Hardware-accelerated Volume Ray Casting

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. Recently the integration of acceleration techniques to reduce per-fragment operations has become a hot topic. It is not possible to implement optimizations, such as empty space skipping or early ray termination, on modern programmable graphics hardware. Discuss the different approaches and give the current state-of-the art in GPU-based volume rendering. How can these approaches can benefit from the ongoing development in graphics hardware?

[Roettger2003] Smart Hardware-Accelerated Volume Rendering
[Krüger2003] Acceleration Techniques for GPU-based Volume Rendering

Interactive Volume Deformation

Volume rendering has become an integral part in a variety of scientific disciplines, such as medicine, natural and computational science as well as visual arts and entertainment. In consequence of this development, in the last couple of years increasing interest in using solid volumetric objects for free-form modelling has arisen. A prominent example is tomographic data which is acquired for surgery planning in medicine. Due to anatomical shifts and tissue resection, the data does not match the actual situation during the intervention. Thus, volume data has to be deformed non-linearly to compensate these misalignments. Another application is the interactive exploration of volumetric datasets, where the user can cut into and open up, spread apart, or peel away parts of the volume in real time, making the interior visible while still retaining surrounding context. Describe different approaches for the interactive deformation of volumes and their applications.

[Rezk-Salama2001] Fast volumetric deformation on general purpose hardware
[McGuffin2003] Using Deformations for Browsing Volumetric Data

Pre-integrated Volume Rendering

Pre-integrated volume rendering is a commonly used technique for improving the quality of volume renderings. Because much of the necessary computation is done in advance, this method can generate highquality images with better performance than heavily supersampling the volume. It has been used successfully with many types of rendering algorithms including cell projection, ray casting, and hardware-accelerated methods. Give a detailed description of the pre-integration method. Discuss the efficient computation of pre-integration tables and describe how pre-integration can be used to enhance the quality of different volume rendering algorithms.

[Engel2001] High-quality pre-integrated volume rendering using hardware-accelerated pixel shading
[Lum2004] High-Quality Lighting and Efficient Pre-Integration for Volume Rendering

Volume Rendering using Splatting

Splatting is a popular algorithm for direct volume rendering. The splatting process reconstructs a continuous function from the sampled scalar field using 3D reconstruction kernels associated with each scalar value. For volume rendering, the continuous function is mapped to the screen as a superposition of pre-integrated 3D kernels, which are called 2D footprints. Briefly describe the basic algorithm and discuss optimization techniques. Focus on the use of modern graphics hardware to improve the performance of splatting. Further discuss the application of the splatting algorithm for unstructured volumetric data, such as point clouds.

[Hopf2003] Hierarchical Splatting of Scattered Data
[Chen2004] Hardware-Accelerated Adaptive EWA Volume Splatting

Point-based Volume Representations and Rendering

Volumetric data is often given on a rectilinear grid. The main advantage is that the positions of the data samples are stored implicitly and that it allows efficient spatial addressing of the data. However, the rigid shape of such grids becomes more and more a limitation factor as the data sets are constantly increasing in size due to more advanced acquisition devices. Furthermore, the fraction of non relevant volumetric regions in relation to areas of interest is steadily increasing. Non-relevant volumetric regions, such as empty space, should not be represented explicitly. Point-based approaches do not suffer from these limitations and are therefore investigated as an alternative representation for volumetric data. Find and describe different approaches for the point-based representation and the direct rendering of volume data in the literature.

[Qu2003] A Framework for Sample-based Rendering with O-buffers
[Welsh2003] A Frequency-Sensitive Point Hierarchy for Images and Volumes

Advanced Transfer Functions in Volume Rendering

Direct volume rendering depicts structure in scalar fields through a simple combination of mappings. At each rendered sample point, locally measured numerical quantities (mainly the data value itself) are mapped via the transfer function to optical quantities such as opacity and color. Basic computer graphics routines can then shade, composite, and project the samples into a coherent visualization. In many cases, however, it is very difficult to achieve good results with these simple one-dimensional transfer functions. Investigate advanced methods for defining transfer functions, such as multi-dimensional approaches, methods that take into account derivatives, etc. Give a detailed description of the various approaches and discuss their advantages and disadvantages.

[Kniss2002] Multi-Dimensional Transfer Functions for Interactive Volume Rendering
[Kindlmann2003] Curvature-Based Transfer Functions for Direct Volume Rendering - Methods and Applications

Illustration Techniques for Volume Visualization

Accurately and automatically conveying the structure of a volume model is a problem not fully solved by existing volume rendering approaches. Physics-based volume rendering approaches create images which may match the appearance of translucent materials in nature, but may not embody important structural details. Transfer function approaches allow flexible design of the volume appearance, but generally require substantial hand tuning for each new data set in order to be effective. Volume illustration approaches use non-photorealistic rendering techniques to enhance important features. They try to improve structural perception of volume models through the amplification of features and the addition of illumination effects. Give a report on the current state-of-the-art in volume illustration.

[Csébfalvi2001] Fast Visualization of Object Contours by Non-Photorealistic Volume Rendering
[Mora2004] Instant volumetric understanding with order-independent volume rendering

Visualization of Large Volumetric Data

Datasets of tens of gigabytes are becoming common in computational and experimental science. This development is driven by advances in imaging technology, producing detectors with growing resolutions, as well as availability of cheap processing power and memory capacity in commodity-based computing environments. Describe different techniques for the interactive visualization of large volumetric datasets. What are the technical requirements of these systems, what are their advantages and disadvantages?

[Prohaska2004] Interactive Exploration of Large Remote Micro-CT Scans
[Guthe2002] Interactive Rendering of Large Volume Data Sets

Intersection of Quadric Surfaces

Computing intersection of quadric surfaces is very important in the area of solid modeling, computational geometry and computer graphics. The range of applications covers well-known problems like computing arrangements, boundary evaluation and convex hull computation. Describe different approaches to solve this problem in detail.

[Tu2002] Classifying the nonsingular intersection curve of two quadric surfaces
[Lazard2004] Intersecting Quadrics - An Efficient and Exact Implementation

Generalized Cylinder Visualization for Medical Applications

A generalized cylinder is a volumetric representation defined by a space curve axis and a cross section function at each point along the axis. Examples of a generalized cylinder are cylinder, cone, cube, torus, etc. The spine or axis can be defined by a spline and the cross section function by ellipse. A generalized cylinder is one of the most simply and general way to represent a tubular structure. Generalized cylinders have been used to reconstruct coronary arterial trees from biplane angiograms using X-Ray angiography, model the human body, model the vessel structure on pre-segmented data of human carotid artery, and for modeling cerebral blood vessels. Explain the concept of generalized cylinders in detail and describe their applications.

[Grisoni2003] High performance generalized cylinders visualization
[Raghupathi2004] An Intestinal Surgery Simulator - Real-Time Collision Processing and Visualization

3D Surface Reconstruction from Point Clouds

Because of improved technologies for capturing points from the surfaces of real objects and because improvements in graphics hardware now allow us to handle large numbers of primitives, modeling surfaces with clouds of points is becoming feasible. This is interesting, since constructing meshes and maintaining them through deformations requires a lot of computation. It is useful to be able to define a surface implied by a point cloud. Such point-set surfaces are used for interpolation, shading, meshing and so on. Describe different techniques for reconstructing surfaces from point clouds and discuss their advantages and limitations.

[Pottmann2002] Recognition and reconstruction of special surfaces from point clouds
[Amenta2004] Defining Point-Set Surfaces

T2 Mapping for Orthopedic Applications

While standard anatomic MRI techniques are used to identify morphologic changes in damaged tissues, such as volume, thickness, or lesions, several investigational techniques have been proposed that are sensitive to biochemical and structural changes. The technique of spatially mapping the MRI transverse relaxation time constant (T2) to image colors has been developed for human application, and has been used in cross-sectional population studies. Discuss the basics of T2 mapping and describe the applications of this technique.

[Smith2001] Spatial Variation in Cartilage T2 of the Knee
[Mosher2004] Effect of Gender on In Vivo Cartilage Magnetic Resonance Imaging T2 Mapping