Milos Sramek

3D distance fields: a survey of techniques and applications

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?.

Alias-free voxelization of geometric objects

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.

Fast ray-tracing of rectilinear volume data using distance transforms

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.

The VesselGlyph: Focus & Context Visualization in CT-Angiography

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.

Non-Linear Model Fitting to Parameterize Diseased Blood Vessels

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.

Christmas tree case study: computed tomography as a tool for mastering complex real world objects with applications in computer graphics

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.

Enhanced Voxelization and Representation of Objects with Sharp Details in Truncated Distance Fields

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.

Centerline reformations of complex vascular structures

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.

f3d - a file format an tools for storage an manipulation of volumetric data sets

Different file formats for storage and manipulation of volumetric data exist today, but none of them has been accepted as a standard by the volume visualization and volume graphics communities until now. This paper tries to change this situation by proposing a new, freely available file format f3d, which, as we believe, fulfills the demands of research and educational environments. We hope that this new format will be accepted by the above mentioned communities and thus will provide a basis for improved communication between different groups and applications.

Correction of voxelization artifacts by revoxelization

Earlier proposed antialiasing techniques for voxelization of geometric objects in some cases do not result in completely alias-free data and image renditions. This is often the case for some implicit solids and CSG trees. In this paper we propose a set of operations, which can correct such corrupted data sets and subsequently lead to alias-free image renditions.