Binary-defined 3D objects are common in volume graphics and medical imaging as a result of voxelization algorithms, segmentation methods, and binary operations such as clipping. Traditionally, renderings of binary objects suffer from severe image quality problems, especially when one tries to zoom-in and render the binary data from up close. We present a new rendering technique for discrete binary surfaces. The technique is based on distance-based normal estimation, an accelerated ray casting, and a tricubic interpolator. We demonstrate the quality achieved by our method and report on its interactive rendering speed.

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. In this paper, we 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. We 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, we also find that the reconstruction quality is rather sensitive to the resolution of the framebuffer, and to address this critical issue we 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. We chose SART for its faster convergence properties.

This paper examines the use of the algebraic reconstruction technique (ART) and related techniques to reconstruct 3-D objects from a relatively sparse set of cone-beam projections. Although ART has been widely used for cone-beam reconstruction of high-contrast objects, e.g., in computed angiography, the work presented here explores the more challenging low-contrast case which represents a little-investigated scenario for ART. Preliminary experiments indicate that for cone angles greater than 20 degrees, traditional ART produces reconstructions with strong aliasing artifacts. These artifacts are in addition to the usual off-midplane inaccuracies of cone-beam tomography with planar orbits. We find that the source of these artifacts is the nonuniform reconstruction grid sampling and correction by the cone-beam rays during the ART projection-backprojection procedure. A new method to compute the weights of the reconstruction matrix is devised, which replaces the usual constant-size interpolation filter by one whose size and amplitude is dependent on the source-voxel distance. This enables the generation of reconstructions free of cone-beam aliasing artifacts, at only little extra cost. An alternative analysis reveals that simultaneous ART (SART) also produces reconstructions without aliasing artifacts, however, at greater computational cost. Finally, we thoroughly investigate the influence of various ART parameters, such as volume initialization, relaxation coefficient lambda, correction scheme, number of iterations, and noise in the projection data on reconstruction quality. We find that ART typically requires only three iterations to render satisfactory reconstruction results.

The prime motivation of this work is to devise techniques that make the algebraic reconstruction technique (ART) and related methods more efficient for routine clinical use, while not compromising their accuracy. Since most of the computational effort of ART is spent for projection/backprojection operations, we first seek to optimize the projection algorithm. Existing projection algorithms are surveyed and it is found that these algorithms either lack accuracy or speed, or are not suitable for cone-beam reconstruction. We hence devise a new and more accurate extension to the splatting algorithm, a well-known voxel-driven projection method. We also describe a new three-dimensional (3-D) ray-driven projector that is considerably faster than the voxel-driven projector and, at the same time, more accurate and perfectly suited for the demands of cone beam. We then devise caching schemes for both ART and simultaneous ART (SART), which minimize the number of redundant computations for projection and backprojection and, at the same time, are very memory conscious. We find that with caching, the cost for an ART projection/backprojection operation can be reduced to the equivalent cost of 1.12 projections. We also find that SART, due to its image-based volume correction scheme, is considerably harder to accelerate with caching. Implementations of the algorithms yield run-time ratios TSART/TART between 1.5 and 1.15, depending on the amount of caching used.

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, we 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. We extract an algorithm from LEGION dynamics and propose an adaptive scheme for grouping. We 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, we compare our algorithm with other algorithms for medical-image segmentation, as well as with manual segmentation. LEGION's computational and architectural properties make it a promising approach for real-time medical-image segmentation.

We introduce a new approach for mapping texture on volumetric iso-surfaces and parametric surfaces. Our approach maps 2D images on surfaces while maintaining continuity and preserving the size of the mapped images on the models. Our approach is fully automatic. It eliminates the need for manual mapping of texture maps. We use the curvature of a surface at a point in order to continuously vary the scale of the mapped image. This makes our approach dependent only on local attributes of a point (position, normal and its derivatives) and independent of the global shape and topology of an object. Our method can map high resolution images on low resolution volumes, hence enhancing the visual appearance of rendered volume data. We describe a general framework useful for all surface types that have a C/sup 1/ continuous normal. We demonstrate the new method for painting volume data and for mapping cavities on volume data.

The paper describes three new results for volume rendering algorithms utilizing splatting. First, an antialiasing extension to the basic splatting algorithm is introduced that mitigates the spatial aliasing for high resolution volumes. Aliasing can be severe for high resolution volumes or volumes where a high depth of field leads to converging samples along the perspective axis. Next, an analysis of the common approximation errors in the splatting process for perspective viewing is presented. In this context, we give different implementations, distinguished by efficiency and accuracy, for adding the splat contributions to the image plane. We then present new results in controlling the splatting errors and also show their behavior in the framework of our new antialiasing technique. Finally, current work in progress on extensions to splatting for temporal antialiasing is demonstrated. We present a simple but highly effective scheme for adding motion blur to fast moving volumes.

Object dataflow is a popular approach used in parallel rendering. The data representing the 3D scene is statically distributed among processors and objects are fetched and cached only on demand. Most previous object dataflow methods were implemented on shared memory architectures and exploited spatial coherency to reduce hardware cache misses. We propose an efficient model for object dataflow parallel volume rendering on message passing machines. The algorithm is introduced and its ray storage mechanism is used to support latency hiding by postponing computation on inactive rays. Memory usage is optimized by letting objects migrate and replicate at different processors rather than the common static assignments. Our cache only memory approach uses a distributed directory scheme to trace the location of objects at other nodes. A mechanism to minimize network congestion was implemented which optimizes channel utilization. Unlike previous methods, our approach can benefit from temporal coherence and effectively minimizes communication costs during animation on limited bandwidth multiprocessing environments. We report results of the algorithm's implementation on several platforms like Cray T3D, Convex SPP and DEC alpha cluster of workstations (COWs), and achieved higher efficiency and scalability than existing algorithms.

The task of reconstructing the derivative of a discrete function is essential for its shading and rendering as well as being widely used in image processing and analysis. We survey the possible methods for normal estimation in volume rendering and divide them into two classes based on the delivered numerical accuracy. The three members of the first class determine the normal in two steps by employing both interpolation and derivative filters. Among these is a new method which has never been realized. The members of the first class are all equally accurate. The second class has only one member and employs a continuous derivative filter obtained through the analytic derivation of an interpolation filter. We use the new method to analytically compare the accuracy of the first class with that of the second. As a result of our analysis we show that even inexpensive schemes can in fact be more accurate than high order methods. We describe the theoretical computational cost of applying the schemes in a volume rendering application and provide guidelines for helping one choose a scheme for estimating derivatives. In particular we find that the new method can be very inexpensive and can compete with the normal estimations which pre-shade and pre-classify the volume (M. Levoy, 1988).

Splatting is a popular direct volume rendering algorithm. However, the algorithm does not correctly render cases where the volume sampling rate is higher than the image sampling rate (e.g. more than one voxel maps into a pixel). This situation arises with orthographic projections of high-resolution volumes, as well as with perspective projections of volumes of any resolution. The result is potentially severe spatial and temporal aliasing artifacts. Some volume ray-casting algorithms avoid these artifacts by employing reconstruction kernels which vary in width as the rays diverge. Unlike ray-casting algorithms, existing splatting algorithms do not have an equivalent mechanism for avoiding these artifacts. The authors propose such a mechanism, which delivers high-quality splatted images and has the potential for a very efficient hardware implementation.

It is often the case that images generated by image synthesis algorithms are judged by visual examination. The user resorts to an iterative refinement process of inspection and rendering until a satisfactory image is obtained. In this paper we propose quantitative metrics to compare images that arise from an image synthesis algorithm. The intent is to be able to guide the refinement process inherent in image synthesis. The Mean‐Square‐Error (MSE) has been traditionally employed to guide this process. However, it is not a viable metric for image synthesis control. We propose the use of a wavelet based perceptual metric which incorporates the frequency response of the Human Visual System. A useful aspect of the wavelet based metric is its ability to selectively measure the changes to structures of different sizes and scales in specific locations. Also, by resorting to the use of wavelets of various degrees of regularity, one can seek different levels of smoothness in an image. It is rare that such level of control can be obtained from a metric other than a wavelet based metric. We show the usefulness of our metric by examining its effectiveness in providing insights for common operations of an image synthesis algorithm (e.g., blurring). We also provide some examples of its use in rendering algorithms frequently used in graphics.

A typical ray tracing algorithm traces a ray through each screen-pixel and spawns secondary rays at ray–object intersection points. Unlike traditional ray tracers which follow these rays recursively, we assign a priority value to each newly spawned ray and insert it into a priority queue. The priority assigned to each ray can be based on a variety of criteria, some of which we explore here. The next ray we trace is always the one with the highest priority in the queue. Occasionally, we trigger display updates when a checkpoint or predefined threshold is reached, providing intermediate images for review and evaluation. Classical ray tracers, once given the rendering specifications, are not controllable by the user. The priority-driven ray tracing, on the other hand, provides the user with a mechanism to steer the rendering and deliver intermediate images amid processing. This paper describes the illumination model of the non-recursive priority-driven ray tracer and evaluates its memory and time requirements. We show that although worst-case memory requirements can be overwhelming, in practice, our method is both useful and feasible. © 1997 by John Wiley & Sons, Ltd.

The order in which the projections are applied in the algebraic reconstruction technique (ART) has a great effect on speed of convergence, accuracy, and the amount of noise-like artifacts in the reconstructed image. In this paper, a new projection ordering scheme for ART is presented: the weighted-distance scheme (WDS). It heuristically optimizes the angular distance of a newly selected projection with respect to an extended sequence of previously applied projections. This sequence of influential projections may incorporate the complete set of all previously applied projections or any limited time interval subset thereof. The selection algorithm results in uniform sampling of the projection access space, minimizing correlation in the projection sequence. This produces more accurate images with less noise-like artifacts than previously suggested projection ordering schemes.

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.

We present a new visualization approach to support design for manufacturing (DFM). This involves the correlation of manufacturing problems with the causative geometric characteristics. We then discuss the use of distance transform and 3-D thinning to extract these characteristics from a voxelized object. In contrast to current computer aided engineering (CAE) tools, our system is very efficient and simple to use. It does not require the skill and experience to generate and control a numerical mesh and interpret the results. The specifically tailored visualization system makes the results self-evident. Though the current domain is die casting, it could potentially be applied to many net shape processes.

In many mechanical design-related activities, the visualization tool needs to convey not only the shape of the objects, but also their interior problem regions. Due to the binary nature of these models, existing shading models often fall short of supporting a realistic display. In this case study, we present several new contextual shading methods that we originally developed for our design visualization tools. The results are then compared with gray-scale shading applied to a gray-level version of the binary object. The comparison shows that our method can be applied to any binary object and yields promising results.

Volume ray casting is based on sampling the data along sight rays. In this technique, reconstruction is achieved by a convolution, which collects the contribution of multiple voxels to one sample point. Splatting, on the other hand, is based on projecting data points on to the screen, and reconstruction is implemented by an "inverted convolution", where the contribution of one data element is distributed to many sample points (i.e. pixels). Splatting produces images of a quality comparable to ray casting but at greater speeds. This is achieved by pre-computing the projection footprint that the interpolation kernel leaves on the image plane. However, while fast incremental schemes can be utilized for orthographic projection, the perspective projection complicates the mapping of the footprints and is therefore rather slow. In this paper, we merge the technique of splatting with the principles of ray casting to yield a ray-driven splatting approach. We imagine splats as being suspended in object space, a splat at every voxel. Rays are then spawned to traverse the space and intersect the splats. An efficient and accurate way of intersecting and addressing the splats is described. Not only is ray-driven splatting inherently insensitive to the complexity of the perspective viewing transform, it also offers acceleration methods such as early ray termination and bounding volumes, which are methods that traditional voxel-driven splatting cannot benefit from. This results in competitive or superior performance for parallel projection, and superior performance for perspective projection.

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.

Reconstruction is prerequisite whenever a discrete signal needs to be resampled as a result of transformations such as texture mapping, image manipulation, volume slicing, and rendering. We present a new method for the characterization and measurement of reconstruction error in the spatial domain. Our method uses the Classical Shannon's Sampling Theorem as a basis to develop error bounds. We use this formulation to provide, for the first time, an efficient way to guarantee an error bound at every point by varying the size of the reconstruction filter. We go further to support position-adaptive reconstruction and data-adaptive reconstruction which adjusts the filter size to the location of the reconstruction point and to the data values in its vicinity. We demonstrate the effectiveness of our methods with 1D signals, 2D signals (images), and 3D signals (volumes).

Because of the nature of the die casting process, the part geometry severely restricts the die geometry and hence affects the quality of the part. However, as is often the case in other manufacturing processes, diecastings are currently designed purely based on their function. The manufacturability of the diecastings is not considered until the design has been nearly completed and detailed. This is due to the design support limitations of current CAE tools. We present a new volume-based approach to support diecastability evaluation, especially in preliminary design. Our approach can be applied to arbitrarily shaped parts without pre-defined feature libraries. The focus is on the identification of geometric characteristics, e.g. heavy mass regions, that could be responsible for thermal-related part defects. A distance transform with city-block metric is used to extract this geometric property. Volume visualization techniques are also adopted to allow users to visualize the results in a clear and precise way.

This paper advocates the use of a group of renderers rather than any specific rendering method. We describe a bundle containing four alternative approaches to visualizing volume data. One new approach uses realistic volumetric gas rendering techniques to produce photo-realistic images and animations. The second uses ray casting that is based on a simpler illumination model and is mainly centered around a versatile new tool for the design of transfer functions. The third method employs a simple illumination model and rapid rendering mechanisms to provide efficient preview capabilities. The last one reduces data magnitude by displaying the most visible components and exploits rendering hardware to provide real time browsing capabilities. We show that each rendering tool provides a unique service and demonstrate the combined utility of our group of volume renderers in computational fluid dynamic (CFD) visualization. While one tool allows the explorer to render rapidly for navigation through the data, another tool allows one to emphasize data features (e.g., shock waves), and yet another tool allows one to realistically render the data. We believe that only through the deployment of groups of renderers will the scientist be well served and equipped to form numerous perspectives of the same dataset, each providing different insights into the data.>

The paper describes three alternative volume rendering approaches to visualizing computational fluid dynamics (CFD) data. One new approach uses realistic volumetric gas rendering techniques to produce photo-realistic images and animations from scalar CFD data. The second uses ray casting that is based an a sampler illumination model and is mainly centered around a versatile new tool for the design of transfer functions. The third method employs a simple illumination model and rapid rendering mechanisms to provide efficient preview capabilities. These tools provide a large range of volume rendering capabilities to be used by the CFD explorer to render rapidly for navigation through the data, to emphasize data features (e.g., shock waves) with a specific transfer function, or to present a realistic rendition of the model.>

Rendering volumes represented as a 3D grid of voxels requires an overwhelming amount of processing power In this paper we investigate eficient techniques for rendering semi-transparent volumes on vector and parallel processors.Parallelism inherent in a regular grid is obtained by decomposing the volume into geometric primitives called beams, slices and slabs of voxels.By using the adjacency properties of voxels in beams and slices, eficient incremental transformation schemes are developed.The slab decomposition of the volume allows the implementation of an eficient parallel feed-forward renderer which includes the splatting technique for image reconstruction and a back-to-front method for creating images.We report the implementation of this feed-forward volume renderer on a hierarchical shared memory machine with individual pipelined processors.

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.>

Abstract 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.

A set of volume visualization tools that are based on the use of recursive ray tracing as the primary vehicle for realistic volume imaging is presented. The tools include shadows, mirrors, specularity, and constructive solid geometry. The underlying representation for the ray tracer is a 3-D raster of voxels that holds the discrete form of the scene. Unlike traditional volume rendering techniques, the discrete recursive ray tracer models many illumination phenomena by traversing discrete rays in voxel space. The approach provides true ray tracing of sampled or computed datasets, as well as ray tracing of hybrid scenes where sampled or computed data are intermixed with geometric models and enhances the understanding of complex biomedical datasets.>

No abstract available.

The authors discuss the special properties of volumetric cell data (e.g., noise, discontinuity, raggedness) and the particular difficulties encountered when trying to visualize them in three dimensions. The authors describe some of the solutions adopted, specifically in surface discrimination and shading. Nerve cells (neuroblastoma) grown in tissue culture were selected as the biological preparation because these cells possess very rich actin structures. The cells were stained with a fluorescent probe specific for actin (rhodamine-phalloidin) and were viewed and optically sectioned using the Bio-Rad MRC 600 confocal fluorescence microscope. The slice dataset was then reconstructed and processed in the BioCube environment, a comprehensive system developed for volume visualization of cellular structures. The actin cytoskeleton of single cells was visualized and manipulated using this system.>