## Tensor Splats: Visualising Tensor Fields by Texture Mapped Volume Rendering (2003)

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Venue: | In Sixth International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI’03 |

Citations: | 10 - 0 self |

### BibTeX

@INPROCEEDINGS{Bhalerao03tensorsplats:,

author = {Abhir Bhalerao and Carl-fredrik Westin},

title = {Tensor Splats: Visualising Tensor Fields by Texture Mapped Volume Rendering},

booktitle = {In Sixth International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI’03},

year = {2003},

pages = {294--901},

publisher = {Springer}

}

### Years of Citing Articles

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### Abstract

We describe a new method for visualising tensor fields using a textured mapped volume rendering approach, tensor-splatting. We use an image order method to calculate the 2D Gaussian splats or footprints of the projected 3D Gaussians at an arbitrary number of standard deviations from the centroid. These footprints are then mapped and composited front to back to the view plane by texture mapping within the framebu#er pipeline to e#ect a volume rendering. One of the features of tensor-splatting is that opacity transfer control, which can be used to emphasise the tensor shape, can be achieved trivially by hardware acceleration because it requires only remapping the opacity and colour of the composited texture splats. We illustrate our method on MR di#usion weighted tensor data.

### Citations

149 | Interactive volume rendering using multidimensional transfer functions and direct manipulation widgets
- Kniss, Kindlmann, et al.
- 2001
(Show Context)
Citation Context ...rent (or opaque). With proper control of the opacity transfer function, direct rendering thus enables data exploration without the need to making firm assumptions about the boundaries between objects =-=[4]-=-. Direct rendering of vector and tensor fields is an important topic in visualisation and graphics because of the numerous sources of data which are either inherently vector valued (flow and velocity ... |

75 |
Inferring microstructural features and the physiological state of tissues from diffusion-weighted images
- Basser
- 1995
(Show Context)
Citation Context ...urement of local differential properties of the data [3]. An example of the former is a diffusion weighted magnetic resonance image (DWI) which elucidates the fibrous white matter tracks in the brain =-=[1]-=-. An example of the latter is the tensor formed by the principal components of a Hessian operator on an image which indicate the local shape of the image intensity [5]. In both cases, graphically show... |

62 | Strategies for direct volume rendering of diffusion tensor fields
- Kindlmann, Weinstein, et al.
(Show Context)
Citation Context ...ow and velocity measurements, multispectral data), but also because of derived vector and tensor fields when the tensor is a derived frameless measurement of local differential properties of the data =-=[3]-=-. An example of the former is a diffusion weighted magnetic resonance image (DWI) which elucidates the fibrous white matter tracks in the brain [1]. An example of the latter is the tensor formed by th... |

54 | Tissue classification based on 3D local intensity structures for volume rendering
- Sato, Westin, et al.
- 1997
(Show Context)
Citation Context ...white matter tracks in the brain [1]. An example of the latter is the tensor formed by the principal components of a Hessian operator on an image which indicate the local shape of the image intensity =-=[5]-=-. In both cases, graphically showing the shape of the tensor i.e., the direction and extent of the principal axes is vital. Furthermore, since it is often the case the goal is to determine paths or tr... |

45 | Image processing for diffusion tensor magnetic resonance imaging
- Westin, Maier, et al.
- 1999
(Show Context)
Citation Context ...endering (excluding any regularisation or denoising step), whether the geometrical shape of the tensor is apparent and to what degree the rank of the tensor can be used to affect the opacity transfer =-=[8]-=-. Two main approaches to producing a volume rendering are: ray-casting where the colour at each viewplane pixel is computed by following a ray of light from the eye, through the viewplane and intersec... |

40 | EWA Volume Splatting
- Zwicker, Pfister, et al.
- 2001
(Show Context)
Citation Context ...eas to produce a direct volume rendering method of tensor fields, what we have named Tensor Splatting. It uses 2D texture mapping of Gaussian footprint functions (following the work of Zwicker et. al =-=[9]-=-), but whose shape and orientation on the viewplane is controlled by samples from the tensor field, hence tensor-splat. We describe a first-order approximation of the method admitting some distortion ... |

12 | Merging and Transformation of Raster Images for Cartoon Animation
- Wallace
- 1981
(Show Context)
Citation Context ... (digital compositing), known as the over operation. The associative property of this operation allows successive voxels along the ray to be independently composited enabling parallel implementations =-=[7]-=-. Or, as used here, we are free to independently composite parts of the ray integral and leave the final composite to the hardware accelerated blending operation. 2. The integral is numerically evalua... |

10 | Tensor field visualisation using adaptive filtering of noise fields combined with glyph rendering
- Sigfridsson, Ebbers, et al.
- 2002
(Show Context)
Citation Context ...E. Ellis and T.M. Peters (Eds.): MICCAI 2003, LNCS 2879, pp. 294–302, 2003. c○ Springer-Verlag Berlin Heidelberg 2003sTensor Splats: Visualising Tensor Fields 295 into the rendering is important a=-=lso [6]. -=-In DWI, the tensor’s rank indicates the relative anisotropy of the diffusion and hence the likely path of any fibre, and analogously, in the case of derived structure tensors, the rank describes whe... |

4 | A Fourier Approach to 3D Local Feature Estimation from Volume Data
- Bhalerao, Wilson
- 2001
(Show Context)
Citation Context ...ping widget to control the colour and opacity transfer function according to the anisotropy indices, cp,cl,cs, of a tensor field derived from a synthetic data set using block-based Fourier transform (=-=[2]-=-). A scattergram of points on the control indicate the clustering of shapes in the tensor-field. The vertices of the triangle represent the maximum index values cp = cl = cp = 1. The user can position... |