Search

Bike-sharing systems are a popular mode of public transportation, increasing in number and size around the world. Public bike-sharing systems attend to the needs of a large number of commuters while synchronizing to the rhythm of big cities. To better understand the usage of such systems, we introduce an interactive visualization system to explore the dynamics of public bike-sharing systems by profiling its historical dataset. By coordinating a pixel-oriented timeline with a map, and introducing a scheme of partial reordering of time series, our design supports the identification of several patterns in temporal and spatial domains. We take New York City׳s bike-sharing program, Citi Bike, as a use case and implement a prototype to show changes in the system over a period of ten months, ranking stations by different properties, using any time interval in daily and monthly timelines. Different analyses are presented to validate the visualization system as a useful operational tool that can support the staff of bike-sharing programs of big cities in the exploration of such large datasets, in order to understand the commuting dynamics to overcome management problems and provide a better service to commuters. [ABSTRACT FROM AUTHOR]

The traffic infrastructure greatly impacts the quality of life in urban environments. To optimize this infrastructure, engineers and decision makers need to explore traffic data. In doing so, they face two important challenges: the sparseness of speed sensors that cover only a limited number of road segments, and the complexity of traffic patterns they need to analyze. In this paper we take a first step at addressing these challenges. We use New York City (NYC) taxi trips as sensors to capture traffic information. While taxis provide substantial coverage of the city, the data captured about taxi trips contain neither the location of taxis at frequent intervals nor their routes. We propose an efficient traffic model to derive speed and direction information from these data, and show that it provides reliable estimates. Using these estimates, we define a time-varying vector-valued function on a directed graph representing the road network, and adapt techniques used for vector fields to visualize the traffic dynamics. We demonstrate the utility of our technique in several case studies that reveal interesting mobility patterns in NYC's traffic. These patterns were validated by experts from NYC's Department of Transportation and the NYC Taxi & Limousine Commission, who also provided interesting insights into these results. [ABSTRACT FROM AUTHOR]

Simplicial meshes are useful as discrete approximations of continuous spaces in numerical simulations. In some applications, however, meshes need to be modified over time. Mesh update operations are often expensive and brittle, making the simulations unstable. In this paper we propose a framework for updating simplicial meshes that undergo geometric and topological changes. Instead of explicitly maintaining connectivity information, we keep a collection of weights associated with mesh vertices, using a Weighted Delaunay Triangulation (WDT). These weights implicitly define mesh connectivity and allow direct merging of triangulations. We propose two formulations for computing the weights, and two techniques for merging triangulations, and finally illustrate our results with examples in two and three dimensions. [ABSTRACT FROM AUTHOR]

Scientists study trajectory data to understand trends in movement patterns, such as human mobility for traffic analysis and urban planning. In this paper, we introduce a novel trajectory clustering technique whose central idea is to use vector fields to induce a notion of similarity between trajectories, letting the vector fields themselves define and represent each cluster. We present an efficient algorithm to find a locally optimal clustering of trajectories into vector fields, and demonstrate how vector-field k-means can find patterns missed by previous methods. We present experimental evidence of its effectiveness and efficiency using several datasets, including historical hurricane data, GPS tracks of people and vehicles, and anonymous cellular radio handoffs from a large service provider. [ABSTRACT FROM AUTHOR]

Deformable image registration in the presence of considerable contrast differences and large size and shape changes presents significant research challenges. First, it requires a robust registration framework that does not depend on intensity measurements and can handle large nonlinear shape variations. Second, it involves the expensive computation of nonlinear deformations with high degrees of freedom. Often it takes a significant amount of computation time and thus becomes infeasible for practical purposes. In this paper, we present a solution based on two key ideas: a new registration method that generates a mapping between anatomies represented as a multicompartment model of class posterior images and geometries and an implementation of the algorithm using particle mesh approximation on Graphical Processing Units (GPUs) to fulfill the computational requirements. We show results on the registrations of neonatal to 2-year old infant MRIs. Quantitative validation demonstrates that our proposed method generates registrations that better maintain the consistency of anatomical structures over time and provides transformations that better preserve structures undergoing large deformations than transformations obtained by standard intensity-only registration. We also achieve the speedup of three orders of magnitudes compared to a CPU reference implementation, making it possible to use the technique in time-critical applications. [ABSTRACT FROM AUTHOR]

Abstract: In this work we introduce a new hierarchical surface decomposition method for multiscale analysis of surface meshes. In contrast to other multiresolution methods, our approach relies on spectral properties of the surface to build a binary hierarchical decomposition. Namely, we utilize the first nontrivial eigenfunction of the Laplace–Beltrami operator to recursively decompose the surface. For this reason we coin our surface decomposition the Fiedler tree. Using the Fiedler tree ensures a number of attractive properties, including: mesh-independent decomposition, well-formed and nearly equi-areal surface patches, and noise robustness. We show how the evenly distributed patches can be exploited for generating multiresolution high quality uniform meshes. Additionally, our decomposition permits a natural means for carrying out wavelet methods, resulting in an intuitive method for producing feature-sensitive meshes at multiple scales. [Copyright &y& Elsevier]

We propose a new framework design for exploiting multi-core architectures in the context of visualization dataflow systems. Recent hardware advancements have greatly increased the levels of parallelism available with all indications showing this trend will continue in the future. Existing visualization dataflow systems have attempted to take advantage of these new resources, though they still have a number of limitations when deployed on shared memory multi-core architectures. Ideally, visualization systems should be built on top of a parallel dataflow scheme that can optimally utilize CPUs and assign resources adaptively to pipeline elements. We propose the design of a flexible dataflow architecture aimed at addressing many of the shortcomings of existing systems including a unified execution model for both demand-driven and event-driven models; a resource scheduler that can automatically make decisions on how to allocate computing resources; and support for more general streaming data structures which include unstructured elements. We have implemented our system on top of VTK with backward compatibility. In this paper, we provide evidence of performance improvements on a number of applications. [ABSTRACT FROM AUTHOR]

Interactive visualization of time-varying volume data is essential for many scientific simulations. This is a challenging problem since this data is often large, can be organized in different formats (regular or irregular grids), with variable instances of time (from hundreds to thousands) and variable domain fields. It is common to consider subsets of this problem, such as time-varying scalar fields (TVSFs) on static structured grids, which are suitable for compression using multi-resolution techniques and can be efficiently rendered using texture-mapping hardware. In this work we propose a rendering system that considers unstructured grids, which do not have the same regular properties crucial to compression and rendering. Our solution simultaneously leverages multiple processors and the graphics processing unit (GPU) to perform decompression, level-of-detail selection, and volume visualization of dynamic data. The resulting framework is general enough to adaptively handle visualization tasks such as direct volume rendering and isosurfacing while allowing the user to control the speed and quality of the animation. [Copyright &y& Elsevier]

We propose a novel surface remeshing algorithm. While many remeshing algorithms are based on global parametrization or local mesh optimization, our algorithm is closely related to surface reconstruction techniques and it requires no explicit parameterization. Our approach is based on the advancing-front paradigm, and it can be used to both incrementally remesh the complete surface, or simply to remesh a portion of it with a high-quality mesh. It is accurate, fast, robust, and suitable for use with interactive mesh processing applications that require local remeshing. We show a number of applications, including matching the resolution of meshes when doing Boolean operations such as unions and intersections. We also show how to adapt the algorithm to blend and merge mixed-mode objects — for example, to compute the union of a point-set surface and a triangle mesh. [ABSTRACT FROM AUTHOR]

Direct volume rendering based on projective methods works by projecting, in visibility order, the polyhedral cells of a mesh onto the image plane, and incrementally compositing the cell's color and opacity into the final image. Crucial to this method is the computation of a visibility ordering of the cells. If the mesh is "well-behaved" (acyclic and convex), then the MPVO method of Williams provides a very fast sorting algorithm; however, this method only computes an approximate ordering in general datasets, resulting in visual artifacts when rendered. A recent method of Silva et al. removed the assumption that the mesh is convex, by means of a sweep algorithm used in conjunction with the MPVO method; their algorithm is substantially faster than previous exact methods for general meshes. In this paper we propose a new technique, which we call BSP-XMPVO, which is based on a fast and simple way of using binary space partitions on the boundary elements of the mesh to augment the ordering produced by MPVO. Our results are shown to be orders of magnitude better than previous exact methods of sorting cells. [ABSTRACT FROM AUTHOR]

Background  The trapezius muscle is often utilized as a muscle or nerve donor for repairing shoulder function in those with brachial plexus birth palsy (BPBP). To evaluate the native role of the trapezius in the affected limb, we demonstrate use of the Motion Browser, a novel visual analytics system to assess an adolescent with BPBP. Method  An 18-year-old female with extended upper trunk (C5-6-7) BPBP underwent bilateral upper extremity three-dimensional motion analysis with Motion Browser. Surface electromyography (EMG) from eight muscles in each limb which was recorded during six upper extremity movements, distinguishing between upper trapezius (UT) and lower trapezius (LT). The Motion Browser calculated active range of motion (AROM), compiled the EMG data into measures of muscle activity, and displayed the results in charts. Results  All movements, excluding shoulder abduction, had similar AROM in affected and unaffected limbs. In the unaffected limb, LT was more active in proximal movements of shoulder abduction, and shoulder external and internal rotations. In the affected limb, LT was more active in distal movements of forearm pronation and supination; UT was more active in shoulder abduction. Conclusion  In this female with BPBP, Motion Browser demonstrated that the native LT in the affected limb contributed to distal movements. Her results suggest that sacrificing her trapezius as a muscle or nerve donor may affect her distal functionality. Clinicians should exercise caution when considering nerve transfers in children with BPBP and consider individualized assessment of functionality before pursuing surgery., Competing Interests: Conflict of Interest None declared., (The Author(s). This is an open access article published by Thieme under the terms of the Creative Commons Attribution License, permitting unrestricted use, distribution, and reproduction so long as the original work is properly cited. ( https://creativecommons.org/licenses/by/4.0/ ).)

Public transportation schedules are designed by agencies to optimize service quality under multiple constraints. However, real service usually deviates from the plan. Therefore, transportation analysts need to identify, compare and explain both eventual and systemic performance issues that must be addressed so that better timetables can be created. The purely statistical tools commonly used by analysts pose many difficulties due to the large number of attributes at trip- and station-level for planned and real service. Also challenging is the need for models at multiple scales to search for patterns at different times and stations, since analysts do not know exactly where or when relevant patterns might emerge and need to compute statistical summaries for multiple attributes at different granularities. To aid in this analysis, we worked in close collaboration with a transportation expert to design TR-EX, a visual exploration tool developed to identify, inspect and compare spatio-temporal patterns for planned and real transportation service. TR-EX combines two new visual encodings inspired by Marey's Train Schedule: Trips Explorer for trip-level analysis of frequency, deviation and speed; and Stops Explorer for station-level study of delay, wait time, reliability and performance deficiencies such as bunching. To tackle overplotting and to provide a robust representation for a large numbers of trips and stops at multiple scales, the system supports variable kernel bandwidths to achieve the level of detail required by users for different tasks. We justify our design decisions based on specific analysis needs of transportation analysts. We provide anecdotal evidence of the efficacy of TR-EX through a series of case studies that explore NYC subway service, which illustrate how TR-EX can be used to confirm hypotheses and derive new insights through visual exploration.

Evaluation methodologies in visualization have mostly focused on how well the tools and techniques cater to the analytical needs of the user. While this is important in determining the effectiveness of the tools and advancing the state-of-the-art in visualization research, a key area that has mostly been overlooked is how well established visualization theories and principles are instantiated in practice. This is especially relevant when domain experts, and not visualization researchers, design visualizations for analysis of their data or for broader dissemination of scientific knowledge. There is very little research on exploring the synergistic capabilities of cross-domain collaboration between domain experts and visualization researchers. To fill this gap, in this paper we describe the results of an exploratory study of climate data visualizations conducted in tight collaboration with a pool of climate scientists. The study analyzes a large set of static climate data visualizations for identifying their shortcomings in terms of visualization design. The outcome of the study is a classification scheme that categorizes the design problems in the form of a descriptive taxonomy. The taxonomy is a first attempt for systematically categorizing the types, causes, and consequences of design problems in visualizations created by domain experts. We demonstrate the use of the taxonomy for a number of purposes, such as, improving the existing climate data visualizations, reflecting on the impact of the problems for enabling domain experts in designing better visualizations, and also learning about the gaps and opportunities for future visualization research. We demonstrate the applicability of our taxonomy through a number of examples and discuss the lessons learnt and implications of our findings.

The explosion in the volume of data about urban environments has opened up opportunities to inform both policy and administration and thereby help governments improve the lives of their citizens, increase the efficiency of public services, and reduce the environmental harms of development. However, cities are complex systems and exploring the data they generate is challenging. The interaction between the various components in a city creates complex dynamics where interesting facts occur at multiple scales, requiring users to inspect a large number of data slices over time and space. Manual exploration of these slices is ineffective, time consuming, and in many cases impractical. In this paper, we propose a technique that supports event-guided exploration of large, spatio-temporal urban data. We model the data as time-varying scalar functions and use computational topology to automatically identify events in different data slices. To handle a potentially large number of events, we develop an algorithm to group and index them, thus allowing users to interactively explore and query event patterns on the fly. A visual exploration interface helps guide users towards data slices that display interesting events and trends. We demonstrate the effectiveness of our technique on two different data sets from New York City (NYC): data about taxi trips and subway service. We also report on the feedback we received from analysts at different NYC agencies.

Elucidation of transcriptional regulatory networks (TRNs) is a fundamental goal in biology, and one of the most important components of TRNs are transcription factors (TFs), proteins that specifically bind to gene promoter and enhancer regions to alter target gene expression patterns. Advances in genomic technologies as well as advances in computational biology have led to multiple large regulatory network models (directed networks) each with a large corpus of supporting data and gene-annotation. There are multiple possible biological motivations for exploring large regulatory network models, including: validating TF-target gene relationships, figuring out co-regulation patterns, and exploring the coordination of cell processes in response to changes in cell state or environment. Here we focus on queries aimed at validating regulatory network models, and on coordinating visualization of primary data and directed weighted gene regulatory networks. The large size of both the network models and the primary data can make such coordinated queries cumbersome with existing tools and, in particular, inhibits the sharing of results between collaborators. In this work, we develop and demonstrate a web-based framework for coordinating visualization and exploration of expression data (RNA-seq, microarray), network models and gene-binding data (ChIP-seq). Using specialized data structures and multiple coordinated views, we design an efficient querying model to support interactive analysis of the data. Finally, we show the effectiveness of our framework through case studies for the mouse immune system (a dataset focused on a subset of key cellular functions) and a model bacteria (a small genome with high data-completeness).

We propose an approach for verification of volume rendering correctness based on an analysis of the volume rendering integral, the basis of most DVR algorithms. With respect to the most common discretization of this continuous model (Riemann summation), we make assumptions about the impact of parameter changes on the rendered results and derive convergence curves describing the expected behavior. Specifically, we progressively refine the number of samples along the ray, the grid size, and the pixel size, and evaluate how the errors observed during refinement compare against the expected approximation errors. We derive the theoretical foundations of our verification approach, explain how to realize it in practice, and discuss its limitations. We also report the errors identified by our approach when applied to two publicly available volume rendering packages.

As increasing volumes of urban data are captured and become available, new opportunities arise for data-driven analysis that can lead to improvements in the lives of citizens through evidence-based decision making and policies. In this paper, we focus on a particularly important urban data set: taxi trips. Taxis are valuable sensors and information associated with taxi trips can provide unprecedented insight into many different aspects of city life, from economic activity and human behavior to mobility patterns. But analyzing these data presents many challenges. The data are complex, containing geographical and temporal components in addition to multiple variables associated with each trip. Consequently, it is hard to specify exploratory queries and to perform comparative analyses (e.g., compare different regions over time). This problem is compounded due to the size of the data-there are on average 500,000 taxi trips each day in NYC. We propose a new model that allows users to visually query taxi trips. Besides standard analytics queries, the model supports origin-destination queries that enable the study of mobility across the city. We show that this model is able to express a wide range of spatio-temporal queries, and it is also flexible in that not only can queries be composed but also different aggregations and visual representations can be applied, allowing users to explore and compare results. We have built a scalable system that implements this model which supports interactive response times; makes use of an adaptive level-of-detail rendering strategy to generate clutter-free visualization for large results; and shows hidden details to the users in a summary through the use of overlay heat maps. We present a series of case studies motivated by traffic engineers and economists that show how our model and system enable domain experts to perform tasks that were previously unattainable for them.

Creating high-quality quad meshes from triangulated surfaces is a highly nontrivial task that necessitates consideration of various application specific metrics of quality. In our work, we follow the premise that automatic reconstruction techniques may not generate outputs meeting all the subjective quality expectations of the user. Instead, we put the user at the center of the process by providing a flexible, interactive approach to quadrangulation design. By combining scalar field topology and combinatorial connectivity techniques, we present a new framework, following a coarse to fine design philosophy, which allows for explicit control of the subjective quality criteria on the output quad mesh, at interactive rates. Our quadrangulation framework uses the new notion of Reeb atlas editing, to define with a small amount of interactions a coarse quadrangulation of the model, capturing the main features of the shape, with user prescribed extraordinary vertices and alignment. Fine grain tuning is easily achieved with the notion of connectivity texturing, which allows for additional extraordinary vertices specification and explicit feature alignment, to capture the high-frequency geometries. Experiments demonstrate the interactivity and flexibility of our approach, as well as its ability to generate quad meshes of arbitrary resolution with high-quality statistics, while meeting the user’s own subjective requirements.

Image population analysis is the class of statistical methods that plays a central role in understanding the development, evolution, and disease of a population. However, these techniques often require excessive computational power and memory that are compounded with a large number of volumetric inputs. Restricted access to supercomputing power limits its influence in general research and practical applications. In this paper we introduce ISP, an Image-Set Processing streaming framework that harnesses the processing power of commodity heterogeneous CPU/GPU systems and attempts to solve this computational problem. In ISP, we introduce specially designed streaming algorithms and data structures that provide an optimal solution for out-of-core multiimage processing problems both in terms of memory usage and computational efficiency. ISP makes use of the asynchronous execution mechanism supported by parallel heterogeneous systems to efficiently hide the inherent latency of the processing pipeline of out-of-core approaches. Consequently, with computationally intensive problems, the ISP out-of-core solution can achieve the same performance as the in-core solution. We demonstrate the efficiency of the ISP framework on synthetic and real datasets.

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.

Public genealogical databases are becoming increasingly populated with historical data and records of the current population's ancestors. As this increasing amount of available information is used to link individuals to their ancestors, the resulting trees become deeper and more dense, which justifies the need for using organized, space-efficient layouts to display the data. Existing layouts are often only able to show a small subset of the data at a time. As a result, it is easy to become lost when navigating through the data or to lose sight of the overall tree structure. On the contrary, leaving space for unknown ancestors allows one to better understand the tree's structure, but leaving this space becomes expensive and allows fewer generations to be displayed at a time. In this work, we propose that the H-tree based layout be used in genealogical software to display ancestral trees. We will show that this layout presents an increase in the number of displayable generations, provides a nicely arranged, symmetrical, intuitive and organized fractal structure, increases the user's ability to understand and navigate through the data, and accounts for the visualization requirements necessary for displaying such trees. Finally, user-study results indicate potential for user acceptance of the new layout.

Most multidimensional projection techniques rely on distance (dissimilarity) information between data instances to embed high-dimensional data into a visual space. When data are endowed with Cartesian coordinates, an extra computational effort is necessary to compute the needed distances, making multidimensional projection prohibitive in applications dealing with interactivity and massive data. The novel multidimensional projection technique proposed in this work, called Part-Linear Multidimensional Projection (PLMP), has been tailored to handle multivariate data represented in Cartesian high-dimensional spaces, requiring only distance information between pairs of representative samples. This characteristic renders PLMP faster than previous methods when processing large data sets while still being competitive in terms of precision. Moreover, knowing the range of variation for data instances in the high-dimensional space, we can make PLMP a truly streaming data projection technique, a trait absent in previous methods.

We introduce a flexible technique for interactive exploration of vector field data through classification derived from user-specified feature templates. Our method is founded on the observation that, while similar features within the vector field may be spatially disparate, they share similar neighborhood characteristics. Users generate feature-based visualizations by interactively highlighting well-accepted and domain specific representative feature points. Feature exploration begins with the computation of attributes that describe the neighborhood of each sample within the input vector field. Compilation of these attributes forms a representation of the vector field samples in the attribute space. We project the attribute points onto the canonical 2D plane to enable interactive exploration of the vector field using a painting interface. The projection encodes the similarities between vector field points within the distances computed between their associated attribute points. The proposed method is performed at interactive rates for enhanced user experience and is completely flexible as showcased by the simultaneous identification of diverse feature types.

Deformable image registration in the presence of considerable contrast differences and large-scale size and shape changes represents a significant challenge for image registration. A representative driving application is the study of early brain development in neuroimaging, which requires co-registration of images of the same subject across time or building 4-D population atlases. Growth during the first few years of development involves significant changes in size and shape of anatomical structures but also rapid changes in tissue properties due to myelination and structuring that are reflected in the multi-modal Magnetic Resonance (MR) contrast measurements. We propose a new registration method that generates a mapping between brain anatomies represented as a multi-compartment model of tissue class posterior images and geometries. We transform intensity patterns into combined probabilistic and geometric descriptors that drive the matching in a diffeomorphic framework, where distances between geometries are represented using currents which does not require geometric correspondence. We show preliminary results on the registrations of neonatal brain MRIs to two-year old infant MRIs using class posteriors and surface boundaries of structures undergoing major changes. Quantitative validation demonstrates that our proposed method generates registrations that better preserve the consistency of anatomical structures over time.

Visual representations of isosurfaces are ubiquitous in the scientific and engineering literature. In this paper, we present techniques to assess the behavior of isosurface extraction codes. Where applicable, these techniques allow us to distinguish whether anomalies in isosurface features can be attributed to the underlying physical process or to artifacts from the extraction process. Such scientific scrutiny is at the heart of verifiable visualization--subjecting visualization algorithms to the same verification process that is used in other components of the scientific pipeline. More concretely, we derive formulas for the expected order of accuracy (or convergence rate) of several isosurface features, and compare them to experimentally observed results in the selected codes. This technique is practical: in two cases, it exposed actual problems in implementations. We provide the reader with the range of responses they can expect to encounter with isosurface techniques, both under "normal operating conditions" and also under adverse conditions. Armed with this information--the results of the verification process--practitioners can judiciously select the isosurface extraction technique appropriate for their problem of interest, and have confidence in its behavior.

We investigate the influence of bandwidth selection in the reconstruction quality of point-based surfaces. While the problem has received relatively little attention in the literature, we show that appropriate selection plays a significant role in the quality of reconstructed surfaces. We show how to compute optimal bandwidths for one class of moving least-squares surfaces by formulating the polynomial fitting step as a kernel regression problem for both noiseless and noisy data. In the context of Levin's projection, we also discuss the implications of the two-step projection for bandwidth selection. We show experimental comparisons of our method, which outperforms heuristically chosen functions and weights previously proposed. We also show the influence of bandwidth on the reconstruction quality of different formulations of point-based surfaces. We provide, to the best of our knowledge, the first quantitative comparisons between different MLS surface formulations and their optimal bandwidths. Using these experiments, we investigate the choice of effective bandwidths for these alternative formulations. We conclude with a discussion of how to effectively compare the different MLS formulations in the literature.

Marching Cubes is a popular choice for isosurface extraction from regular grids due to its simplicity, robustness, and efficiency. One of the key shortcomings of this approach is the quality of the resulting meshes, which tend to have many poorly shaped and degenerate triangles. This issue is often addressed through post processing operations such as smoothing. As we demonstrate in experiments with several datasets, while these improve the mesh, they do not remove all degeneracies, and incur an increased and unbounded error between the resulting mesh and the original isosurface. Rather than modifying the resulting mesh, we propose a method to modify the grid on which Marching Cubes operates. This modification greatly increases the quality of the extracted mesh. In our experiments, our method did not create a single degenerate triangle, unlike any other method we experimented with. Our method incurs minimal computational overhead, requiring at most twice the execution time of the original Marching Cubes algorithm in our experiments. Most importantly, it can be readily integrated in existing Marching Cubes implementations, and is orthogonal to many Marching Cubes enhancements (particularly, performance enhancements such as out-of-core and acceleration structures).

Recent results have shown a link between geometric properties of isosurfaces and statistical properties of the underlying sampled data. However, this has two defects: not all of the properties described converge to the same solution, and the statistics computed are not always invariant under isosurface-preserving transformations. We apply Federer's Coarea Formula from geometric measure theory to explain these discrepancies. We describe an improved substitute for histograms based on weighting with the inverse gradient magnitude, develop a statistical model that is invariant under isosurface-preserving transformations, and argue that this provides a consistent method for algorithm evaluation across multiple datasets based on histogram equalization. We use our corrected formulation to reevaluate recent results on average isosurface complexity, and show evidence that noise is one cause of the discrepancy between the expected figure and the observed one.

Marching Cubes is the most popular isosurface extraction algorithm due to its simplicity, efficiency and robustness. It has been widely studied, improved, and extended. While much early work was concerned with efficiency and correctness issues, lately there has been a push to improve the quality of Marching Cubes meshes so that they can be used in computational codes. In this work we present a new classification of MC cases that we call Edge Groups, which helps elucidate the issues that impact the triangle quality of the meshes that the method generates. This formulation allows a more systematic way to bound the triangle quality, and is general enough to extend to other polyhedral cell shapes used in other polygonization algorithms. Using this analysis, we also discuss ways to improve the quality of the resulting triangle mesh, including some that require only minor modifications of the original algorithm.

Building visualization and analysis pipelines is a large hurdle in the adoption of visualization and workflow systems by domain scientists. In this paper, we propose techniques to help users construct pipelines by consensus--automatically suggesting completions based on a database of previously created pipelines. In particular, we compute correspondences between existing pipeline subgraphs from the database, and use these to predict sets of likely pipeline additions to a given partial pipeline. By presenting these predictions in a carefully designed interface, users can create visualizations and other data products more efficiently because they can augment their normal work patterns with the suggested completions. We present an implementation of our technique in a publicly-available, open-source scientific workflow system and demonstrate efficiency gains in real-world situations.

Visualization is often employed as part of the simulation science pipeline-it's the window through which scientists examine their data for deriving new science, and the lens used to view modeling and discretization interactions within their simulations. We advocate that as a component of the simulation science pipeline, visualization must be explicitly considered as part of the validation and verification (V&V) process. In this article, the authors define V&V in the context of computational science, discuss the role of V&V in the scientific process, and present arguments for the need for verifiable visualization.

Unstructured tetrahedral meshes are commonly used in scientific computing to represent scalar, vector, and tensor fields in three dimensions. Visualization of these meshes can be difficult to perform interactively due to their size and complexity. By reducing the size of the data, we can accomplish real-time visualization necessary for scientific analysis. We propose a two-step approach for streaming simplification of large tetrahedral meshes. Our algorithm arranges the data on disk in a streaming, I/O-efficient format that allows coherent access to the tetrahedral cells. A quadric-based simplification is sequentially performed on small portions of the mesh in-core. Our output is a coherent streaming mesh which facilitates future processing. Our technique is fast, produces high quality approximations, and operates out-of-core to process meshes too large for main memory.

We describe a new progressive technique that allows real-time rendering of extremely large tetrahedral meshes. Our approach uses a client-server architecture to incrementally stream portions of the mesh from a server to a client which refines the quality of the approximate rendering until it converges to a full quality rendering. The results of previous steps are re-used in each subsequent refinement, thus leading to an efficient rendering. Our novel approach keeps very little geometry on the client and works by refining a set of rendered images at each step. Our interactive representation of the dataset is efficient, light-weight, and high quality. We present a framework for the exploration of large datasets stored on a remote server with a thin client that is capable of rendering and managing full quality volume visualizations.

Isosurfaces are ubiquitous in many fields, including visualization, graphics, and vision. They are often the main computational component of important processing pipelines (e.g. , surface reconstruction), and are heavily used in practice. The classical approach to compute isosurfaces is to apply the Marching Cubes algorithm, which although robust and simple to implement, generates surfaces that require additional processing steps to improve triangle quality and mesh size. An important issue is that in some cases, the surfaces generated by Marching Cubes are irreparably damaged, and important details are lost which can not be recovered by subsequent processing. The main motivation of this work is to develop a technique capable of constructing high-quality and high-fidelity isosurfaces. We propose a new advancing front technique that is capable of creating high-quality isosurfaces from regular and irregular volumetric datasets. Our work extends the guidance field framework of Schreiner et al. to implicit surfaces, and improves it in significant ways. In particular, we describe a set of sampling conditions that guarantee that surface features will be captured by the algorithm. We also describe an efficient technique to compute a minimal guidance field, which greatly improves performance. Our experimental results show that our technique can generate high-quality meshes from complex datasets.

Harvesting the power of modern graphics hardware to solve the complex problem of real-time rendering of large unstructured meshes is a major research goal in the volume visualization community. While, for regular grids, texture-based techniques are well-suited for current GPUs, the steps necessary for rendering unstructured meshes are not so easily mapped to current hardware. We propose a novel volume rendering technique that simplifies the CPU-based processing and shifts much of the sorting burden to the GPU, where it can be performed more efficiently. Our hardware-assisted visibility sorting algorithm is a hybrid technique that operates in both object-space and image-space. In object-space, the algorithm performs a partial sort of the 3D primitives in preparation for rasterization. The goal of the partial sort is to create a list of primitives that generate fragments in nearly sorted order. In image-space, the fragment stream is incrementally sorted using a fixed-depth sorting network. In our algorithm, the object-space work is performed by the CPU and the fragment-level sorting is done completely on the GPU. A prototype implementation of the algorithm demonstrates that the fragment-level sorting achieves rendering rates of between one and six million tetrahedral cells per second on an ATI Radeon 9800.

Projection methods for volume rendering unstructured data work by projecting, in visibility order, the polyhedral cells of the mesh onto the image plane, and incrementally compositing each cell's color and opacity into the final image. Normally, such methods require an algorithm to determine a visibility order of the cells. The Meshed Polyhedra Visibility Order (MPVO) algorithm can provide such an order for convex meshes by considering the implications of local ordering relations between cells sharing a common face. However, in nonconvex meshes, one must also consider ordering relations along viewing rays which cross empty space between cells. In order to include these relations, the algorithm described in this paper, the scanning exact meshed polyhedra visibility ordering (SXMPVO) algorithm, scan-converts the exterior faces of the mesh and saves the ray-face intersections in an A-Buffer data structure which is then used for retrieving the extra ordering relations. The image which SXMPVO produces is the same as would be produced by ordering the cells exactly, even though SXMPVO does not compute an exact visibility ordering. This is because the image resolution used for computing the visibility ordering relations is the same as that which is used for the actual volume rendering and we choose our A-Buffer rays at the same sample points that are used to establish a polygon's pixel coverage during hardware scan conversion. Thus, the algorithm is image-space correct. The SXMPVO algorithm has several desirable features; among them are speed, simplicity of implementation, and no extra (i.e., with respect to MPVO) preprocessing.