Reconstruction Issues in Volume Visualization

Theußl, Thomas; Möller, Torsten B.; Hladůvka, Jiřı́; Gröller, M. Eduard

doi:10.1007/978-1-4615-1177-9_8

Cited by 8 publications

(8 citation statements)

References 19 publications

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“…The literature shows that designing an appropriate model for the visualization of volume data is always a compromise between computational efficiency and visual quality, where the most successful methods are based on local reconstructions. For further information on the field, we refer the interested reader to the recent books [20], [21], the surveys [22]- [26] and the references therein.…”

Section: A Background and Related Workmentioning

confidence: 99%

Reconstruction of volume data with quadratic super splines

Rössl

Seidel

Zeilfeider³

et al. 2004

IEEE Trans. Visual. Comput. Graphics

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Abstract-We propose a new approach to reconstruct nondiscrete models from gridded volume samples. As a model, we use quadratic trivariate super splines on a uniform tetrahedral partition. We discuss the smoothness and approximation properties of our model and compare to alternative piecewise polynomial constructions. We observe as a non-standard phenomenon that the derivatives of our splines yield optimal approximation order for smooth data, while the theoretical error of the values is nearly optimal due to the averaging rules. Our approach enables efficient reconstruction and visualization of the data. As the piecewise polynomials are of the lowest possible total degree two, we can efficiently determine exact ray intersections with an iso-surface for ray-casting. Moreover, the optimal approximation properties of the derivatives allow to simply sample the necessary gradients directly from the polynomial pieces of the splines. Our results confirm the efficiency of the quasi-interpolating method and demonstrate high visual quality for rendered isosurfaces.

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Section: A Background and Related Workmentioning

confidence: 99%

Reconstruction of volume data with quadratic super splines

Rössl

Seidel

Zeilfeider³

et al. 2004

IEEE Trans. Visual. Comput. Graphics

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“…The increasing interest in these techniques in the last decade (see [1,2,3,5,9,17,21,32,35], and the references therein) mainly comes from the fact that this is a key technology for many fields of application. To name two of them, we mention the particular, but wide, areas of medical applications and industrial quality control, where one is interested in efficient methods for high-quality visualization.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, in the standard approach the models involve no smoothness conditions and therefore the evaluation of the necessary gradient field requires a separate model. This is one of the reasons why different models of the discrete data have been proposed [4,15,18,19,20,32,33] as tools for the visualization with improved visual quality. Here, the models are often local approximations with tensor-product splines of higher degrees (for instance triquadratic and tricubic splines) involving smoothness conditions.…”

Section: Introductionmentioning

confidence: 99%

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Fast Visualization by Shear-Warp on Quadratic Super-Spline Models Using Wavelet Data Decompositions

Schlosser

Hesser

Zeilfelder

et al.

IEEE Visualization 2005 - (VIS'05)

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We develop the first approach for interactive volume visualization based on a sophisticated rendering method of shear-warp type, wavelet data encoding techniques, and a trivariate spline model, which has been introduced [24] recently. As a first step of our algorithm, we apply standard wavelet expansions [6,31] to represent and decimate the given gridded three-dimensional data. Based on this data encoding, we give a sophisticated version of the shearwarp based volume rendering method [13]. Our new algorithm visits each voxel only once taking advantage of the particular data organization of octrees. In addition, the hierarchies of the data guide the local (re)construction of the quadratic super-spline models, which we apply as a pure visualization tool. The low total degree of the polynomial pieces allows to numerically approximate the volume rendering integral efficiently. Since the coefficients of the splines are almost immediately available from the given data, Bernstein-Bézier techniques can be fully employed in our algorithms. In this way, we demonstrate that these models can be successfully applied to full volume rendering of hierarchically organized data. Our computational results show that (even when hierarchical approximations are used) the new approach leads to almost artifact-free visualizations of high quality for complicated and noise-contaminated volume data sets, while the computational effort is considerable low, i.e. our current implementation yields 1-2 frames per second for parallel perspective rendering a 256 3 volume data set (using simple opacity transfer functions) in a 512 2 view-

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“…Interactive volume rendering is devoted to techniques for the visualization of volumetric data sets obtained from computer tomography (CT), magnetic resonance imaging (MRI) or 3D ultrasound. The increasing interest in these techniques in the last decade (see [1,2,3,5,9,17,21,32,35], and the references therein) mainly comes from the fact that this is a key technology for many fields of application. To name two of them, we mention the particular, but wide, areas of medical applications and industrial quality control, where one is interested in efficient methods for high-quality visualization.…”

Section: Introductionmentioning

confidence: 99%