Roger Crawfis

Area and volume coherence for efficient visualization of 3D scalar functions

We present an algorithm for compositing a combination of density clouds and contour surfaces used to represent a scalar function on a 3-D volume subdivided into convex polyhedra. The scalar function is interpolated between values defined at the vertices, and the polyhedra are sorted in depth before compositing. For n tetrahedra comprising a Delaunay triangulation, this sorting can always be done in O(n) time. Since a Delaunay triangulation can be efficiently computed for scattered data points, this provides a method for visualizing such data sets. The integrals for opacity and visible intensity along a ray through a convex polyhedron are computed analytically, and this computation is coherent across the polyhedrons projected area.

Texture splats for 3D scalar and vector field visualization

Volume visualization is becoming an important tool for understanding large 3D data sets. A popular technique for volume rendering is known as splatting. With new hardware architectures offering substantial improvements in the performance of rendering texture mapped objects, we present textured splats. An ideal reconstruction function for 3D signals is developed which can be used as a texture map for a splat. Extensions to the basic splatting technique are then developed to additionally represent vector fields.<<ETX>>

A practical evaluation of popular volume rendering algorithms

This paper evaluates and compares four volume rendering algorithms that have become rather popular for rendering datasets described on uniform rectilinear grids: raycasting, splatting, shear-warp, and hardware-assisted 3D texture-mapping. In order to assess both the strengths and the weaknesses of these algorithms in a wide variety of scenarios, a set of real-life benchmark datasets with different characteristics was carefully selected. In the rendering, all algorithm-independent image synthesis parameters, such as viewing matrix, transfer functions, and optical model, were kept constant to enable a fair comparison of the rendering results. Both image quality and computational complexity were evaluated and compared, with the aim of providing both researchers and practitioners with guidelines on which algorithm is most suited in which scenario. Our analysis also indicates the current weakness in each algorithms pipeline, and possible solutions to these as well as pointers for future research are offered.

Flow volumes for interactive vector field visualization

Flow volumes are the volumetric equivalent of stream lines. They provide more information about the vector field being visualized than do stream lines or ribbons. Presented is an efficient method for producing flow volumes, composed of transparently rendered tetrahedra, for use in an interactive system. The problems of rendering, subdivision, sorting, composing artifacts, and user interaction are dealt with. Efficiency comes from rendering only the volume of the smoke, and using hardware texturing and compositing.<<ETX>>

Splatting without the blur

Splatting is a volume rendering algorithm that combines efficient volume projection with a sparse data representation. Only voxels that have values inside the iso-range need to be considered, and these voxels can be projected via efficient rasterization schemes. In splatting, each projected voxel is represented as a radially symmetric interpolation kernel, equivalent to a fuzzy ball. Projecting such a basis function leaves a fuzzy impression, called a footprint or splat, on the screen. Splatting traditionally classifies and shades the voxels prior to projection, and thus each voxel footprint is weighted by the assigned voxel color and opacity. Projecting these fuzzy color balls provides a uniform screen image for homogeneous object regions, but leads to a blurry appearance of object edges. The latter is clearly undesirable, especially when the view is zoomed on the object. In this work, we manipulate the rendering pipeline of splatting by performing the classification and shading process after the voxels have been projected onto the screen. In this way volume contributions outside the iso-range never affect the image. Since shading requires gradients, we not only splat the density volume, using regular splats, but we also project the gradient volume, using gradient splats. However alternative to gradient splats, we can also compute the gradients on the projection plane using central differencing. This latter scheme cuts the number of footprint rasterization by a factor of four since only the voxel densities have to be projected.

High-quality splatting on rectilinear grids with efficient culling of occluded voxels

Splatting is a popular volume rendering algorithm that pairs good image quality with an efficient volume projection scheme. The current axis-aligned sheet-buffer approach, however, bears certain inaccuracies. The effect of these is less noticeable in still images, but clearly revealed in animated viewing, where disturbing popping of object brightness occurs at certain view angle transitions. In previous work, we presented a new variant of sheet-buffered splatting in which the compositing sheets are oriented parallel to the image plane. This scheme not only eliminates the condition for popping, but also produces images of higher quality. In this paper, we summarize this new paradigm and extend it in a number of ways. We devise a new solution to render rectilinear grids of equivalent cost to the traditional approach that treats the anisotropic volume as being warped into a cubic grid. This enables us to use the usual radially symmetric kernels, which can be projected without inaccuracies. Next, current splatting approaches necessitate the projection of all voxels in the iso-interval(s), although only a subset of these voxels may eventually be visible in the final image. To eliminate these wasteful computations we propose a novel front-to-back approach that employs an occlusion map to determine if a splat contributes to the image before it is projected, thus skipping occluded splats. Additional measures are presented for further speedups. In addition, we present an efficient list-based volume traversal scheme that facilitates the quick modification of transfer functions and iso-values.

Functional endoscopic sinus surgery training simulator

Objective/Hypothesis: To determine the efficacy of a haptic (force feedback) device and to compare isosurface and volumetric models of a functional endoscopic sinus surgery (FESS) training simulator. Study Design: A pilot study involving faculty and residents from the Department of Otolaryngology at The Ohio State University. Methods: Objective trials evaluated the haptic devices ability to perceive three‐dimensional shapes (stereognosis) without the aid of image visualization. Ethmoidectomy tasks were performed with both isosurface and volumetric FESS simulators, and surveys compared the two models. Results: The haptic device was 77% effective for stereognosis tasks. There was a preference toward the isosurface model over the volumetric model in terms of visual representation, comfort, haptic‐visual fidelity, and overall performance. Conclusions: The FESS simulator uses both visual and haptic feedback to create a virtual reality environment to teach paranasal sinus anatomy and basic endoscopic sinus surgery techniques to ear, nose, and throat residents. The results of the current study showed that the haptic device was accurate in and of itself, within its current physical limitations, and that the isosurface‐based simulator was preferred. Laryngoscope, 108:1643–1647, 1998

Direct volume visualization of three-dimensional vector fields

Current techniques for direct volume visualization offer only the ability to examine scalar fields. However most scientific explorations require the examination of vector and possibly tensor fields as well as numerous scalar fields. This paper describes an algorithm to directly render three-dimensional scalar and vector fields. The algorithm uses a combination of sampling and splatting techniques, that are extended to integrate display of vector field data within the image.

Visualizing 3D velocity fields near contour surfaces

Vector field rendering is difficult in 3D because the vector icons overlap and hide each other. We propose four different techniques for visualizing vector fields only near surfaces. The first uses motion blurred particles in a thickened region around the surface. The second uses a voxel grid to contain integral curves of the vector field. The third uses many antialiased lines through the surface, and the fourth uses hairs sprouting from the surface and then bending in the direction of the vector field. All the methods use the graphics pipeline, allowing real time rotation and interaction, and the first two methods can animate the texture to move in the flow determined by the velocity field.<<ETX>>

Isosurfacing in higher dimensions

Visualization algorithms have seen substantial improvements in the past several years. However, very few algorithms have been developed for directly studying data in dimensions higher than three. Most algorithms require a sampling in three-dimensions before applying any visualization algorithms. This sampling typically ignores vital features that may be present when examined in oblique cross-sections, and places an undo burden on system resources when animation through additional dimensions is desired. For time-varying data of large data sets, smooth animation is desired at interactive rates. We provide a fast Marching Cubes like algorithm for hypercubes of any dimension. To support this, we have developed a new algorithm to automatically generate the isosurface and triangulation tables for any dimension. This allows the efficient calculation of 4D isosurfaces, which can be interactively sliced to provide smooth animation or slicing through oblique hyperplanes. The former allows for smooth animation in a very compressed format. The latter provide better tools to study time-evolving features as they move downstream. We also provide examples in using this technique to show interval volumes or the sensitivity of a particular isovalue threshold.