Roni Yagel

Volume graphics

Volume graphics, which employs a volume buffer of voxels for 3D scene representation, is discussed. Volume graphics offers advantages over surface graphics: it is viewpoint independent, insensitive to scene and object complexity, and suitable for the representation of sampled and simulated data sets. Moreover, geometric objects can be mixed with these data sets. Volume graphics supports the visualization of internal structures and lends itself to the realization of block operations, constructive solid geometry modeling, irregular voxel sizes, and hierarchical representation. The problems associated with the volume buffer representation (such as discreteness, memory size, processing time, and loss of geometric representation) are discussed.<<ETX>>

Octree-based decimation of marching cubes surfaces

The marching cubes (MC) algorithm is a method for generating isosurfaces. It also generates an excessively large number of triangles to represent an isosurface; this increases the rendering time. This paper presents a decimation method to reduce the number of triangles generated. Decimation is carried out before creating a large number of triangles. Four major steps comprise the algorithm: surface tracking, merging, crack patching and triangulation. Surface tracking is an enhanced implementation of the MC algorithm. Starting from a seed point, the surface tracker visits only those cells likely to compose part of the desired isosurface. The cells making up the extracted surface are stored in an octree that is further processed. A bottom-up approach is taken in merging the cells containing a relatively flat approximating surface. The finer surface details are maintained. Cells are merged as long as the error due to such an operation is within a user-specified error parameter, or a cell acquires more than one connected surface component in it. A crack patching method is described that forces edges of smaller cells to lie along those of the larger neighboring cells. The overall saving in the number of triangles depends both on the specified error value and the nature of the data. Use of the hierarchical octree data structure also presents the potential of incremental representation of surfaces. We can generate a highly smoothed surface representation which can be progressively refined as the user-specified error value is decreased.

Rapid 3-D cone-beam reconstruction with the simultaneous algebraic reconstruction technique (SART) using 2-D texture mapping hardware

Algebraic reconstruction methods, such as the algebraic reconstruction technique (ART) and the related simultaneous ART (SART), reconstruct a two-dimensional (2-D) or three-dimensional (3-D) object from its X-ray projections. The algebraic methods have, in certain scenarios, many advantages over the more popular Filtered Backprojection approaches and have also recently been shown to perform well for 3-D cone-beam reconstruction. However, so far the slow speed of these iterative methods have prohibited their routine use in clinical applications. Here, the authors address this shortcoming and investigate the utility of widely available 2-D texture mapping graphics hardware for the purpose of accelerating the 3-D algebraic reconstruction. They find that this hardware allows 3-D cone-beam reconstructions to be obtained at almost interactive speeds, with speed-ups of over 50 with respect to implementations that only use general-purpose CPUs. However the authors also find that the reconstruction quality is rather sensitive to the resolution of the framebuffer, and to address this critical issue they propose a scheme that extends the precision of a given framebuffer by 4 bits, using the color channels. With this extension, a 12-bit framebuffer delivers useful reconstructions for 0.5% tissue contrast, while an 8-bit framebuffer requires 4%. Since graphics hardware generates an entire image for each volume projection, it is most appropriately used with an algebraic reconstruction method that performs volume correction at that granularity as well, such as SART or SIRT. The authors chose SART for its faster convergence properties.

Discrete ray tracing

Discrete ray tracing, or 3-D raster ray tracing (RRT), which, unlike existing ray tracing methods that use geometric representation for the 3-D scene employs a 3-D discrete raster of voxels for representing the 3-D scene in the same way a 2-D raster of pixels represents a 2-D image, is discussed. Each voxel is a small quantum unit of volume that has numeric values associated with it representing some measurable properties or attributes of the real object or phenomenon at that voxel. It is shown that RRT operates in two phases: preprocessing voxel and discrete ray tracing. In the voxel phase, the geometric model is digitized using 3-D scan-conversion algorithms that convert the continuous representation of the model into a discrete representation within the 3-D raster. In the second phase, RRT employs a discrete variation of the conventional recursive ray tracer in which 3-D discrete rays are traversed through the 3-D raster to find the first surface voxel. Encountering a nontransparent voxel indicates a ray-surface hit. Results obtained by running the RRT software one one 20-MIPS (25-GHz) processor of a Silicon Graphics 4D/240GTX are presented in terms of CPU time. >

Accelerating volume animation by space-leaping

In this work we present a method for speeding the process of volume animation. It exploits coherency between consecutive images to shorten the path rays take through the volume. Rays are provided with the information needed to leap over the empty space and commence volume traversal at the vicinity of meaningful data. The algorithm starts by projecting the volume onto a C-buffer (coordinates-buffer) which stores the object-space coordinates of the first non-empty voxel visible from a pixel. Following a change in the viewing parameters, the C-buffer is transformed accordingly. Next, coordinates that possibly became hidden are discarded. The remaining values serve as an estimate of the point where the new rays should start their volume traversal. This method does not require 3-D preprocessing and does not suffer from any image degradation. It can be combined with existing acceleration techniques and can support any ray traversal algorithm and material modeling scheme.<<ETX>>

Template-Based Volume Viewing

We present an efficient three‐phase algorithm for volume viewing that is based on exploiting coherency between rays in parallel projection. The algorithm starts by building a ray‐template and determining a special plane for projection ‐ the base‐plane. Parallel rays are cast into the volume from within the projected region of the volume on the base‐plane, by repeating the sequence of steps specified in the ray‐template. We carefully choose the type of line to be employed and the way the template is being placed on the base‐plane in order to assure uniform sampling of the volume by the discrete rays. We conclude by describing an optimized software implementation of our algorithm and reporting its performance.

Evaluation and design of filters using a Taylor series expansion

We describe a new method for analyzing, classifying, and evaluating filters that can be applied to interpolation filters as well as to arbitrary derivative filters of any order. Our analysis is based on the Taylor series expansion of the convolution sum. Our analysis shows the need and derives the method for the normalization of derivative filter weights. Under certain minimal restrictions of the underlying function, we are able to compute tight absolute error bounds of the reconstruction process. We demonstrate the utilization of our methods to the analysis of the class of cubic BC-spline filters. As our technique is not restricted to interpolation filters, we are able to show that the Catmull-Rom spline filter and its derivative are the most accurate reconstruction and derivative filters, respectively, among the class of BC-spline filters. We also present a new derivative filter which features better spatial accuracy than any derivative BC-spline filter, and is optimal within our framework. We conclude by demonstrating the use of these optimal filters for accurate interpolation and gradient estimation in volume rendering.

An accurate method for voxelizing polygon meshes

The process of generating discrete surfaces in a volumetric representation, termed voxelization, is confronted with topological considerations as well as accuracy and efficiency requirements. The authors introduce a new method for voxelizing planar objects which, unlike existing methods, provides topological conformity through geometric measures. They extend their approach to provide, for the first time, an accurate and coherent method for voxelizing polygon meshes. This method eliminates common voxelization artifacts at edges and vertices. They prove the methods topological attributes and report performance of their implementation. Finally, they demonstrate that this approach forms a basis for a new set of voxelization algorithms by voxelizing an example cubic object.

Segmentation of medical images using LEGION

Advances in visualization technology and specialized graphic workstations allow clinicians to virtually interact with anatomical structures contained within sampled medical-image datasets. A hindrance to the effective use of this technology is the difficult problem of image segmentation. In this paper, the authors utilize a recently proposed oscillator network called the locally excitatory globally inhibitory oscillator network (LEGION) whose ability to achieve fast synchrony with local excitation and desynchrony with global inhibition makes it an effective computational framework for grouping similar features and segregating dissimilar ones in an image. The authors extract an algorithm from LEGION dynamics and propose an adaptive scheme for grouping. They show results of the algorithm to two-dimensional (2-D) and three-dimensional (3-D) (volume) computerized topography (CT) and magnetic resonance imaging (MRI) medical-image datasets. In addition, the authors compare their algorithm with other algorithms for medical-image segmentation, as well as with manual segmentation. LEGIONs computational and architectural properties make it a promising approach for real-time medical-image segmentation.

Hardware assisted volume rendering of unstructured grids by incremental slicing

Some of the more important research results in computational science rely on the use of simulation methods that operate on unstructured grids. However, these grids, composed of a set of polyhedra, introduce exceptional problems with respect to data visualization. Volume rendering techniques, originally developed to handle rectangular grids, show significant promise for general use with unstructured grids as well. The main disadvantage of this approach, compared to isosurfaces, particles or other visualization tools is its non-interactive performance. We describe an efficient method for rendering unstructured grids that is based on incremental slicing and hardware polygon rendering. For a given view direction, the grid vertices are transformed to image space using available graphics hardware. We then incrementally compute the 2D polygon-meshes that result from letting a set of planes, parallel to the screen plane, intersect (slice) the transformed grid. Finally, we use the graphics hardware to render (interpolate-fill) the polygon-meshes and composite them in visibility order. We show that, in addition to being faster than existing methods, our approach also provides adaptive control and progressive image generation. The adaptive method provides user control to ensure that the contribution of every cell is included in the final image or to limit the number of cells that are missed.