Visualization of vascular structures is a common and frequently performed task in the field of medical imaging. There exist well established and applicable methods such as Maximum Intensity Projection (MIP) and Curved Planar Reformation (CPR). However, when calcified vessel walls are investigated, occlusion hinders exploration of the vessel interior with MIP. In contrast, CPR offers the possibility to visualize the vessel lumen by cutting a single vessel along its centerline. Extending the idea of CPR, we propose a novel technique, called Centerline Reformation (CR), which is capable of visualizing the lumen of spatially arbitrarily oriented vessels not necessarily connected in a tree structure. In order to visually emphasize depth, overlap and occlusion, halos can optionally envelope the vessel lumen. The required vessel centerlines are obtained from volumetric data by performing a scale-space based feature extraction. We present the application of the proposed technique in a focus and context setup. Further, we demonstrate how it facilitates the investigation of dense vascular structures, particularly cervical vessels or vessel data featuring peripheral arterial occlusive diseases or pulmonary embolisms. Finally, feedback from domain experts is given.

Abstract Gaussian filtering is a basic operation commonly used in numerous image and volume processing algorithms. It is, therefore, desirable to perform it as efficiently as possible. Over the last decade CPUs have been successfully extended with several SIMD (Single Instruction Multiple Data) extensions, such as MMX, 3DNow!, and SSE series. In this paper we introduce a new technique for Gaussian filtering of volume data sets—the extended volume—together with its SIMD implementation using the SSE technology. We further introduce a SIMD optimized recursive IIR implementation of the Gaussian filter, and finally, we parallelize the SSE versions with the help of OpenMP (Open Multi‐Processing). Experimental evaluation indicates that the SIMD implementation can significantly speed up both versions of the Gaussian filtering and that the non‐recursive extended volume version is faster than the recursive IIR one for small widths of the Gaussian filter. Copyright © 2010 John Wiley & Sons, Ltd.

This paper presents a new method for voxelization of solid objects containing sharp details. Voxelization is a sampling process that transforms a continuously defined object into a discrete one represented as a voxel field. The voxel field can be used for rendering or other purposes, which often involve a reconstruction of a continuous approximation of the original object. Objects to be voxelized need to fulfill certain representability conditions; otherwise, disturbing artifacts appear during reconstruction. The method proposed here extends the traditional distance-based voxelization by an a-priori detection of sharp object details and their subsequent modification in such a way that the resulting object to be voxelized fulfills the representability conditions. The resulting discrete objects are represented by means of truncated (i.e., narrow-band) distance fields, which provide reduction of memory requirements and further processing by level set techniques. This approach is exemplified by two classes of solid objects that normally contain such sharp details: implicit solids and solids resulting from CSG operations. In both cases, the sharp details are rounded to a specific curvature dictated by the sampling distance.

A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the distance field is signed, we may also determine if the point is internal or external to objects within the domain. The distance field has been found to be a useful construction within the areas of computer vision, physics, and computer graphics. This paper serves as an exposition of methods for the production of distance fields, and a review of alternative representations and applications of distance fields. In the course of this paper, we present various methods from all three of the above areas, and we answer pertinent questions such as How accurate are these methods compared to each other? How simple are they to implement?, and What is the complexity and runtime of such methods?

We present a new technique for CSG operations with voxelized geometric objects, which are represented by truncated discrete distance fields supplemented by additional information about the surface normal. The technique removes artifacts of straightforward volumetric CSG operations by taking into account conditions for object representability, according to which sharp details are not correctly representable in discrete distance fields. The proposed technique solves this shortcoming by rounding edges and other sharp details. It works at the voxel level without the necessity for reconstruction of continuous object models.

Accurate estimation of vessel parameters is a prerequisite for automated visualization and analysis of healthy and diseased blood vessels. The objective of this research is to estimate the dimensions of lower extremity arteries, imaged by computed tomography (CT). These parameters are required to get a good quality visualization of healthy as well as diseased arteries using a visualization technique such as curved planar reformation (CPR). The vessel is modeled using an elliptical or cylindrical structure with specific dimensions, orientation and blood vessel mean density. The model separates two homogeneous regions: its inner side represents a region of density for vessels, and its outer side a region for background. Taking into account the point spread function (PSF) of a CT scanner, a function is modeled with a Gaussian kernel, in order to smooth the vessel boundary in the model. A new strategy for vessel parameter estimation is presented. It stems from vessel model and model parameter optimization by a nonlinear optimization procedure, i.e., the Levenberg-Marquardt technique. The method provides center location, diameter and orientation of the vessel as well as blood and background mean density values. The method is tested on synthetic data and real patient data with encouraging results.

Accurate and reliable visualization of blood vessels is still a challenging problem, notably in the presence of morphologic changes resulting from atherosclerotic diseases. We take advantage of partially segmented data with approximately identified vessel centerlines to comprehensively visualize the diseased peripheral arterial tree. We introduce the VesselGlyph as an abstract notation for novel focus & context visualization techniques of tubular structures such as contrast-medium enhanced arteries in CT-angiography (CTA). The proposed techniques combine direct volume rendering (DVR) and curved planar reformation (CPR) within a single image. The VesselGlyph consists of several regions where different rendering methods are used. The region type, the used visualization method and the region parameters depend on the distance from the vessel centerline and on viewing parameters as well. By selecting proper rendering techniques for different regions, vessels are depicted in a naturally looking and undistorted anatomic context. This may facilitate the diagnosis and treatment planning of patients with peripheral arterial occlusive disease. In this paper we furthermore present a way of how to implement the proposed techniques in software and by means of modern 3D graphics accelerators.

We report on using computed tomography (CT) as a model acquisition tool for complex objects in computer graphics. Unlike other modeling and scanning techniques the complexity of the object is irrelevant in CT, which naturally enables to model objects with, for example, concavities, holes, twists or fine surface details. Once the data is scanned, one can apply post-processing techniques for data enhancement, modification or presentation. For demonstration purposes we chose to scan a Christmas tree which exhibits high complexity which is difficult or even impossible to handle with other techniques. However, care has to be taken to achieve good scanning results with CT. Further, we illustrate post-processing by means of data segmentation and photorealistic as well as non-photorealistic surface and volume rendering techniques.

The paper discusses and experimentally compares distance based acceleration algorithms for ray tracing of volumetric data with an emphasis on the Chessboard Distance (CD) voxel traversal. The acceleration of this class of algorithms is achieved by skipping empty macro regions, which are defined for each background voxel of the volume. Background voxels are labeled in a preprocessing phase by a value, defining the macro region size, which is equal to the voxel distance to the nearest foreground voxel. The CD algorithm exploits the chessboard distance and defines the ray as a nonuniform sequence of samples positioned at voxel faces. This feature assures that no foreground voxels are missed during the scene traversal. Further, due to parallelepipedal shape of the macro region, it supports accelerated visualization of cubic, regular, and rectilinear grids. The CD algorithm is suitable for all modifications of the ray tracing/ray casting techniques being used in volume visualization and volume graphics. However, when used for rendering based on local surface interpolation, it also enables fast search of intersections between rays and the interpolated surface, further improving speed of the process.

Introduces a new concept for alias-free voxelization of geometric objects based on a voxelization model (V-model). The V-model of an object is its representation in 3D continuous space by a trivariate density function. This function is sampled during the voxelization and the resulting values are stored in a volume buffer. This concept enables us to study general issues of sampling and rendering separately from object-specific design issues. It provides us with a possibility to design such V-models, which are correct from the point of view of both the sampling and rendering, thus leading to both alias-free volumetric representation and alias-free rendered images. We performed numerous experiments with different combinations of V-models and reconstruction techniques. We have shown that the V-model with a Gaussian surface density profile combined with tricubic interpolation and Gabor derivative reconstruction outperforms the previously published technique with a linear density profile. This enables higher fidelity of images rendered from volume data due to increased sharpness of edges and thinner surface patches.

The increasing distinguishing capability of tomographic and other 3D scanners as well as the new voxelization algorithms place new demands on visualization techniques aimed at interactivity and rendition quality. Among others, triangulation on a subvoxel level based on the marching cube algorithm has gained popularity in recent years. However without graphics hardware support, rendering many small triangles could be awkward. We present a surface rendering approach based on ray tracing of segmented volumetric data. We show that if a proper interpolation scheme and voxel traversal algorithm are used, high quality images can be obtained within an acceptable time and without hardware support.>