quality, and robust layout of flow lines. A fourth-order Runge-Kutta integrator with adaptive step size and error control is employed for rapid accurate streamline advection. Cubic Hermite polynomial interpolation with large sample-spacing is adopted to create fewer evenly-spaced samples along each streamline to reduce the amount of distance checking. We propose two methods to enhance placement quality. Double queues are used to prioritize topological seeding and to favor long streamlines to minimize discontinuities. Adaptive distance control based on the local flow variance is explored to reduce cavities. Furthermore, we propose a universal, effective, fast, and robust loop detection strategy to address closed and spiraling streamlines. Our algorithm is an order-of-magnitude faster than Jobard and Lefer's algorithm with better placement quality and over 5 times faster than Mebarki et al.'s algorithm with comparable placement quality, but with a more robust solution to loop detection.

Forest management is a costly and time-consuming activity. Remote sensing has the potential to improve the process by making it cheaper and more efficient, but only if appropriate characteristics can be determined from computer-models. This paper describes the implementation of a forest visualization system and a corresponding user study that tests the accuracy of parameter estimation and forest characterization. The study uses data obtained from field-surveys to generate a computer-modeled forest. Five different stands were tested. Based on the quantitative results obtained, generally, there is no statistically significant difference in parameter estimation when comparing field-recorded videos and computer-generated videos.

Unsteady flow line integral convolution (UFLIC) is a texture synthesis technique for visualizing unsteady flows with high temporal-spatial coherence. Unfortunately, UFLIC requires considerable time to generate each frame due to the huge amount of pathline integration that is computed for particle value scattering. This paper presents Accelerated UFLIC (AUFLIC) for near interactive (1 frame/second) visualization with 160,000 particles per frame. AUFLIC reuses pathlines in the value scattering process to reduce computationally expensive pathline integration. A flow-driven seeding strategy is employed to distribute seeds such that only a few of them need pathline integration while most seeds are placed along the pathlines advected at earlier times by other seeds upstream and, therefore, the known pathlines can be reused for fast value scattering. To maintain a dense scattering coverage to convey high temporal-spatial coherence while keeping the expense of pathline integration low, a dynamic seeding controller is designed to decide whether to advect, copy, or reuse a pathline. At a negligible memory cost, AUFLIC is 9 times faster than UFLIC with comparable image quality.

Scientific Visualization (SciVis) has evolved past the point where one undergraduate course can cover all of the necessary topics. So the question becomes "how do we teach SciVis to this generation of students?" Some examples of current courses are: A graduate Computer Science (CS) course that prepares the next generation of SciVis researchers. An undergraduate CS course that prepares the future software architects/developers of packages such as vtk, vis5D and AVS. A class that teaches students how to do SciVis with existing software packages and how to deal with the lack of interoperability between those packages (via either a CS service course or a supercomputing center training course). An inter-disciplinary course designed to prepare computer scientists to work with the "real" scientists (via either a CS or Computational Science course). In this panel, we will discuss these types of courses and the advantages and disadvantages of each. We will also talk about some issues that you have probably encountered at your university: How do we keep the graphics/vis-oriented students from going to industry? How does SciVis fit in with evolving Computational Science programs? Is SciVis destined to be a service course at most universities? How do we deal with the diverse backgrounds of students that need SciVis?

This issue contains extended versions of six of the strongest papers taken from the IEEE Visualization 2003 Conference. This year we have followed a slightly different procedure than in previous years. We intended to give prospective authors more time to prepare an extended version, while simultaneously keeping a short time between the conference and the release of this issue. Therefore, in June 2003, just after the selection of papers for the conference, we started to select the most interesting papers. We, paper cochairs of IEEE Visualization 2003, started from the opinions of the reviewers, followed by several rounds of rereading and discussion. The authors of six outstanding papers were invited to submit an extended and revised version of their original work. Each revised paper was thoroughly reviewed by several experts before it was recommended for acceptance. We are grateful to the reviewers for their thorough and quick reviews, and to David Ebert, Editor-in-Chief of TVCG, for his strong support, wise advise, and always astonishly quick responses. One of the most fascinating aspects of visualization is the width of the field. We selected the papers on quality, but we were delighted to find out that, in the end, our selection covers a wide variety of topics, approaches, and methods. Novel results on feature extraction and simplification are given, but also novel interpolation results; the handling of various standard types of data, including scalar volume data, terrain data, and vector volume data, is discussed, but also a new representation is presented; sophisticated mathematics, including group theory and Morse theory, is used, but also the capabilities of modern graphics hardware are exploited to the limit.

ACHyear the IEEE Visualization Conference continues to be the premiere forum for presenting state-of-the-art research in all topics related to visualization. In this issue, we present revised and extended versions of some of the best papers from the 2004 edition of the conference. The selection process for inviting papers for this special issue followed the pattern set by the 2003 conference. In June 2004, after the conference paper review and selection was complete, the best papers were identified. The chairs considered the written comments from the reviewers as well as their own reading of the papers in this process. The authors of the papers identified were invited to prepare revised and extended versions of their conference papers during the summer and early fall of 2004. We then sent out the revised papers for a full journal-level review by external referees. The results of the revision and review process are the six papers which appear in this issue. The goal of visualization is to generate images that enable people to gain understanding. There are many facets to this endeavor, ranging from complex mathematical issues to issues of how we as humans interact with images. The papers included here span this range of activity. Two of the papers deal with the problem of interactive visualization of massive triangle models. The papers take different approaches to different versions of the problem. They have in common, though, introducing new algorithms based on new data representations that are demonstrated in fully implemented systems. In “Real-Time Optimal Adaptation for Planetary Geometry and Texture: 4-8 Tile Hierarchies,” Hwa, Duchaineau, and Joy consider the problem of terrain visualization. They introduce a unique diamond data structure to represent the mesh. The hierarchical data structure has the interesting property that diamonds in the hierarchy overlap with, but are not coincident with, their children. This structure facilitates more gradual transitions in level of detail than have been possible with previous approaches. The conference paper this is based on received the IEEE Visualization best paper award. “Quick-VDR: Out-of-Core View-Dependent Rendering of Gigantic Models” by Yoon, Salomon, Gayle, and Manocha uses a new representation for general triangle meshes—CHPM, a clustered hierarchy of progressive meshes. These clusters are the basic organization for level of detail management, culling, and out-of-core rendering. The system is demonstrated on a wide range of data sets, ranging from isosurfaces from turbulent flow simulations to data from 3D scanning of cultural heritage objects. Two of the papers focus on visualizing complex fields. Naive visualizations of these types of data sets result in overwhelming clutter. Both papers present robust methods for extracting key topological features to reduce massive data sets to elegantly simple representations revealing their basic structure. Theisel, Weinkauf, Hege, and Seidel consider temporally varying fields in “Topological Methods for 2D TimeDependent Vector Fields Based on Stream Lines and Path Lines.” The visualization of stream line topology has been previously studied. In this paper, the alternative of path line topology is introduced for the same class of data sets. The authors describe how to extract features in both approaches and compare the characteristics of the flow they reveal. Zheng, Parlett, and Pang consider tensor fields in

Presents a method to estimate illumination dependent properties in image synthesis prior to rendering. A preprocessing step is described in which a linear image basis is developed and a lighting-independent formulation defined. A reflection function, similar to hemispherical reflectance, approximates normal Lambertian shading. Intensity errors resulting from this approximation are reduced by use of a polynomial gamma correction function and scaling to a normalized display range. This produces images that are similar to normal Lambertian shading without employing the maximum (max) function. For a single object view, images can then be expressed in a linear form so that lighting direction can be factored out. During normal rendering, image quantities for arbitrary light directions can be found without rendering. This method is demonstrated for estimating image intensity and level-of-detail error prior to rendering an object.

Traditional methods for displaying weather products are generally two-dimensional (2D) plots or just text format. It is hard for forecasters to get the entire picture of the atmosphere using these methods. The problems apparent in 2D with comparing and correlating multiple layers are overcome simply by adding a dimension. This is important because pertinent features in the data sets may lie in multiple layers and span several time steps. However, simply using a three-dimensional (3D) approach is not enough. The capacity for analysis of small-scale, but important, features in 2D are lost when transitioning to 3D. We propose that 3D's advantages can be incorporated with 2D's small-scale analysis by using an immersive virtual environment. In this case study, we evaluate our current standing with the project: have we met our goals, and how should we proceed from this point? To evaluate our application, we invited meteorologists to use the application to explore a data set. Then we presented our goals and asked which ones had we met, from a meteorologist's perspective. The results qualitatively reflected that our application was effective and further research would be worthwhile.

The work presents a method to enable matching of level-of-detail (LOD) models to image-plane resolution over large variations in viewing distances often present in exterior images. A relationship is developed between image sampling rate, viewing distance, object projection, and expected image error due to LOD approximations. This is employed in an error metric to compute error profiles for LOD models. Multirate filtering in the frequency space of a reference object image is utilized to approximate multiple distant views over a range of orientations. An importance sampling method is described to better characterize perspective projection over view distance. A contrast sensitivity function (CSF) is employed to approximate the response of the vision system. Examples are presented for multiresolution spheres and a terrain height field feature. Future directions for extending this method are described.

Summary form only given. We present an efficient algorithm for compressing the data necessary to represent an arbitrary cutting plane extracted from a three-dimensional curvilinear data set. The cutting plane technique is an important visualization method for time-varying 3D simulation results since the data sets are often so large. An efficient compression algorithm for these cutting planes is especially important when the simulation running on a remote server is being tracked or the data set is stored on a remote server. Various aspects of the visualization process are considered in the algorithm design, such as the inherent data reduction in going from 3D to 2D when generating a cutting plane, the numerical accuracy required in the cutting plane, and the potential to decimate the triangle mesh. After separating each floating point number into mantissa and exponent, a block sorting algorithm and an entropy coding algorithm are used to perform lossless compression.

Numerical simulation of physical phenomena is an accepted way of scientific inquiry. However, the field is still evolving, with a profusion of new solution and grid generation techniques being continuously proposed. Concurrent and retrospective visualization are being used to validate the results. There is a need for representation schemes which allow access of structures in an increasing order of smoothness. We describe our methods on datasets obtained from curvilinear grids. Our target application required visualization of a computational simulation performed on a very remote supercomputer. Since no grid adaptation was performed, it was not deemed necessary to simplify or compress the grid. Inherent to the identification of significant structures is determining the location of the scale coherent structures and assigning saliency values to them. Scale coherent structures are obtained as a result of combining the coefficients of a wavelet transform across scales. The result of this operation is a correlation mask that delineates regions containing significant structures. A spatial subdivision is used to delineate regions of interest. The mask values in these subdivided regions are used as a measure of information content. Later, another wavelet transform is conducted within each subdivided region and the coefficients are sorted based on a perceptual function with bandpass characteristics. This allows for ranking of structures based on the order of significance, giving rise to an adaptive and embedded representation scheme. We demonstrate our methods on two datasets from computational field simulations. We show how our methods allow the ranked access of significant structures. We also compare our adaptive representation scheme with a fixed blocksize scheme.

The paper addresses multiresolutional representation of datasets arising from a computational field simulation. The approach determines the regions of interest, breaks the volume into variable size blocks to localize the information, and then codes each block using a wavelet transform. The blocks are then ranked by visual information content so that the most informative wavelet coefficients can be embedded in a bit stream for progressive transmission or access. The technique is demonstrated on a widely-used computational field simulation dataset.

Many times in computational fluid dynamics (CFD) work very large datasets are produced on remote machines. This vast amount of data must often be moved to a local machine for post processing and visualization. However, this can be time consuming because of the large quantity of data that must be transmitted. Compressing the data can speed up the transmission and save several hours of the researchers' time. Progressive transmission can further increase efficiency of the visualization process by giving researchers an approximation of the data very quickly. They can then make a decision based on this approximation about whether to continue the transmission or, if the data is determined to be undesirable, to abort it. A method of lossless compression using wavelets is presented that enables progressive transmission of CFD data in Plot-3D format, a standard format for CFD data. Given a CFD data set, the floating point data is first converted to double-precision floating point format. Although the conversion to double-precision floating point numbers doubles the size of the data set, most of the extra precision retains the value of zero. It can therefore be compressed very well using Huffman codes.

Sampling and analysis of subsurface contaminants comprise the first steps toward environmental remediation of hazardous spills. We have developed software tools to support the analysis phase, using three different schemes for interpolating scattered 3D soil-quality data onto a grid suitable for viewing in an interactive visualization system. A good interpolation scheme is one that respects the distribution of the original data. We find that the original data can be decimated by up to seventy percent while exhibiting graceful degradation in quality. A prototype software system is being deployed to allow technicians to visually determine, while in the field with their monitoring equipment, where the highest concentrations of contaminants lie. The system is now in use by the U.S. Army Corps of Engineers.

Visualization of computational oceanography is traditionally a post-processing step. This batch orientation is clumsy if one wants to observe the effect of a wide range of parameters on the solution. This paper describes the conversion of an ocean circulation model from this traditional design to an interactive program in which the computed solution is viewed in real-time over a wide-area network and the user is given the ability to change the model parameters and immediately observe the impact this has on the solution.

A method of lossless compression using wavelets is presented that enables progressive transmission of computational fluid dynamics (CFD) data in PLOT3D format. The floating point data is first converted to double-precision floating point format to maintain adequate precision throughout the transform process. It is then transformed using Haar wavelets-four times in two spatial dimensions, twice in the third spatial dimension, and twice in time for a total compression factor of 64 times. The double precision format will maintain enough precision during the transform to keep the process lossless. Next, the transformed data is compressed using Huffman coding and transmitted progressively using spectral selection. This allows most of the information to be transmitted in the first pass. Details are transmitted in later passes which ultimately provide for lossless reconstruction of the original data.

Particle path computation in unsteady 3D vector fields given in discrete, structured form (i.e., as a hexahedral curvilinear grid) requires the local approximation of the vector field and the path. Quadrilinear interpolation and Bernstein-Bezier polynomials are used for the local vector field and path approximation. The next point in a sequence of points on a particle path is computed using this local approximation. Bernstein-Bezier polynomials are primarily used in geometric modeling, and their properties allow direct computation of points on a particle path.>

A new progressive transmission scheme using spline biorthogonal wavelet bases is proposed in this paper. First, several wavelet bases are compared with the spline biorthogonal wavelet bases. By exploiting the properties of this set of wavelet bases, a fast algorithm involving only additions and subtractions is developed. Due to the multiresolutional nature of the wavelet transform, this scheme is compatible with hierarchical-structured rendering algorithms. The formula for reconstructing the functional values in a continuous volume space is given in a simple polynomial form. Lossless compression is possible, even when using floating-point numbers. When the algorithm is applied to data from a global ocean model, the lossless compression ratio is about 1.5:1. Even with a compression ratio of 50:1, the reconstructed data is still of good quality. Finally, the reconstructed data is rendered using various visualization algorithms and the results are demonstrated.>

Environmental issues such as global warming are an active area of international research and concern today. This case study describes various visualization paradigms that have been developed and applied in an attempt to elucidate the information provided by environmental models and observations. The ultimate goal is to accurately measure the existence of any long term climatological change. The global ocean is the starting point, since it is a major source and sink of heat within our global environment.>

An important issue in scientific visualization systems is the management of data sets. Most data sets in scientific visualization, whether created by measurement or simulation, are usually voluminous. The goal of data management is to reduce the storage space and the access time of these data sets to speed up the visualization process. A new progressive transmission scheme using spline biorthogonal wavelet bases is proposed in this paper. By exploiting the properties of this set of wavelet bases, a fast algorithm involving only additions and subtractions is developed. Due to the multiresolutional nature of the wavelet transform, this scheme is compatible with hierarchical-structured rendering algorithms. The formula for reconstructing the functional values in a continuous volume space is given in a simple polynomial form. Lossless compression is possible, even when using floating-point numbers. This algorithm has been applied to data from a global ocean model. The lossless compression ratio is about 1.5:1. With a compression ratio of 50:1, the reconstructed data is still of good quality. Several other wavelet bases are compared with the spline biorthogonal wavelet bases. Finally the reconstructed data is visualized using various algorithms and the results are demonstrated.>

This paper presents and analyzes a pel-recursive, motioncompensated, image sequence compression algorithm [1]. The analysis retains all the terms of the Taylor's series expansion and yields a set of equations for which the convergence criteria and the convergence rate of the motion estimate are more easily seen. The existing motion prediction schemes are also reviewed and a new motion prediction scheme is presented which is shown to be superior to the existing schemes. Simulations run on actual image sequences to verify the analytical results indicate that implementing the analytical model as opposed to the generally used heuristic technique does yield a decrease in the information rate and the computational requirements. Simulation results also are included which use the "projection-along-the-motiontrajectory" or PAMT prediction scheme. Third, zeroth-order entropy encoding is shown to reduce the bit rate on the order of 12 percent, and to reduce the mean square error in the reconstructed images on the order of 60 percent when compared to first-order entropy encoding. Fourth, field-to-field motion prediction is compared to frame-to-frame motion prediction.

This paper addresses various aspects of motion-compensated interframe coding. The image sequence data is investigated in an attempt to develop a more thorough analysis of the convergence requirements and the convergence rate. A new motion prediction technique is used which increases the validity of the assumptions made in proving convergence and which decreases the total prediction error. Simulation results are presented to indicate the improvement of the proposed motion prediction scheme and to indicate the results of the convergence analysis.