## Compression Domain Rendering of Time-Resolved Volume Data

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Venue: | PROCEEDINGS OF VISUALIZATION 95, ATLANTA, GA |

Citations: | 36 - 3 self |

### BibTeX

@INPROCEEDINGS{Westermann_compressiondomain,

author = {Rüdiger Westermann},

title = {Compression Domain Rendering of Time-Resolved Volume Data},

booktitle = {PROCEEDINGS OF VISUALIZATION 95, ATLANTA, GA},

year = {},

pages = {168--175},

publisher = {}

}

### Years of Citing Articles

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### Abstract

An important challenge in the visualization of three dimensional volume data is the e cient processing and rendering of time-resolved sequences. Only the use of compression techniques, which allow the reconstruction of the original domain from the compressed onelocally, makes it possible to evaluate these sequences in their entirety. In the following paper a new approach for the extraction and visualization of so called time-features from within time-resolved volume data will be presented. Based on the asymptotic decay of multiscale representations of spatially localized time evolutions of the data, singular points can be discriminated. Also the corresponding Lipschitz exponents, which describe the signals local regularity, can be determined, and can be taken as a measure of the variation in time. The compression ratio and the comprehension of the underlying signal will be improved, if we restore the extracted regions rst, which contain the most important information.

### Citations

2517 | A theory of multiresolution signal decomposition: The wavelet representation
- Mallat
- 1989
(Show Context)
Citation Context ...Many researchers have investigated in more detail the basic concept and theory of wavelet transforms and multiresolution analysis over the past few years, and some introductions can be found in [8][1]=-=[12]-=- and [17]. Basically, a wavelet decomposition is built up from scales and dilates of an infinite energy, self-similiar basis function \Psi(x) with \Psi j k (x) = p 2 j \Psi(2 j x \Gamma k) for k 2 Z: ... |

1822 | Lectures on Wavelets - Daubechies, \Ten - 1992 |

749 | Display of surfaces from volume data
- Levoy
- 1988
(Show Context)
Citation Context ...several methods have been developed to visualize static three dimensional volume data sets. Most of the proposed methods try to approximate more or less accurately the volume rendering integral [4][9]=-=[11]-=-: I(to ; t1 ) = Z t 1 t=t 0 q(t)e \Gamma R t s=t 0 oe(s)ds dt (1) where oe(s) defines the attenuation function, q(t) is the volume source term, and t0 and t1 are the start and end points on the view r... |

450 | Footprint Evaluation for Volume Rendering
- Westover
- 1990
(Show Context)
Citation Context ...g a ray, which is scaled by a material dependent attenuation factor to get the final intensity. Basically, all methods can be classified into fast object space driven back-to-front projection methods =-=[20]-=-[21], and in general slower but more accurate image space driven methods. The latter technique resamples the volume along the ray of sight, and is closely related to general integration rules, which e... |

412 | Singularity Detection and Processing with Wavelets
- Mallat, Hwang
- 1992
(Show Context)
Citation Context ...s, with jx \Gamma x0 jss, (2) implies a O(s ff ) decay, whereas for other points the decay is controlled by their distance to x0 . For practical computations of the Lipschitz exponents, Mallat et al. =-=[13]-=- proposed an efficient method, which is based on the observation, that the local maxima of the wavelet transform on every scale define scalespacescurves. Connecting those maxima which proceed from a c... |

393 | Volume Rendering
- Drebin, Carpenter, et al.
(Show Context)
Citation Context ...years several methods have been developed to visualize static three dimensional volume data sets. Most of the proposed methods try to approximate more or less accurately the volume rendering integral =-=[4]-=-[9][11]: I(to ; t1 ) = Z t 1 t=t 0 q(t)e \Gamma R t s=t 0 oe(s)ds dt (1) where oe(s) defines the attenuation function, q(t) is the volume source term, and t0 and t1 are the start and end points on the... |

219 | Ray tracing volume densities
- Kajiya, Herzen
- 1984
(Show Context)
Citation Context ...rs several methods have been developed to visualize static three dimensional volume data sets. Most of the proposed methods try to approximate more or less accurately the volume rendering integral [4]=-=[9]-=-[11]: I(to ; t1 ) = Z t 1 t=t 0 q(t)e \Gamma R t s=t 0 oe(s)ds dt (1) where oe(s) defines the attenuation function, q(t) is the volume source term, and t0 and t1 are the start and end points on the vi... |

217 |
Wavelets and dilation equations: A brief introduction
- Strang
- 1989
(Show Context)
Citation Context ...archers have investigated in more detail the basic concept and theory of wavelet transforms and multiresolution analysis over the past few years, and some introductions can be found in [8][1][12] and =-=[17]-=-. Basically, a wavelet decomposition is built up from scales and dilates of an infinite energy, self-similiar basis function \Psi(x) with \Psi j k (x) = p 2 j \Psi(2 j x \Gamma k) for k 2 Z: At each s... |

120 | An Overview of Wavelet Based Multiresolution Analyses
- Jawerth, Sweldens
- 1994
(Show Context)
Citation Context ...ring. Many researchers have investigated in more detail the basic concept and theory of wavelet transforms and multiresolution analysis over the past few years, and some introductions can be found in =-=[8]-=-[1][12] and [17]. Basically, a wavelet decomposition is built up from scales and dilates of an infinite energy, self-similiar basis function \Psi(x) with \Psi j k (x) = p 2 j \Psi(2 j x \Gamma k) for ... |

111 |
A Coherent Projection Approach for Direct Volume Rendering
- Wilhelms, Geldern
- 1991
(Show Context)
Citation Context ...ray, which is scaled by a material dependent attenuation factor to get the final intensity. Basically, all methods can be classified into fast object space driven back-to-front projection methods [20]=-=[21]-=-, and in general slower but more accurate image space driven methods. The latter technique resamples the volume along the ray of sight, and is closely related to general integration rules, which evalu... |

105 |
Wavelets: A Tutorial in Theory and Applications
- Chui
- 1998
(Show Context)
Citation Context ...g. Many researchers have investigated in more detail the basic concept and theory of wavelet transforms and multiresolution analysis over the past few years, and some introductions can be found in [8]=-=[1]-=-[12] and [17]. Basically, a wavelet decomposition is built up from scales and dilates of an infinite energy, self-similiar basis function \Psi(x) with \Psi j k (x) = p 2 j \Psi(2 j x \Gamma k) for k 2... |

68 | A multiresolution framework for volume rendering
- Westermann
- 1994
(Show Context)
Citation Context ... the rendering integral on the compressed domain. One possible solution is to evaluate the volume rendering integral on multiresolution representations of the original three dimensional signal [6][14]=-=[19]-=-. Due to the sparse representation of projections into cascades of difference spaces, impressive compression ratios can be achieved. Furthermore, the rendering process can be performed on the compress... |

53 |
Hypertexture
- PERLIN, HOFFERT
- 1989
(Show Context)
Citation Context ...p from 64 128 3 volume data sets, was generated from a time varying stochastic fractal, simulating three dimensional cloud structures. The generation process is based on Perlins hypertexture function =-=[16]-=-, adding multiple scaled and dilated copies of a random noise function, to obtain the typical 1=f spectrum of stochastical fractals. Based on Taylors frozen turbulence hypothesis [5], the variations o... |

43 |
Approximation and rendering of volume data using wavelet transforms
- Muraki
- 1992
(Show Context)
Citation Context ...n of the rendering integral on the compressed domain. One possible solution is to evaluate the volume rendering integral on multiresolution representations of the original three dimensional signal [6]=-=[14]-=-[19]. Due to the sparse representation of projections into cascades of difference spaces, impressive compression ratios can be achieved. Furthermore, the rendering process can be performed on the comp... |

25 |
The application of transport theory to visualization of 3-D scalar data fields
- Krueger
- 1991
(Show Context)
Citation Context ... attenuation function, q(t) is the volume source term, and t0 and t1 are the start and end points on the view ray. This reduced formulation of the more general and physically based transport equation =-=[10]-=-, describes the summation of the light along a ray, which is scaled by a material dependent attenuation factor to get the final intensity. Basically, all methods can be classified into fast object spa... |

20 |
A new Method to Approximate the Volume Rendering Equation Using Wavelets and Piecewise Polynomials
- Gross, Lippert, et al.
- 1995
(Show Context)
Citation Context ...tion of the rendering integral on the compressed domain. One possible solution is to evaluate the volume rendering integral on multiresolution representations of the original three dimensional signal =-=[6]-=-[14][19]. Due to the sparse representation of projections into cascades of difference spaces, impressive compression ratios can be achieved. Furthermore, the rendering process can be performed on the ... |

14 | Multiscale 3D Edge Representation of Volume Data by aDOGWavelet - Muraki - 1994 |

11 |
Polynomial splines and wavelets—a signal processing perspective
- Unser, Aldroubi
(Show Context)
Citation Context ...This choice was motivated by the regularity property of polynomial splines, which are indeed the interpolants which oscillate the least among all other interpolants for a certain degree. Unser et al. =-=[18]-=- proposed a general framework for the generation of polynomial splines of certain degree and the corresponding filter sequences for the wavelet expansion. This allows us to increase the number of vani... |

7 | Wavelet Probing for Compression Based Segmentation
- Deng, Jawerth, et al.
- 1993
(Show Context)
Citation Context ... error tolerance for the reconstruction process, which allows us to eliminate a larger number of coefficients. This method is closely related to the wavelet probing algorithm, proposed by Deng et al. =-=[3]-=-. They split up the signal into smooth segments that can be compressed separately, based on wavelets which are defined over an interval. Compared to our approach, their method also prevents discontinu... |

1 |
Fundamentals and Applications
- Frost, Moulden
- 1977
(Show Context)
Citation Context ...ture function [16], adding multiple scaled and dilated copies of a random noise function, to obtain the typical 1=f fi spectrum of stochastical fractals. Based on Taylors frozen turbulence hypothesis =-=[5]-=-, the variations of the fractal in time are equivalent to its spatial behaviours and properties. This observation allows the generation of each time step as a snapshot of a four dimensional stochastic... |

1 |
Exposants de Holder en des points donnes et coefficients d'onolettes
- Jaffarth
- 1989
(Show Context)
Citation Context ...distinction between these parts by considering their local regularity. The question that remains to be answered is how to detect the singularities and how to compute the Lipschitz exponents. Jaffarth =-=[7]-=- proved a general theorem, which states that the singularities of a signal can be detected from its multiscale representation, and that the local Lipschitz regularity can be computed from the decay of... |

1 |
Tutorial in Theory and Applications
- Wavelets-A
- 1992
(Show Context)
Citation Context ...g. Many researchers have investigated in more detail the basic concept and theory of wavelet transforms and multiresolution analysis over the past few years, and some introductions can be found in [8]=-=[1]-=-[12] and [17]. Basically, awavelet decomposition is built up from scales and dilates of an in nite energy, self-similiar basis function (x) with j (x) =p2 k j (2 j x ; k) for k 2 Z: At eachscale 2 j ,... |

1 |
Exposants de Holder en des points donnes et coe cients d'onolettes
- arth
- 1989
(Show Context)
Citation Context ... distinction between these parts by considering their local regularity. The question that remains to be answered is how to detect the singularities and how to compute the Lipschitz exponents. Ja arth =-=[7]-=- proved a general theorem, which states that the singularities of a signal can be detected from its multiscale representation, and that the local Lipschitz regularity can be computed from the decay of... |