## EWA Volume Splatting (2001)

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Citations: | 40 - 6 self |

### BibTeX

@MISC{Zwicker01ewavolume,

author = {Matthias Zwicker and Hanspeter Pfister and Jeroen van Baar and Markus Gross},

title = { EWA Volume Splatting},

year = {2001}

}

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### Abstract

In this paper we present a novel framework for direct volume rendering using a splatting approach based on elliptical Gaussian kernels. To avoid aliasing artifacts, we introduce the concept of a resampling filter combining a reconstruction with a low-pass kernel. Because of the similarity to Heckbert’s EWA (elliptical weighted average) filter for texture mapping we call our technique EWA volume splatting. It provides high image quality without aliasing artifacts or excessive blurring even with non-spherical kernels. Hence it is suitable for regular, rectilinear, and irregular volume data sets. Moreover, our framework introduces a novel approach to compute the footprint function. It facilitates efficient perspective projection of arbitrary elliptical kernels at very little additional cost. Finally, we show that EWA volume reconstruction kernels can be reduced to surface reconstruction kernels. This makes our splat primitive universal in reconstructing surface and volume data.

### Citations

726 | Display of surfaces from volume data
- LEVOY
- 1988
(Show Context)
Citation Context ...but refer to [13] or [20] for a thorough discussion. 3.2 Splatting Algorithms We review the low albedo approximation of the volume rendering equation [5, 12] as used for fast, direct volume rendering =-=[19, 6, 13, 8]-=-. The left part of Figure 2 illustrates the corresponding situation in 2D. Starting from this form of the rendering equation, we discuss several simplifying assumptions leading to the well known splat... |

466 |
Accelerated volume rendering and tomographic reconstruction using texture mapping hardware
- Cabral, Cam, et al.
- 1994
(Show Context)
Citation Context ...ge plane instead of parallel to an axis of the volume data. Additionally, they splat several slices of each reconstruction kernel separately. This technique is similar to slice-based volume rendering =-=[2, 1]-=- and does not suffer from popping artifacts. Mueller and Yagel [15] combine splatting with ray casting techniques to accelerate rendering with perspective projection. Laur and Hanrahan [7] describe a ... |

446 | Fast volume rendering using a shear-warp factorization of the viewing transformation
- Lacroute
- 1995
(Show Context)
Citation Context ...but refer to [13] or [20] for a thorough discussion. 3.2 Splatting Algorithms We review the low albedo approximation of the volume rendering equation [5, 12] as used for fast, direct volume rendering =-=[19, 6, 13, 8]-=-. The left part of Figure 2 illustrates the corresponding situation in 2D. Starting from this form of the rendering equation, we discuss several simplifying assumptions leading to the well known splat... |

443 | Footprint Evaluation for Volume Rendering
- Westover
- 1990
(Show Context)
Citation Context ... ideal volume rendering algorithm reconstructs a continuous function in 3D, transforms this 3D function into screen space, and then evaluates opacity integrals along line-of-sights. In 1989, Westover =-=[18, 19]-=- introduced splatting for interactive volume rendering, which approximates this procedure. Splatting algorithms interpret volume data as a set of particles that are absorbing and emitting light. Line ... |

245 | Optical models for direct volume rendering
- Max
- 1995
(Show Context)
Citation Context ...cation and shading in a forward mapping pipeline, but refer to [13] or [20] for a thorough discussion. 3.2 Splatting Algorithms We review the low albedo approximation of the volume rendering equation =-=[5, 12]-=- as used for fast, direct volume rendering [19, 6, 13, 8]. The left part of Figure 2 illustrates the corresponding situation in 2D. Starting from this form of the rendering equation, we discuss severa... |

238 |
Hierarchical splatting: A progressive refinement algorithm for volume rendering
- Laur, Hanrahan
(Show Context)
Citation Context ...endering [2, 1] and does not suffer from popping artifacts. Mueller and Yagel [15] combine splatting with ray casting techniques to accelerate rendering with perspective projection. Laur and Hanrahan =-=[7]-=- describe a hierarchical splatting algorithm enabling progressive refinement during rendering. Furthermore, Lippert [9] introduced a splatting algorithm that directly uses a wavelet representation of ... |

181 | Survey of texture mapping
- HECKBERT
- 1986
(Show Context)
Citation Context ...here wij denotes an element of W. This can be interpreted as a concatenation of a 2D to 3D with a 3D to 2D mapping, resulting in a compound 2D to 2D mapping similar as in conventional texture mapping =-=[3]-=-. We illustrate this process schematically in Figure 5 and more intuitively in Figure 6. The first stage is a parameterization of a 3D plane. It maps a circular 2D texture kernel onto a plane defined ... |

169 | Fundamentals of Texture Mapping and Image Warping
- Heckbert
- 1989
(Show Context)
Citation Context ...g algorithms integrating an elliptical Gaussian reconstruction kernel and a low-pass filter. Our derivation proceeds along similar lines as Heckbert’s elliptical weighted average (EWA) texture filte=-=r [4]-=-, therefore we call our algorithm EWA volume splatting. EWA volume rendering is attractive because it prevents aliasing artifacts in the output image while avoiding excessive blurring. Moreover, it wo... |

121 | Ewa splatting
- Zwicker, Pfister, et al.
- 2002
(Show Context)
Citation Context ... of Heckbert [4], who introduced EWA filtering to avoid aliasing of surface textures. We recently extended his framework to represent and render texture functions on irregularly pointsampled surfaces =-=[21]-=-. Section 5 will show the connection between EWA volume and surface splatting. 3 Preliminaries 3.1 The Volume Rendering Pipeline We distinguish two fundamental approaches to volume rendering: backward... |

111 |
The Visualization Toolkit
- Schroeder, Martin, et al.
- 1998
(Show Context)
Citation Context ...ace kernels. camera space 6 Implementation We implemented a volume rendering algorithm based on the EWA splatting equation. Our implementation is embedded in the VTK (visualization toolkit) framework =-=[16]-=-. We did not optimize our code for rendering speed. We use a sheet buffer to first accumulate splats from planes in the volume that are most parallel to the projection plane [19]. In a second step, th... |

100 | Interactive volume rendering - Westover - 1989 |

99 | tracing volume densities - Ray - 1984 |

87 | Direct volume rendering with shading via three-dimensional textures
- Gelder, Kim
- 1996
(Show Context)
Citation Context ...ge plane instead of parallel to an axis of the volume data. Additionally, they splat several slices of each reconstruction kernel separately. This technique is similar to slice-based volume rendering =-=[2, 1]-=- and does not suffer from popping artifacts. Mueller and Yagel [15] combine splatting with ray casting techniques to accelerate rendering with perspective projection. Laur and Hanrahan [7] describe a ... |

75 | Surface Splatting
- Zwicker, Pfister, et al.
- 2001
(Show Context)
Citation Context ... of Heckbert [4], who introduced EWA filtering to avoid aliasing of surface textures. We recently extended his framework to represent and render texture functions on irregularly pointsampled surfaces =-=[21]-=-. Section 5 will show the connection between EWA volume and surface splatting. 3 Preliminaries 3.1 The Volume Rendering Pipeline We distinguish two fundamental approaches to volume rendering: backward... |

48 | Fast wavelet based volume rendering by accumulation of transparent texture maps
- Lippert, Gross
- 1995
(Show Context)
Citation Context ...echniques to accelerate rendering with perspective projection. Laur and Hanrahan [7] describe a hierarchical splatting algorithm enabling progressive refinement during rendering. Furthermore, Lippert =-=[9] i-=-ntroduced a splatting algorithm that directly uses a wavelet representation of the volume data. Westover’s original framework does not deal with sampling rate changes due to perspective projections.... |

44 |
Splatting without the blur
- Mueller, Möller, et al.
- 1999
(Show Context)
Citation Context ...n in the following explanations. However, it can be easily incorporated in an implementation. Moreover, we do not discuss volume classification and shading in a forward mapping pipeline, but refer to =-=[13]-=- or [20] for a thorough discussion. 3.2 Splatting Algorithms We review the low albedo approximation of the volume rendering equation [5, 12] as used for fast, direct volume rendering [19, 6, 13, 8]. T... |

42 | Opacity-Weighted Color Interpolation For Volume Sampling - Wittenbrink, Malzbender, et al. - 1998 |

38 |
Eliminating popping artifacts in sheet buffer-based splatting
- Mueller, Crawfis
- 1998
(Show Context)
Citation Context ...r bleeding. Later, Westover [19] solved the problem using an axis-aligned sheet buffer. However, this technique is plagued by disturbing popping artifacts in animations. Recently, Mueller and Crawfis =-=[14]-=- proposed to align the sheet buffers parallel to the image plane instead of parallel to an axis of the volume data. Additionally, they splat several slices of each reconstruction kernel separately. Th... |

33 |
Fast Perspective Volume Rendering with Splatting by Utilizing a Ray-Driven Approach
- Mueller, Yagel
- 1996
(Show Context)
Citation Context ...lly, they splat several slices of each reconstruction kernel separately. This technique is similar to slice-based volume rendering [2, 1] and does not suffer from popping artifacts. Mueller and Yagel =-=[15]-=- combine splatting with ray casting techniques to accelerate rendering with perspective projection. Laur and Hanrahan [7] describe a hierarchical splatting algorithm enabling progressive refinement du... |

27 |
Splatting of non rectilinear volumes through stochastic resampling
- Mao
- 1996
(Show Context)
Citation Context ...s such as splotches occur in the image. For rectilinear grids, Westover [19] proposes using elliptical footprints that are warped back to a circular footprint. To render curvilinear grids, Mao et al. =-=[10]-=- usesstochastic Poisson resampling to generate a set of new points whose kernels are spheres or ellipsoids. They compute the elliptical footprints very similar to Westover [19]. As pointed out in Sect... |

20 |
Splatting of curvilinear volumes
- Mao, Hong, et al.
- 1995
(Show Context)
Citation Context ... elements contain the squared distances between voxels along each coordinate axis. Curvilinear and irregular grids have to be resampled to a more regular structure in general. For example, Mao et al. =-=[11]-=- describe a stochastic sampling approach with a method to compute the variance matrices for curvilinear volumes. We denote camera coordinates by a vector u =(u0,u1,u2) T . Object coordinates are trans... |

14 | An Anti-Aliasing Technique for Splatting
- Swan, Mueller, et al.
- 1997
(Show Context)
Citation Context ...pling rate changes due to perspective projections. Aliasing artifacts may occur in areas of the volume where the sampling rate of diverging rays falls below the volume grid sampling rate. Swan et al. =-=[17]-=- use a distance-dependent stretch of the footprints to make them act as low-pass filters. This antialiasing method is closely related to EWA volume splatting, and we will discuss it further in Section... |

13 |
An anti-aliasing technique for splatting
- Swan, Mueller, et al.
- 1997
(Show Context)
Citation Context ...pling rate changes due to perspective projections. Aliasing artifacts may occur in areas of the volume where the sampling rate of diverging rays falls below the volume grid sampling rate. Swan et al. =-=[17]-=- use a distance-dependent stretch of the footprints to make them act as low-pass filters. This antialiasing method is closely related to EWA volume splatting, and we will discuss it further in Section... |