## Using distance maps for accurate surface representation in sampled volumes (1998)

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Venue: | In IEEE Vol. Vis |

Citations: | 59 - 3 self |

### BibTeX

@INPROCEEDINGS{Gibson98usingdistance,

author = {Sarah F. F. Gibson},

title = {Using distance maps for accurate surface representation in sampled volumes},

booktitle = {In IEEE Vol. Vis},

year = {1998},

pages = {23--30}

}

### Years of Citing Articles

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### Abstract

Figure 1: Shaded, volume rendered spheres stored with two values per voxel: a value indicating the distance to the closest surface point; and a binary intensity value. The sphere in a) has radius 30 voxels and is stored in an array of size. The spheres in b), c), and d) have radii 3 voxels, 2 voxels and 1.5 voxels respectively and are stored in arrays of size. The surface normal used in surface shading was calculated using a 6-point central difference operator on the distance values. Remarkably smooth shading can be achieved for these low resolution data volumes because the function of the distance-to-closest surface varies smoothly across surfaces. (See color plate.) High quality rendering and physics-based modeling in volume graphics have been limited because intensity-based volumetric data do not represent surfaces well. High spatial frequencies due to abrupt intensity changes at object surfaces result in jagged or terraced surfaces in rendered images. The use of a distance-to-closestsurface function to encode object surfaces is proposed. This function varies smoothly across surfaces and hence can be accurately reconstructed from sampled data. The zero-value iso-surface of the distance map yields the object surface and the derivative of the distance map yields the surface normal. Examples of rendered images are presented along with a new method for calculating distance maps from sampled binary data.

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Citation Context ...pace [35, 27]. Schroeder et al. [26] used distance maps to generate a swept volume for a moving polygonal model and then constructed a polygonal surface model of the swept volume using Marching Cubes =-=[16]-=-. In robotics, discrete distance maps are used for path planning by generating potential fields around obstacles that decrease with the square of the distance from the obstacles (e.g. [14, 10]). Yagel... |

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Citation Context ...mber of image-space and object-space shading methods that have been used for shading volumetric objects [12]. In this paper, we assume the use of a shading model, such as the Phong illumination model =-=[4]-=-, which requires an estimate of the object surface normal for shading calculations. This paper focuses on volumetric data that originates as analytic functions, polygonal models, or binary samples. In... |

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Citation Context ... and 2) due to the nature of discrete sampling, volumetric data sets do not represent arbitrarily oriented surfaces well. While hardware and software developments have addressed the first point (e.g. =-=[15, 8, 24, 23]-=-), the inability to represent surfaces remains an important limitation of volume graphics. In computer graphics, an accurate representation of surfaces is important for a number of reasons. First, the... |

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Citation Context ...odels that may be problematic in die casting. In image processing, a technique known as watershed segmentation uses a map of distances from edges or features to help separate adjoining features (e.g. =-=[25]-=-). This paper is distinct from these approaches. It uses distance maps to explicitly encode surfaces into sampled volumetric data for high quality shading in volume rendering. 3 Volume Rendering from ... |

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Citation Context ...torus), distance maps for polygonal objects (e.g. cube and tetrahedron) were generated from the mathematical description of polygonal faces using an method adapted from collision detection algorithms =-=[19]-=-, and distance maps for binary data were generated from an algorithm described in Section 5. For simplicity, these examples use binary object intensities, with a value of 255 inside the object and a v... |

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Citation Context ... can be critical in medical applications. There have been a number of studies of filters for image reconstruction and gradient estimation. Most of these are based on frequency analysis of the filters =-=[3, 18, 2]-=- and all of them apply to grey-scale data. Moller et al. [20] analyzed interpolation and gradient estimation filters in the spatial domain. By expressing the filtered image intensity using Taylor seri... |

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Citation Context ...filters [28] which approximate the surface normal from the state of local neighbors. One approach that has produced good quality images is to blur the binary image by filtering with a low pass filter =-=[30, 31, 1, 21]-=-. This method creates a grey-scale image from the binary data where surface normals are well represented by the gradient of the smoothed image. When the filter value decreases monotonically with dista... |

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Citation Context ...r, as discussed in Section 5, there are times when a binary segmentation of the grey-scale data is preferable for surface shading. Some existing methods store surface normals of known analytic models =-=[32]-=- or polygonal models [17] at each data point. These sampled surface normals are used to reconstruct normals for samples between data elements during rendering. However, this method requires the storag... |

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Citation Context ...distance. This linearity allows us to use a simple trilinear interpolation function and a 6-point central difference filter to accurately reconstruct the distance map and its derivative near surfaces =-=[20]-=-. Hence, the distance map provides a way to encode object surfaces into sampled, volumetric data so that they can be accurately reconstructed with relatively low-cost reconstruction filters. This pape... |

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Citation Context ... can be critical in medical applications. There have been a number of studies of filters for image reconstruction and gradient estimation. Most of these are based on frequency analysis of the filters =-=[3, 18, 2]-=- and all of them apply to grey-scale data. Moller et al. [20] analyzed interpolation and gradient estimation filters in the spatial domain. By expressing the filtered image intensity using Taylor seri... |

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Citation Context ...his is not true, (for example in binary sampled data), rendered images have characteristic terraced or jagged surfaces. This image aliasing can be reduced by low-pass filtering the sampled data (e.g. =-=[30]-=-) but such filters blur surfaces indiscriminately, eliminating detail than may be important. In this paper, surfaces are represented with a function that varies smoothly across surfaces. Low spatial f... |

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Citation Context ...g, image processing, and robotics that have used discrete distance maps. Distance maps have been used to accelerate volume rendering by reducing the sampling of empty space [35, 27]. Schroeder et al. =-=[26]-=- used distance maps to generate a swept volume for a moving polygonal model and then constructed a polygonal surface model of the swept volume using Marching Cubes [16]. In robotics, discrete distance... |

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Citation Context ...filters [28] which approximate the surface normal from the state of local neighbors. One approach that has produced good quality images is to blur the binary image by filtering with a low pass filter =-=[30, 31, 1, 21]-=-. This method creates a grey-scale image from the binary data where surface normals are well represented by the gradient of the smoothed image. When the filter value decreases monotonically with dista... |

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Citation Context ...hods produce artifacts in shaded surfaces which are especially significant when the voxel data is not isometric (i.e. when the data is sampled at different resolutions along the three major axes). In =-=[7]-=-, a new method for generating a smooth surface representation from binary sampled data is presented. This method, Constrained Elastic Surface Nets, is described here briefly. Surface Nets produce surf... |

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Citation Context ...tions in rendering, modeling, image processing, and robotics that have used discrete distance maps. Distance maps have been used to accelerate volume rendering by reducing the sampling of empty space =-=[35, 27]-=-. Schroeder et al. [26] used distance maps to generate a swept volume for a moving polygonal model and then constructed a polygonal surface model of the swept volume using Marching Cubes [16]. In robo... |

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Citation Context ...ding from a distance map representation. The size of the brain data set is 137x146x119. The size of the knee data is 304x300x91 (inplane spacing 0.27 mm, between-plane spacing 1.0 mm). Both the brain =-=[13]-=- and knee data originated as binary segmented MRI. The distance maps were created from a constrained elastic surface net that was stretched over the surface of the binary data. (See color plate.)s5.1 ... |

33 |
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Citation Context ...ching Cubes [16]. In robotics, discrete distance maps are used for path planning by generating potential fields around obstacles that decrease with the square of the distance from the obstacles (e.g. =-=[14, 10]-=-). Yagel et al. [34] use discrete distance maps for visualizing thick regions of models that may be problematic in die casting. In image processing, a technique known as watershed segmentation uses a ... |

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Citation Context ... and 2) due to the nature of discrete sampling, volumetric data sets do not represent arbitrarily oriented surfaces well. While hardware and software developments have addressed the first point (e.g. =-=[15, 8, 24, 23]-=-), the inability to represent surfaces remains an important limitation of volume graphics. In computer graphics, an accurate representation of surfaces is important for a number of reasons. First, the... |

19 |
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Citation Context ...he distance map provides the location of the surface. been discarded. Shading from grey-scale data can produce good quality images when the data is band limited and appropriate filters are used (e.g. =-=[9]-=-) so that the use of a distance map for surface normal calculation is not necessary. However, as discussed in Section 5, there are times when a binary segmentation of the grey-scale data is preferable... |

15 |
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Citation Context ...tions in rendering, modeling, image processing, and robotics that have used discrete distance maps. Distance maps have been used to accelerate volume rendering by reducing the sampling of empty space =-=[35, 27]-=-. Schroeder et al. [26] used distance maps to generate a swept volume for a moving polygonal model and then constructed a polygonal surface model of the swept volume using Marching Cubes [16]. In robo... |

11 | Normal estimation in 3d discrete space
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Citation Context ... abrupt change in data values at object surfaces, resulting in reconstruction artifacts due to undersampling. There are a number of methods that have been used to shade binary volumes (see reviews in =-=[12, 33]-=-). These include shading the six faces of each non-empty element, producing a blocky appearance, and various methods using look-up tables [17], smoothing filters, and surface estimation filters [28] w... |

9 |
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Citation Context ...filters [28] which approximate the surface normal from the state of local neighbors. One approach that has produced good quality images is to blur the binary image by filtering with a low pass filter =-=[30, 31, 1, 21]-=-. This method creates a grey-scale image from the binary data where surface normals are well represented by the gradient of the smoothed image. When the filter value decreases monotonically with dista... |

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Citation Context ...2, 33]). These include shading the six faces of each non-empty element, producing a blocky appearance, and various methods using look-up tables [17], smoothing filters, and surface estimation filters =-=[28]-=- which approximate the surface normal from the state of local neighbors. One approach that has produced good quality images is to blur the binary image by filtering with a low pass filter [30, 31, 1, ... |

8 |
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Citation Context ... and 2) due to the nature of discrete sampling, volumetric data sets do not represent arbitrarily oriented surfaces well. While hardware and software developments have addressed the first point (e.g. =-=[15, 8, 24, 23]-=-), the inability to represent surfaces remains an important limitation of volume graphics. In computer graphics, an accurate representation of surfaces is important for a number of reasons. First, the... |

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Citation Context ...t methods. In addition, while operations such as object cutting, slicing, or tearing are challenging for surface-based models, they can be performed relatively easily with a volumetric representation =-=[5]-=-. In applications such as surgical simulation, tissue complexity and the need to be able to model volume deformation and object cutting and tearing make volumetric models very attractive. While signif... |

2 |
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Citation Context ...l, Boston MA). In binary-sampled data, exact knowledge of the underlying object surface is missing and hence distance maps must be approximated from the binary data rather than from the true surface. =-=[6]-=- presents experimental results for 5 methods that estimate the distance map from binary sampled data. These include methods that estimate distances directly from the binary values (such as chessboard ... |

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Citation Context ...n 5, there are times when a binary segmentation of the grey-scale data is preferable for surface shading. Some existing methods store surface normals of known analytic models [32] or polygonal models =-=[17]-=- at each data point. These sampled surface normals are used to reconstruct normals for samples between data elements during rendering. However, this method requires the storage of 3 floating point val... |

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Citation Context ...1) using a higher order interpolation and gradient estimation filters (such as filters that reconstruct spherical or cylindrical fields) and 2) using the optional gradient estimator from Tiede et al. =-=[29]-=-, which estimates the surface normals of thin structures from an optimal subset of the 6 neighbors of the sample point. 5 Calculating Distances from Binary Data One of the most common sources of binar... |

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Citation Context ... can be critical in medical applications. There have been a number of studies of filters for image reconstruction and gradient estimation. Most of these are based on frequency analysis of the filters =-=[3, 18, 2]-=- and all of them apply to grey-scale data. Moller et al. [20] analyzed interpolation and gradient estimation filters in the spatial domain. By expressing the filtered image intensity using Taylor seri... |

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Citation Context ...ching Cubes [16]. In robotics, discrete distance maps are used for path planning by generating potential fields around obstacles that decrease with the square of the distance from the obstacles (e.g. =-=[14, 10]-=-). Yagel et al. [34] use discrete distance maps for visualizing thick regions of models that may be problematic in die casting. In image processing, a technique known as watershed segmentation uses a ... |

1 |
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Citation Context ...d texture and can have a strong effect on the visual realism of a rendered scene. There are a number of image-space and object-space shading methods that have been used for shading volumetric objects =-=[12]-=-. In this paper, we assume the use of a shading model, such as the Phong illumination model [4], which requires an estimate of the object surface normal for shading calculations. This paper focuses on... |

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Citation Context ...otics, discrete distance maps are used for path planning by generating potential fields around obstacles that decrease with the square of the distance from the obstacles (e.g. [14, 10]). Yagel et al. =-=[34]-=- use discrete distance maps for visualizing thick regions of models that may be problematic in die casting. In image processing, a technique known as watershed segmentation uses a map of distances fro... |