Multiresolution representation and visualization of volume data

A system to represent and visualize scalar volume data at multiple resolution is presented. The system is built on a multiresolution model based on tetrahedral meshes with scattered vertices that can be obtained from any initial dataset. The model is built off-line through data simplification techniques, and stored in a compact data structure that supports fast on-line access. The system supports interactive visualization of a representation at an arbitrary level of resolution through isosurface and projective methods. The user can interactively adapt the quality of visualization to requirements of a specific application task and to the performance of a specific hardware platform. Representations at different resolutions can be used together to further enhance interaction and performance through progressive and multiresolution rendering     

Large steps in GPU-based deformable bodies simulation

The interactive deformation and visualization of volumetric objects is still a challenging problem for many application areas. We present a novel integrated system which implements physically-based deformation and volume visualization of tetrahedral meshes on modern graphics hardware by exploiting the last features of vertex and fragment shaders.We achieve fast and stable deformation of tetrahedral meshes by means of a GPU-based implicit solver and present a hardware-based single-pass raycaster for deformed tetrahedral meshes. Thus, direct visualization of the inner structures of the deformed mesh is possible, while keeping the data on the graphics hardware throughout the entire simulation.     

Hierarchical grid conversion

Hierarchical grids appear in various applications in computer graphics such as subdivision and multiresolution surfaces, and terrain models. Since the different grid types perform better at different tasks, it is desired to switch between regular grids to take advantages of these grids. Based on a 2D domain obtained from the connectivity information of a mesh, we can define simple conversions to switch between regular grids. In this paper, we introduce a general framework that can be used to convert a given grid to another and we discuss the properties of these refinements such as their transformations. This framework is hierarchical meaning that it provides conversions between meshes at different level of refinement. To describe the use of this framework, we define new regular and near-regular refinements with good properties such as small factors. We also describe how grid conversion enables us to use patch-based data structures for hexagonal cells and near-regular refinements. To do so, meshes are converted to a set of quadrilateral patches that can be stored in simple structures. Near-regular refinements are also supported by defining two sets of neighborhood vectors that connect a vertex to its neighbors and are useful to address connectivity queries.     

Time Lattice: A Data Structure for the Interactive Visual Analysis of Large Time Series

Advances in technology coupled with the availability of low‐cost sensors have resulted in the continuous generation of large time series from several sources. In order to visually explore and compare these time series at different scales, analysts need to execute online analytical processing (OLAP) queries that include constraints and group‐by's at multiple temporal hierarchies. Effective visual analysis requires these queries to be interactive. However, while existing OLAP cube‐based structures can support interactive query rates, the exponential memory requirement to materialize the data cube is often unsuitable for large data sets. Moreover, none of the recent space‐efficient cube data structures allow for updates. Thus, the cube must be re‐computed whenever there is new data, making them impractical in a streaming scenario. We propose Time Lattice, a memory‐efficient data structure that makes use of the implicit temporal hierarchy to enable interactive OLAP queries over large time series. Time Lattice is a subset of a fully materialized cube and is designed to handle fast updates and streaming data. We perform an experimental evaluation which shows that the space efficiency of the data structure does not hamper its performance when compared to the state of the art. In collaboration with signal processing and acoustics research scientists, we use the Time Lattice data structure to design the Noise Profiler, a web‐based visualization framework that supports the analysis of noise from cities. We demonstrate the utility of Noise Profiler through a set of case studies.     

Interactive point-based rendering of higher-order tetrahedral data

Computational simulations frequently generate solutions defined over very large tetrahedral volume meshes containing many millions of elements. Furthermore, such solutions may often be expressed using non-linear basis functions. Certain solution techniques, such as discontinuous Galerkin methods, may even produce non-conforming meshes. Such data is difficult to visualize interactively, as it is far too large to fit in memory and many common data reduction techniques, such as mesh simplification, cannot be applied to non-conforming meshes. We introduce a point-based visualization system for interactive rendering of large, potentially non-conforming, tetrahedral meshes. We propose methods for adaptively sampling points from non-linear solution data and for decimating points at run time to fit GPU memory limits. Because these are streaming processes, memory consumption is independent of the input size. We also present an order-independent point rendering method that can efficiently render volumes on the order of 20 million tetrahedra at interactive rates.     

An adaptive learning approach for 3-D surface reconstruction from point clouds.

In this paper, we propose a multiresolution approach for surface reconstruction from clouds of unorganized points representing an object surface in 3-D space. The proposed method uses a set of mesh operators and simple rules for selective mesh refinement, with a strategy based on Kohonen's self-organizing map (SOM). Basically, a self-adaptive scheme is used for iteratively moving vertices of an initial simple mesh in the direction of the set of points, ideally the object boundary. Successive refinement and motion of vertices are applied leading to a more detailed surface, in a multiresolution, iterative scheme. Reconstruction was experimented on with several point sets, including different shapes and sizes. Results show generated meshes very close to object final shapes. We include measures of performance and discuss robustness.     

Adaptive and Feature-Preserving Subdivision for High-Quality Tetrahedral Meshes

We present an adaptive subdivision scheme for unstructured tetrahedral meshes inspired by the       -subdivision scheme for triangular meshes. Existing tetrahedral subdivision schemes do not support adaptive refinement and have traditionally been driven by the need to generate smooth three-dimensional deformations of solids. These schemes use edge bisections to subdivide tetrahedra, which generates octahedra in addition to tetrahedra. To split octahedra into tetrahedra one routinely chooses a direction for the diagonals for the subdivision step. We propose a new topology-based refinement operator that generates only tetrahedra and supports adaptive refinement. Our tetrahedral subdivision algorithm is motivated by the need to have one representation for the modeling, the simulation and the visualization and so to bridge the gap between CAD and CAE. Our subdivision algorithm design emphasizes on geometric quality of the tetrahedral meshes, local and adaptive refinement operations, and preservation of sharp geometric features on the boundary and in the interior of the physical domain.     

Adaptive extraction of time-varying isosurfaces

We present an algorithm for adaptively extracting and rendering isosurfaces from compressed time-varying volume data sets. Tetrahedral meshes defined by longest edge bisection are used to create a multiresolution representation of the volume in the spatial domain that is adapted overtime to approximate the time-varying volume. The reextraction of the isosurface at each time step is accelerated with the vertex programming capabilities of modern graphics hardware. A data layout scheme which follows the access pattern indicated by mesh refinement is used to access the volume in a spatially and temporally coherent manner. This data layout scheme allows our algorithm to be used for out-of-core visualization.     

递进网格的一种快速生成算法

递进网格表示法能高效地存储网格信息，并能生成连续的细节层次模型，支持模型的多分辨率表示、递进传输、网格压缩和有选择精化。此文给出了一种递进网格的生成算法，该算法能有效地控制简化网格与原始网格的误差，速度较快并能很好地保持原模型的边界特征     

Out-of-core streamline visualization on large unstructured meshes

This paper presents an out-of-core approach for interactive streamline construction on large unstructured tetrahedral meshes containing millions of elements. The out-of-core algorithm uses an octree to partition and restructure the raw data into subsets stored into disk files for fast data retrieval. A memory management policy tailored to the streamline calculations is used such that, during the streamline construction, only a very small amount of data are brought into the main memory on demand. By carefully scheduling computation and data fetching, the overhead of reading data from the disk is significantly reduced and good memory performance results. This out-of-core algorithm makes possible interactive streamline visualization of large unstructured-grid data sets on a single mid-range workstation with relatively low main-memory capacity: 5-15 megabytes. We also demonstrate that this approach is much more efficient than relying on virtual memory and operating system's paging algorithms     

Visualization of cellular and microvascular relationships

Understanding the structure of microvasculature structures and their relationship to cells in biological tissue is an important and complex problem. Brain microvasculature in particular is known to play an important role in chronic diseases. However, these networks are only visible at the microscopic level and can span large volumes of tissue. Due to recent advances in microscopy, large volumes of data can be imaged at the resolution necessary to reconstruct these structures. Due to the dense and complex nature of microscopy data sets, it is important to limit the amount of information displayed. In this paper, we describe methods for encoding the unique structure of microvascular data, allowing researchers to selectively explore microvascular anatomy. We also identify the queries most useful to researchers studying microvascular and cellular relationships. By associating cellular structures with our microvascular framework, we allow researchers to explore interesting anatomical relationships in dense and complex data sets.     

Multiresolution Surface Representation Based on Displacement Volumes

We propose a new representation for multiresolution models which uses volume elements enclosed between thedifferent resolution levels to encode the detail information. Keeping these displacement volumes locally constantduring a deformation of the base surface leads to a natural behaviour of the detail features. The correspondingreconstruction operator can be implemented efficiently by a hierarchical iterative relaxation scheme, providingclose to interactive response times for moderately complex models. Based on this representation we implement a multiresolution editing tool for irregular polygon meshes that allowsthe designer to freely edit the base surface of a multiresolution model without having to care about self‐intersectionsin the respective detailed surface. We demonstrate the effectiveness and robustness of the reconstructionby several examples with real‐world data.     

Feature preserving Delaunay mesh generation from 3D multi-material images

Generating realistic geometric models from 3D segmented images is an important task in many biomedical applications. Segmented 3D images impose particular challenges for meshing algorithms because they contain multi-material junctions forming features such as surface patches, edges and corners. The resulting meshes should preserve these features to ensure the visual quality and the mechanical soundness of the models. We present a feature preserving Delaunay refinement algorithm which can be used to generate high-quality tetrahedral meshes from segmented images. The idea is to explicitly sample corners and edges from the input image and to constrain the Delaunay refinement algorithm to preserve these features in addition to the surface patches. Our experimental results on segmented medical images have shown that, within a few seconds, the algorithm outputs a tetrahedral mesh in which each material is represented as a consistent submesh without gaps and overlaps. The optimization property of the Delaunay triangulation makes these meshes suitable for the purpose of realistic visualization or finite element simulations.     

Extension of half-edges for the representation of multiresolution subdivision surfaces

We address in this paper the problem of the data structures used for the representation and the manipulation of multiresolution subdivision surfaces. The classically used data structures are based on quadtrees, straightforwardly derived from the nested hierarchy of faces generated by the subdivision schemes. Nevertheless, these structures have some drawbacks: specificity to the kind of mesh (triangle or quad); the time complexity of neighborhood queries is not optimal; topological cracks are created in the mesh in the adaptive subdivision case. We present in this paper a new topological model for encoding multiresolution subdivision surfaces. This model is an extension to the well-known half-edge data structure. It allows instant and efficient navigation at any resolution level of the mesh. Its generality allows the support of many subdivision schemes including primal and dual schemes. Moreover, subdividing the mesh adaptively does not create topological cracks in the mesh. The extension proposed here is formalized in the combinatorial maps framework. This allows us to give a very general formulation of our extension.     

Hierarchical GTM: constructing localized nonlinear projectionmanifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets and, therefore, a hierarchical visualization system is desirable. In this paper, we extend an existing locally linear hierarchical visualization system PhiVis in several directions: 1) We allow for nonlinear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). 2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. 3) Using tools from differential geometry, we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets     

Rendering continuous level-of-detail meshes by Masking Strips

In this paper we present a new continuous multiresolution approach which has been developed for the interactive visualization of meshes in real-time applications. Our interest is to offer an efficient solution which considers submeshes, textures, normals and bones for skeletal animations. The model has been designed to give view-independent continuous levels-of-detail and uses triangle strips for exploiting vertex cache and coherence for minimizing bus traffic. Furthermore, its data structures allow for an efficient extraction process where all unnecessary information is eliminated and also for progressive transmission. A new simplification strategy has also been developed, which preserves appearance and attributes. In the results section we present different images to show the visual quality obtained with this simplification method, as well as a study of the storage and rendering costs.     

Semisupervised learning of hierarchical latent trait models for data visualization

Recently, we have developed the hierarchical generative topographic mapping (HGTM), an interactive method for visualization of large high-dimensional real-valued data sets. We propose a more general visualization system by extending HGTM in three ways, which allows the user to visualize a wider range of data sets and better support the model development process. 1) We integrate HGTM with noise models from the exponential family of distributions. The basic building block is the latent trait model (LTM). This enables us to visualize data of inherently discrete nature, e.g., collections of documents, in a hierarchical manner. 2) We give the user a choice of initializing the child plots of the current plot in either interactive, or automatic mode. In the interactive mode, the user selects "regions of interest", whereas in the automatic mode, an unsupervised minimum message length (MML)-inspired construction of a mixture of LTMs is employed. The unsupervised construction is particularly useful when high-level plots are covered with dense clusters of highly overlapping data projections, making it difficult to use the interactive mode. Such a situation often arises when visualizing large data sets. 3) We derive general formulas for magnification factors in latent trait models. Magnification factors are a useful tool to improve our understanding of the visualization plots, since they can highlight the boundaries between data clusters. We illustrate our approach on a toy example and evaluate it on three more complex real data sets.     

Hardware-assisted feature analysis and visualization of procedurally encoded multifield volumetric data

We take a new approach to interactive visualization and feature detection of large scalar, vector, and multifield computational fluid dynamics data sets that is also well suited for meshless CFD methods. Radial basis functions (RBFs) are used to procedurally encode both scattered and irregular gridded scalar data sets. The RBF encoding creates a complete, unified, functional representation of the scalar field throughout 3D space, independent of the underlying data topology, and eliminates the need for the original data grid during visualization. The capability of commodity PC graphics hardware to accelerate the reconstruction and rendering and to perform feature detection from this functional representation is a powerful tool for visualizing procedurally encoded volumes. Our RBF encoding and GPU-accelerated reconstruction, feature detection, and visualization tool provides a flexible system for visually exploring and analyzing large, structured, scattered, and unstructured scalar, vector, and multifield data sets at interactive rates on desktop PCs.