Lars Linsen

Geometric modeling for scientific visualization

1. Surface Reconstruction and Interpolation Marietta E. Cameron, Kenneth R. Sloan, and Ying Sun: Reconstruction from Unorganized Point Sets using Gamma Shapes Ingrid Hotz and Hans Hagen: Isometric embedding for a discrete metric David Levin: Mesh-Independent Surface Interpolation Robert Mencl and Heinrich Mueller: Empirical Analysis of Surface Interpolation by Spatial Environment Graphs 2. Surface Interrogation and Modeling Georges-Pierre Bonneau and Stefanie Hahmann: Smooth Polylines on Polygon Meshes Mark A. Duchaineau and Kenneth I. Joy: Progressive Precision Surface Design Helwig Hauser, Thomas Theussl, Andreas Konig, and Eduard Groller: Smart Surface Interrogation for Advanced Visualization Techniques Yootai Kim, Raghu Machiraju, and David Thompson: Modeling Rough Surfaces Georgios Stylianou: A Feature Based Method for Rigid Registration of Anatomical Surfaces 3. Wavelets and Compression on Surfaces Martin Bertram: Lifting Biorthogonal B-spline Wavelets Ioannis Ivrissimtzis, Christian Roessl, and Hans-Peter Seidel: Tree-based Data Structures for Triangle Mesh Connectivity Encoding Andrei Khodakovsky and Igor Guskov: Compression of Normal Meshes Gabriel Taubin: New Results in Signal Processing and Compression of Polygon Meshes 4. Topology, Distance Fields and Solid Modeling Jian Huang and Roger Crawfis: Adaptively Refined Complete Distance Fields of Polygonal Models Marcelo Kallmann, Hanspeter Bieri, and Daniel Thalmann: Fully Dynamic Constrained Delaunay Triangulations Jorge Rodriguez, Dolors Ayala, and Antonio Aguilera: EVM: A Complete Solid Model for Surface Rendering Xavier Tricoche and Gerik Scheuermann: Topology Simplification of Symmetric, Second-Order 2D Tensor

Discrete Sibson interpolation

Natural-neighbor interpolation methods, such as Sibsons method, are well-known schemes for multivariate data fitting and reconstruction. Despite its many desirable properties, Sibsons method is computationally expensive and difficult to implement, especially when applied to higher-dimensional data. The main reason for both problems is the methods implementation based on a Voronoi diagram of all data points. We describe a discrete approach to evaluating Sibsons interpolant on a regular grid, based solely on finding nearest neighbors and rendering and blending d-dimensional spheres. Our approach does not require us to construct an explicit Voronoi diagram, is easily implemented using commodity three-dimensional graphics hardware, leads to a significant speed increase compared to traditional approaches, and generalizes easily to higher dimensions. For large scattered data sets, we achieve two-dimensional (2D) interpolation at interactive rates and 3D interpolation (3D) with computation times of a few seconds.

Hierarchical representation of time-varying volume data with /sup 4//spl radic/2 subdivision and quadrilinear B-spline wavelets

Multiresolution methods for representing data at multiple levels of detail are widely used for large-scale two- and three-dimensional data sets. We present a four-dimensional multiresolution approach for time-varying volume data. This approach supports a hierarchy with spatial and temporal scalability. The hierarchical data organization is based on /sup 4//spl radic/2 subdivision. The /sup n//spl radic/2-subdivision scheme only doubles the overall number of grid points in each subdivision step. This fact leads to fine granularity and high adaptivity, which is especially desirable in the spatial dimensions. For high-quality data approximation on each level of detail, we use quadrilinear B-spline wavelets. We present a linear B-spline wavelet lifting scheme based on /sup n//spl radic/2 subdivision to obtain narrow masks for the update rules. Narrow masks provide a basis for out-of-core data exploration techniques and view-dependent visualization of sequences of time steps.

Surface Extraction from Multi-field Particle Volume Data Using Multi-dimensional Cluster Visualization

Data sets resulting from physical simulations typically contain a multitude of physical variables. It is, therefore, desirable that visualization methods take into account the entire multi-field volume data rather than concentrating on one variable. We present a visualization approach based on surface extraction from multi-field particle volume data. The surfaces segment the data with respect to the underlying multi-variate function. Decisions on segmentation properties are based on the analysis of the multi-dimensional feature space. The feature space exploration is performed by an automated multi-dimensional hierarchical clustering method, whose resulting density clusters are shown in the form of density level sets in a 3D star coordinate layout. In the star coordinate layout, the user can select clusters of interest. A selected cluster in feature space corresponds to a segmenting surface in object space. Based on the segmentation property induced by the cluster membership, we extract a surface from the volume data. Our driving applications are smoothed particle hydrodynamics (SPH) simulations, where each particle carries multiple properties. The data sets are given in the form of unstructured point-based volume data. We directly extract our surfaces from such data without prior resampling or grid generation. The surface extraction computes individual points on the surface, which is supported by an efficient neighborhood computation. The extracted surface points are rendered using point-based rendering operations. Our approach combines methods in scientific visualization for object-space operations with methods in information visualization for feature-space operations.

Direct isosurface extraction from scattered volume data

Isosurface extraction is a standard visualization method for scalar volume data and has been subject to research for decades. Nevertheless, to our knowledge, no isosurface extraction method exists that directly extracts surfaces from scattered volume data without 3D mesh generation or reconstruction over a structured grid. We propose a method based on spatial domain partitioning using a kd-tree and an indexing scheme for efficient neighbor search. Our approach consists of a geometry extraction and a rendering step. The geometry extraction step computes points on the isosurface by linearly interpolating between neighboring pairs of samples. The neighbor information is retrieved by partitioning the 3D domain into cells using a kd-tree. The cells are merely described by their index and bitwise index operations allow for a fast determination of potential neighbors. We use an angle criterion to select appropriate neighbors from the small set of candidates. The output of the geometry step is a point cloud representation of the isosurface. The final rendering step uses point-based rendering techniques to visualize the point cloud. Our direct isosurface extraction algorithm for scattered volume data produces results of quality close to the results from standard isosurface extraction algorithms for gridded volume data (like marching cubes). In comparison to 3D mesh generation algorithms (like Delaunay tetrahedrization), our algorithm is about one order of magnitude faster for the examples used in this paper.

Fan clouds: an alternative to meshes

A fan cloud is a set of triangles that can be used to visualize and work with point clouds. It is fast to compute and can replace a triangular mesh representation: We discuss visualization, multiresolution reduction, refinement, and selective refinement. Algorithms for triangular meshes can also be applied to fan clouds. They become even simpler, because fans are not interrelated. This localness of fan clouds is one of their main advantages. No remeshing is necessary for local or adaptive refinement and reduction.

Visualization in Medicine and Life Sciences

Visualization technology is becoming increasingly important for medical and biomedical data processing and analysis. This technology complements traditional image processing methods as it allows scientists to visually interact with large, high- resolution three-dimensional image data, for example. Further, an ever increasing number of new data acquisition methods are being used in medicine and the life sciences, in particular in genomics and proteomics. This book discusses some of the latest visualization techniques and systems for effective analysis of such diverse, large, complex, and multi-source data. Experts from all over the world had been invited to participate in a workshop held in July 2006 on the island Rgen in Germany. About 40 participants presented state-of-the-art research on the topic. Research and survey papers have been solicited and carefully refereed, resulting in this collection. The topics covered include Segmentation and Feature Detection, Surface Extraction, Volume Visualization, Graph and Network Visualization, Visual Data Exploration, Multivariate and Multidimensional Data Visualization, Large Data Visualization. The book will be of great interest to researchers, graduate students, and professionals dealing with visualization and its application in medicine and life sciences.

Smooth Surface Extraction from Unstructured Point-based Volume Data Using PDEs

Smooth surface extraction using partial differential equations (PDEs) is a well-known and widely used technique for visualizing volume data. Existing approaches operate on gridded data and mainly on regular structured grids. When considering unstructured point-based volume data where sample points do not form regular patterns nor are they connected in any form, one would typically resample the data over a grid prior to applying the known PDE-based methods. We propose an approach that directly extracts smooth surfaces from unstructured point-based volume data without prior resampling or mesh generation. When operating on unstructured data one needs to quickly derive neighborhood information. The respective information is retrieved by partitioning the 3D domain into cells using a fed-tree and operating on its cells. We exploit neighborhood information to estimate gradients and mean curvature at every sample point using a four-dimensional least-squares fitting approach. Gradients and mean curvature are required for applying the chosen PDE-based method that combines hyperbolic advection to an isovalue of a given scalar field and mean curvature flow. Since we are using an explicit time-integration scheme, time steps and neighbor locations are bounded to ensure convergence of the process. To avoid small global time steps, one can use asynchronous local integration. We extract a smooth surface by successively fitting a smooth auxiliary function to the data set. This auxiliary function is initialized as a signed distance function. For each sample and for every time step we compute the respective gradient, the mean curvature, and a stable time step. With these informations the auxiliary function is manipulated using an explicit Euler time integration. The process successively continues with the next sample point in time. If the norm of the auxiliary function gradient in a sample exceeds a given threshold at some time, the auxiliary function is reinitialized to a signed distance function. After convergence of the evolvution, the resulting smooth surface is obtained by extracting the zero isosurface from the auxiliary function using direct isosurface extraction from unstructured point-based volume data and rendering the extracted surface using point-based rendering methods.

A framework for exploring multidimensional data with 3D projections

Visualization of high‐dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e.g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high‐dimensional data to 3D visual spaces, based on a generalization of the Least‐Square Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the frameworks applicability for both visual exploration of multidimensional abstract (non‐spatial) data as well as the feature space of multi‐variate spatial data.

Multiclustertree: interactive visual exploration of hierarchical clusters in multidimensional multivariate data

Visual analytics of multidimensional multivariate data is a challenging task because of the difficulty in understanding metrics in attribute spaces with more than three dimensions. Frequently, the analysis goal is not to look into individual records but to understand the distribution of the records at large and to find clusters of records with similar attribute values. A large number of (typically hierarchical) clustering algorithms have been developed to group individual records to clusters of statistical significance. However, only few visualization techniques exist for further exploring and understanding the clustering results. We propose visualization and interaction methods for analyzing individual clusters as well as cluster distribution within and across levels in the cluster hierarchy. We also provide a clustering method that operates on density rather than individual records. To not restrict our search for clusters, we compute density in the given multidimensional multivariate space. Clusters are formed by areas of high density. We present an approach that automatically computes a hierarchical tree of high density clusters. To visually represent the cluster hierarchy, we present a 2D radial layout that supports an intuitive understanding of the distribution structure of the multidimensional multivariate data set. Individual clusters can be explored interactively using parallel coordinates when being selected in the cluster tree. Furthermore, we integrate circular parallel coordinates into the radial hierarchical cluster tree layout, which allows for the analysis of the overall cluster distribution. This visual representation supports the comprehension of the relations between clusters and the original attributes. The combination of the 2D radial layout and the circular parallel coordinates is used to overcome the overplotting problem of parallel coordinates when looking into data sets with many records. We apply an automatic coloring scheme based on the 2D radial layout of the hierarchical cluster tree encoding hue, saturation, and value of the HSV color space. The colors support linking the 2D radial layout to other views such as the standard parallel coordinates or, in case data is obtained from multidimensional spatial data, the distribution in object space.