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FAST VOLUME RENDERING USING A SHEARWARP FACTORIZATION OF THE VIEWING TRANSFORMATION
, 1995
"... Volume rendering is a technique for visualizing 3D arrays of sampled data. It has applications in areas such as medical imaging and scientific visualization, but its use has been limited by its high computational expense. Early implementations of volume rendering used bruteforce techniques that req ..."
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Cited by 442 (2 self)
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Volume rendering is a technique for visualizing 3D arrays of sampled data. It has applications in areas such as medical imaging and scientific visualization, but its use has been limited by its high computational expense. Early implementations of volume rendering used bruteforce techniques that require on the order of 100 seconds to render typical data sets on a workstation. Algorithms with optimizations that exploit coherence in the data have reduced rendering times to the range of ten seconds but are still not fast enough for interactive visualization applications. In this thesis we present a family of volume rendering algorithms that reduces rendering times to one second. First we present a scanlineorder volume rendering algorithm that exploits coherence in both the volume data and the image. We show that scanlineorder algorithms are fundamentally more efficient than commonlyused ray casting algorithms because the latter must perform analytic geometry calculations (e.g. intersecting rays with axisaligned boxes). The new scanlineorder algorithm simply streams through the volume and the image in storage order. We describe variants of the algorithm for both parallel and perspective projections and
Frequency Domain Volume Rendering
, 1993
"... The Fourier projectionslice theorem allows projections of volume data to be generated in O(n 2 log n) time for a volume of size n 3 . The method operates by extracting and inverse Fourier transforming 2D slices from a 3D frequency domain representation of the volume. Unfortunately, these projec ..."
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Cited by 84 (0 self)
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The Fourier projectionslice theorem allows projections of volume data to be generated in O(n 2 log n) time for a volume of size n 3 . The method operates by extracting and inverse Fourier transforming 2D slices from a 3D frequency domain representation of the volume. Unfortunately, these projections do not exhibit the occlusion that is characteristic of conventional volume renderings. We present a new frequency domain volume rendering algorithm that replaces much of the missing depth and shape cues by performing shading calculations in the frequency domain during slice extraction. In particular, we demonstrate frequency domain methods for computing linear or nonlinear depth cueing and directional diffuse reflection. The resulting images can be generated an order of magnitude faster than volume renderings and may be more useful for many applications. CR Categories: I.3.7 [Computer Graphics]: Threedimensional Graphics and Realism.; I.3.3 [Computer Graphics ]: Picture/Image Generati...
Volume Rendering using the Fourier ProjectionSlice Theorem
 Also Stanford University
, 1992
"... The Fourier projectionslice theorem states that the inverse transform of a slice extracted from the frequency domain representation of a volume yields a projection of the volume in a direction perpendicular to the slice. This theorem allows the generation of attenuationonly renderings of volume da ..."
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Cited by 48 (1 self)
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The Fourier projectionslice theorem states that the inverse transform of a slice extracted from the frequency domain representation of a volume yields a projection of the volume in a direction perpendicular to the slice. This theorem allows the generation of attenuationonly renderings of volume data in O (N 2 log N) time for a volume of size N 3 . In this paper, we show how more realistic renderings can be generated using a class of shading models whose terms are Fourier projections. Models are derived for rendering depth cueing by linear attenuation of variable energy emitters and for rendering directional shading by Lambertian reflection with hemispherical illumination. While the resulting images do not exhibit the occlusion that is characteristic of conventional volume rendering, they provide sufficient depth and shape cues to give a strong illusion that occlusion exists. Keywords: Volume rendering, Fourier projections, Shading models, Scientific visualization, Medical imaging...
Volvis: A diversified volume visualization system
 Proc. Visualization’ 94
, 1994
"... VolVis is a diversified, easy to use, extensible, high performance, and portable volume visualization system for scientists and engineers as well as for visualization developers and researchers. VolVis accepts as input 3D scalar volumetric data as well as 3D volumesampled and classical geometric mo ..."
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Cited by 31 (3 self)
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VolVis is a diversified, easy to use, extensible, high performance, and portable volume visualization system for scientists and engineers as well as for visualization developers and researchers. VolVis accepts as input 3D scalar volumetric data as well as 3D volumesampled and classical geometric models. Interaction with the data is controlled by a variety of 3D input devices in an input deviceindependent environment. VolVis output includes navigation preview, static images, and animation sequences. A variety of volume rendering algorithms are supported, ranging from fast rough approximations, to compressiondomain rendering, toaccurate volumetric ray tracing and radiosity, and irregular grid rendering. 1.
Iterative tomographic image reconstruction using Fourierbased forward and back projectors
 IEEE Trans. Med. Imag
, 2004
"... Fourierbased reprojection methods have the potential to reduce the computation time in iterative tomographic image reconstruction. Interpolation errors are a limitation of Fourierbased reprojection methods. We apply a minmax interpolation method for the nonuniform fast Fourier transform (NUFFT) t ..."
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Cited by 23 (4 self)
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Fourierbased reprojection methods have the potential to reduce the computation time in iterative tomographic image reconstruction. Interpolation errors are a limitation of Fourierbased reprojection methods. We apply a minmax interpolation method for the nonuniform fast Fourier transform (NUFFT) to minimize the interpolation errors. Numerical results show that the minmax NUFFT approach provides substantially lower approximation errors in tomographic reprojection and backprojection than conventional interpolation methods.
Integrated Volume Compression and Visualization
, 1997
"... Volumetric data sets require enormous storage capacity even at moderate resolution levels. The excessive storage demands not only stress the capacity of the underlying storage and communications systems, but also seriously limit the speed of volume rendering due to data movement and manipulation. A ..."
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Cited by 19 (3 self)
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Volumetric data sets require enormous storage capacity even at moderate resolution levels. The excessive storage demands not only stress the capacity of the underlying storage and communications systems, but also seriously limit the speed of volume rendering due to data movement and manipulation. A novel volumetric data visualization scheme is proposed and implemented in this work that renders 2D images directly from compressed 3D data sets. The novelty of this algorithm is that rendering is performed on the compressed representation of the volumetric data without predecompression. As a result, the overheads associated with both data movement and rendering processing are significantly reduced. The proposed algorithm generalizes previously proposed wholevolume frequencydomain rendering schemes by first dividing the 3D data set into subcubes, transforming each subcube to a frequencydomain representation, and applying the Fourier Projection Theorem to produce the projected 2D images a...
Highquality volume rendering with resampling in the frequency domain
 IN PROCEEDINGS OF EUROGRAPHICS / IEEE VGTC SYMPOSIUM ON VISUALIZATION
, 2005
"... This work introduces a volume rendering technique that is conceptually based on the shearwarp factorization. We propose to perform the shear transformation entirely in the frequency domain. Unlike the standard shearwarp algorithm, we allow for arbitrary sampling distances along the viewing rays, i ..."
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Cited by 11 (2 self)
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This work introduces a volume rendering technique that is conceptually based on the shearwarp factorization. We propose to perform the shear transformation entirely in the frequency domain. Unlike the standard shearwarp algorithm, we allow for arbitrary sampling distances along the viewing rays, independent of the view direction. The accurate scaling of the volume slices is achieved by using the zero padding interpolation property. Finally, a high quality gradient estimation scheme is presented which uses the derivative theorem of the Fourier transform. Experimental results have shown that the presented method outperforms established algorithms in the quality of the produced images. If the data is sampled above the Nyquist rate the presented method is capable of a perfect reconstruction of the original function.
Voxels as a Computational Representation of Geometry
 in The Computational Representation of Geometry. SIGGRAPH '94 Course Notes
, 1994
"... This paper is a survey of volume visualization, volume graphics, and volume rendering techniques. It focuses specifically on the use of the voxel representation and volumetric techniques for geometric applications. 1. Introduction Volume data are 3D entities that may have information inside them, ..."
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Cited by 7 (0 self)
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This paper is a survey of volume visualization, volume graphics, and volume rendering techniques. It focuses specifically on the use of the voxel representation and volumetric techniques for geometric applications. 1. Introduction Volume data are 3D entities that may have information inside them, might not consist of surfaces and edges, or might be too voluminous to be represented geometrically . Volume visualization is a method of extracting meaningful information from volumetric data using interactive graphics and imaging, and it is concerned with volume data representation, modeling, manipulation, and rendering [49]. Volume data are obtained by sampling, simulation, or modeling techniques. For example, a sequence of 2D slices obtained from Magnetic Resonance Imaging (MRI) or Computed Tomography (CT) is 3D reconstructed into a volume model and visualized for diagnostic purposes or for planning of treatment or surgery. The same technology is often used with industrial CT for nondes...
Designing Optimal Parallel Volume Rendering Algorithms
, 1993
"... Designing Optimal Parallel Volume Rendering Algorithms by Craig Michael Wittenbrink Chairperson of the Supervisory Committee: Professor Arun K. Somani Department of Electrical Engineering and Department of Computer Science and Engineering Volume rendering is a method for visualizing volumes of sam ..."
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Cited by 4 (4 self)
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Designing Optimal Parallel Volume Rendering Algorithms by Craig Michael Wittenbrink Chairperson of the Supervisory Committee: Professor Arun K. Somani Department of Electrical Engineering and Department of Computer Science and Engineering Volume rendering is a method for visualizing volumes of sampled data such as CT, MRI, and finite element simulations. Visualization of medical and simulation data improves understanding and interpretation, but volume rendering is expensive and each frame takes from minutes to hours to calculate. Parallel computers provide the potential for interactive volume rendering, but parallel algorithms have not matched sequential algorithm 's features, nor have they provided the speedup possible. I introduce a methodology to control the complexity in designing parallel algorithms, and apply this methodology to volume rendering. The result is parallel algorithms with all of the features of sequential ones that deliver the promise of parallelism. My algorithms ...