Rüdiger Westermann

Linear algebra operators for GPU implementation of numerical algorithms

In this work, the emphasis is on the development of strategies to realize techniques of numerical computing on the graphics chip. In particular, the focus is on the acceleration of techniques for solving sets of algebraic equations as they occur in numerical simulation. We introduce a framework for the implementation of linear algebra operators on programmable graphics processors (GPUs), thus providing the building blocks for the design of more complex numerical algorithms. In particular, we propose a stream model for arithmetic operations on vectors and matrices that exploits the intrinsic parallelism and efficient communication on modern GPUs. Besides performance gains due to improved numerical computations, graphics algorithms benefit from this model in that the transfer of computation results to the graphics processor for display is avoided. We demonstrate the effectiveness of our approach by implementing direct solvers for sparse matrices, and by applying these solvers to multi-dimensional finite difference equations, i.e. the 2D wave equation and the incompressible Navier-Stokes equations.

Acceleration techniques for GPU-based volume rendering

Nowadays, direct volume rendering via 3D textures has positioned itself as an efficient tool for the display and visual analysis of volumetric scalar fields. It is commonly accepted, that for reasonably sized data sets appropriate quality at interactive rates can be achieved by means of this technique. However, despite these benefits one important issue has received little attention throughout the ongoing discussion of texture based volume rendering: the integration of acceleration techniques to reduce per-fragment operations. In this paper, we address the integration of early ray termination and empty-space skipping into texture based volume rendering on graphical processing units (GPU). Therefore, we describe volume ray-casting on programmable graphics hardware as an alternative to object-order approaches. We exploit the early z-test to terminate fragment processing once sufficient opacity has been accumulated, and to skip empty space along the rays of sight. We demonstrate performance gains up to a factor of 3 for typical renditions of volumetric data sets on the ATI 9700 graphics card.

Efficiently using graphics hardware in volume rendering applications

OpenGLand its extensionsprovide accessto advancedper-pixel operationsavailable in the rasterizationstageand in the frame buffer hardware of modern graphicsworkstations. With these mechanisms, completelynew renderingalgorithmscanbedesigned andimplementedin a very particularway. In this paperwe extend theideaof extensi vely usinggraphicshardwarefor therenderingof volumetricdatasetsin variousways. First, we introducethe conceptof clipping geometriesby meansof stencilbuffer operations, and we exploit pixel texturesfor the mappingof volume datato sphericaldomains.We show waysto use3D texturesfor the renderingof lightedandshadediso-surfacesin real-timewithout extractingany polygonalrepresentation. Second,wedemonstratethat even for volumedataon unstructuredgrids, whereonly software solutionsexist up to now, bothmethods,iso-surfaceextractionand directvolumerendering,canbeacceleratedto new ratesof interactivity by simplepolygondrawing andframebuffer operations. CR Categories: I.3.7 [ComputerGraphics]:Three-Dimensional GraphicsandRealism—Graphics Hardware, 3D Textures, Volume Rendering, Unstructured Grids

Real-time exploration of regular volume data by adaptive reconstruction of isosurfaces

Recent advances in the technology of 3D sensors and in the performance of numerical simulations result in the generation of volume data at ever growing size. In order to allow real-time exploration of even the highest resolution data sets, adaptive techniques benefiting from the hierarchical nature of multi-resolution representations have gained special attention. In this paper we propose an adaptive approach to the fast reconstruction of iso-surfaces from regular volume data at arbitrary levels of detail. The algorithm has been designed to enable real-time navigation through complex structures while providing user-adjustable resolution levels. Since adaptive on-the-fly reconstruction and rendering is performed from a hierarchical octree representation of the volume data, the method does not depend on pre-processing with respect to a specific iso-value thus allowing the user to interactively browse through the set of all possible iso-surfaces. Special attention is paid to the fixing of cracks in the surface where the adaptive reconstruction level changes and to the efficient estimation of the iso-surface’s curvature.

Level-of-detail volume rendering via 3D textures

In this paper we present an adaptive approach to volume rendering via 3D textures at arbitrary levels of detail. The algorithm has been designed to enable interactive exploration of large-scale data sets while providing user-adjustable resolution levels. A texture map hierarchy is constructed in a way that minimizes the amount of texture memory with respect to the power-of-two restriction imposed by OpenGL implementations. In addition, our hierarchical level-of-detail representation guarantees consistent interpolation between different resolution levels. Special attention has been paid to the fixing of rendering artifacts that are introduced by non-corrected opacities at level transitions. By adapting the sample slice distance with regard to the desired level-of-detail, the number of texture lookups is reduced significantly.

ClearView: An Interactive Context Preserving Hotspot Visualization Technique

Volume rendered imagery often includes a barrage of 3D information like shape, appearance and topology of complex structures, and it thus quickly overwhelms the user. In particular, when focusing on a specific region a user cannot observe the relationship between various structures unless he has a mental picture of the entire data. In this paper we present ClearView, a GPU-based, interactive framework for texture-based volume ray-casting that allows users which do not have the visualization skills for this mental exercise to quickly obtain a picture of the data in a very intuitive and user-friendly way. ClearView is designed to enable the user to focus on particular areas in the data while preserving context information without visual clutter. ClearView does not require additional feature volumes as it derives any features in the data from image information only. A simple point-and-click interface enables the user to interactively highlight structures in the data. ClearView provides an easy to use interface to complex volumetric data as it only uses transparency in combination with a few specific shaders to convey focus and context information

Applications of pixel textures in visualization and realistic image synthesis

With fast3D graphicsbecomingmoreandmoreavailableevenon low endplatforms,thefocusin developingnew graphicshardware is beginning to shift towardshigher quality renderingand additional functionality insteadof simply higher performanceimplementationsof the traditionalgraphicspipeline. On this searchfor improved quality it is importantto identify a powerful set of orthogonalfeaturesto be implementedin hardware,which canthen beflexibly combinedto form new algorithms. Pixel texturesareanOpenGLextensionby SiliconGraphicsthat fits into this category. In this paper , we demonstratethebenefitsof thisextensionby presentingseveraldifferentalgorithmsexploiting its functionalityto achievehighquality, highperformancesolutions for a variety of differentapplicationsfrom scientificvisualization andrealisticimagesynthesis.Weconcludethatpixel texturesarea valuable,powerful featurethatshouldbecomea standardin future graphicssystems. CR Categories: I.3.3 [Computer Graphics]: Picture/Image Generation—Bitmapand framebuffer operationsI.3.3 [Computer Graphics]: Picture/ImageGeneration—Displayalgorithms I.3.6 [ComputerGraphics]: Methodologyand Techniques—Standards I.3.7 [Computer Graphics]: Three-DimensionalGraphics and Realism—Color , Shading,Shadowing andTexture

A particle system for interactive visualization of 3D flows

We present a particle system for interactive visualization of steady 3D flow fields on uniform grids. For the amount of particles we target, particle integration needs to be accelerated and the transfer of these sets for rendering must be avoided. To fulfill these requirements, we exploit features of recent graphics accelerators to advect particles in the graphics processing unit (GPU), saving particle positions in graphics memory, and then sending these positions through the GPU again to obtain images in the frame buffer. This approach allows for interactive streaming and rendering of millions of particles and it enables virtual exploration of high resolution fields in a way similar to real-world experiments. The ability to display the dynamics of large particle sets using visualization options like shaded points or oriented texture splats provides an effective means for visual flow analysis that is far beyond existing solutions. For each particle, flow quantities like vorticity magnitude and A2 are computed and displayed. Built upon a previously published GPU implementation of a sorting network, visibility sorting of transparent particles is implemented. To provide additional visual cues, the GPU constructs and displays visualization geometry like particle lines and stream ribbons.

Compression domain volume rendering

A survey of graphics developers on the issue of texture mapping hardware for volume rendering would most likely find that the vast majority of them view limited texture memory as one of the most serious drawbacks of an otherwise fine technology. In this paper, we propose a compression scheme for static and time-varying volumetric data sets based on vector quantization that allows us to circumvent this limitation. We describe a hierarchical quantization scheme that is based on a multiresolution covariance analysis of the original field. This allows for the efficient encoding of large-scale data sets, yet providing a mechanism to exploit temporal coherence in non-stationary fields. We show, that decoding and rendering the compressed data stream can be done on the graphics chip using programmable hardware. In this way, data transfer between the CPU and the graphics processing unit (GPU) can be minimized thus enabling flexible and memory efficient real-time rendering options. We demonstrate the effectiveness of our approach by demonstrating interactive renditions of Gigabyte data sets at reasonable fidelity on commodity graphics hardware.

Random walks for interactive organ segmentation in two and three dimensions: implementation and validation

A new approach to interactive segmentation based on random walks was recently introduced that shows promise for allowing physicians more flexibility to segment arbitrary objects in an image. This report has two goals: To introduce a novel computational method for applying the random walker algorithm in 2D/3D using the Graphics Processing Unit (GPU) and to provide quantitative validation studies of this algorithm relative to different targets, imaging modalities and interaction strategies.