## BLIC: bi-level isosurface compression (2002)

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Venue: | In Proc. of IEEE Visualization |

Citations: | 12 - 0 self |

### BibTeX

@INPROCEEDINGS{Taubin02blic:bi-level,

author = {Gabriel Taubin},

title = {BLIC: bi-level isosurface compression},

booktitle = {In Proc. of IEEE Visualization},

year = {2002},

pages = {451--458},

publisher = {IEEE Computer Society}

}

### OpenURL

### Abstract

294,018 vertices, compressed to 0.7437 bits per face. C: UNC CThead data set, level 1160, 312,488 faces, 312,287 vertices, compressed to 0.8081 bits per face. In this paper we introduce a new and simple algorithm to compress isosurface data. This is the data extracted by isosurface algorithms from scalar functions defined on volume grids, and used to generate polygon meshes or alternative representations. In this algorithm the mesh connectivity and a substantial proportion of the geometric information are encoded to a fraction of a bit per Marching Cubes vertex with a context based arithmetic coder closely related to the JBIG binary image compression standard. The remaining optional geometric information that specifies the location of each Marching Cubes vertex more precisely along its supporting intersecting grid edge, is efficiently encoded in scan-order with the same mechanism. Vertex normals can optionally be computed as normalized gradient vectors by the encoder and included in the bitstream after quantization and entropy encoding, or computed by the decoder in a postprocessing smoothing step. These choices are determined by trade-offs associated with an in-core vs. out-of-core decoder structure. The main features of our algorithm are its extreme simplicity and high compression rates.

### Citations

2074 | Marching cubes: A high resolution 3d surface construction algorithm
- Lorensen, Cline
- 1987
(Show Context)
Citation Context ...construct polygon mesh approximations to level sets of scalar functions specified at the vertices of a 3D regular grid. The most popular isosurface algorithms [9] are Cuberille [1] and Marching Cubes =-=[14]-=-. In this paper we refer to the polygon meshes produced by these and related algorithms as isosurface meshes. Despite the widespread use of these meshes in scientific visualization and medical applica... |

664 |
Arithmetic coding for data compression
- Witten, Neal, et al.
- 1987
(Show Context)
Citation Context ...re infrequently. The absolute lower bound for the total number of bits necessary to represent the sequence X with no loss of information is given by the entropy [23]. In practice the arithmetic coder =-=[34]-=- asymptotically achieves the entropy. Arithmetic coding is used as the basis of many image and data compression schemes and applications [15], very good public domain software implementations [33], an... |

522 | A signal processing approach to fair surface design
- Taubin
- 1995
(Show Context)
Citation Context ...rtices can then be computed by local averaging, or by using more accurate schemes [4, 27]. In addition, the client can apply a number of subsequent smoothing algorithms to improve the mesh appearance =-=[26, 28]-=-. The situation is similar for normals. If computed in the server as the gradient of the scalar function at the edge intersection points [36, 16, 19], and included in the compressed data, the Marching... |

424 | Qsplat: a multiresolution point rendering system for large meshes
- Rusinkiewicz, Levoy
- 2000
(Show Context)
Citation Context ...eam. It is not even necessary for the decoder to produce a polygon mesh as output. For visualization purposes, and in particular if normals are included in the compressed data, a point-based approach =-=[22]-=- could be very effective. 3 ENCODER The encoder algorithm scans the volume data, determines which grid edges intersect the isosurface, computes the location of the intersection points along the corres... |

318 | Geometry compression
- DEERING
- 1995
(Show Context)
Citation Context ...nt approaches in section 8, after the relevant concepts are introduced. Polygon Mesh Coding A number of general purpose polygon mesh compression algorithms have been proposed in recent years. Deering =-=[3]-=- developed a mesh compression scheme for hardware acceleration. Taubin and Rossignac [30], Touma and Gotsman [31], Rossignac [21], Gumhold and Strasser [5], and others, introduced methods to encode th... |

296 |
GOTSMAN C.: Triangle mesh compression
- TOUMA
- 1998
(Show Context)
Citation Context ...purpose polygon mesh compression algorithms have been proposed in recent years. Deering [3] developed a mesh compression scheme for hardware acceleration. Taubin and Rossignac [30], Touma and Gotsman =-=[31]-=-, Rossignac [21], Gumhold and Strasser [5], and others, introduced methods to encode the connectivity of triangle meshes with no loss of information. King et. al. [12] developed a method to compress q... |

270 | Metro: Measuring Error on Simplified Surfaces
- Cignoni, Rocchini, et al.
- 1998
(Show Context)
Citation Context ...try) for the polygon meshes of figures 8, 9, and 11, with the polygonmesh coder of Khodakovsky et.al. [10]. the reference mesh. This is not the most common way of measuring distortion. The Metro tool =-=[2]-=-, which measures the Haussdorf distance between two meshes, has become a de-facto standard, but incompatible file formats and time constraints have prevented us from reporting results based on this to... |

262 | Edgebreaker: Connectivity compression for triangle meshes
- Rossignac
- 1999
(Show Context)
Citation Context ...mesh compression algorithms have been proposed in recent years. Deering [3] developed a mesh compression scheme for hardware acceleration. Taubin and Rossignac [30], Touma and Gotsman [31], Rossignac =-=[21]-=-, Gumhold and Strasser [5], and others, introduced methods to encode the connectivity of triangle meshes with no loss of information. King et. al. [12] developed a method to compress quadrilateral mes... |

190 | Progressive Geometry Compression
- Khodakovsky, Schroeder, et al.
- 2000
(Show Context)
Citation Context ...n addition,sall of these approaches are incompatible with the out-of-core nature of isosurface extraction algorithms that visit the voxels in scan order. Resampling and Subdivision Khodakovsky et.al. =-=[11]-=- follow a different approach to compress large connected and uniformly sampled meshes of low topological complexity, based on resampling, subdivision and wavelets. They obtain up to one order of magni... |

176 | W.: Real time compression of triangle mesh connectivity
- GURNHOLD, STRASSER
- 1998
(Show Context)
Citation Context ... have been proposed in recent years. Deering [3] developed a mesh compression scheme for hardware acceleration. Taubin and Rossignac [30], Touma and Gotsman [31], Rossignac [21], Gumhold and Strasser =-=[5]-=-, and others, introduced methods to encode the connectivity of triangle meshes with no loss of information. King et. al. [12] developed a method to compress quadrilateral meshes. Methods to encode the... |

141 |
Data Compression: The Complete Reference
- Salomon
- 2004
(Show Context)
Citation Context ... 4 ENTROPY ENCODING Entropy encoding is the problem of how to represent with a minimum number of bits a sequence of independent symbols X = (x1,...,xN ) that belong to a finite alphabet Σ={σ1,...,σn} =-=[23]-=-. Symbols that appear more often in the sequence should be represented with fewer bits than those that appear more infrequently. The absolute lower bound for the total number of bits necessary to repr... |

126 | Progressive forest split compression
- Taubin, Guéziec, et al.
- 1998
(Show Context)
Citation Context ...parameter B results in roughly one bit increase in the compression bitrate. In our experience, this high entropy in the quantized intersection points is due to the lack of predictors. For example, in =-=[29]-=- a smoothing operator is used as a predictor to efficiently encode vertex displacements from a coarse mesh to a refined mesh. We could do the same here to predict each bitplane of the quantized inters... |

96 | Topological considerations in isosurface generation
- Gelder, Wilhelms
(Show Context)
Citation Context ...sistencies Since some of the cases admit multiple polygonizations, care should be taken during the construction of the table to avoid the generation of polygon meshes with topological inconsistencies =-=[32]-=-. One such approach is based on estimating the value at the cell center using tri-linear interpolation within each cell. In the continuum, the surface defined by a level set of a smooth function witho... |

91 | Semi-regular mesh extraction from volumes
- Wood, Desbrun, et al.
- 2000
(Show Context)
Citation Context ...e order of magnitude better compression rates than with the connectivity preserving schemes, by approximating the mesh geometry with a subdivision mesh, and compressing this mesh instead. Wood et.al. =-=[35]-=- introduced a method based on surface wave propagation to extract isosurfaces from distance volumes that produces semi-regular multi-resolution meshes. These meshes can be compressed with Khodakovsky’... |

85 | Face Fixer: Compressing Polygon Meshes with
- SNOEYINK
- 2001
(Show Context)
Citation Context ...eshes with no loss of information. King et. al. [12] developed a method to compress quadrilateral meshes. Methods to encode the connectivity of polygon meshes were introduced by Isenburg and Snoeyink =-=[6]-=-, Konrod and Gotsman [13], and Khodakovsky et.al. [10]. These algorithms focus on compressing the connectivity information very efficiently, and are all based on a traversal of the primal or dual grap... |

52 | Nearoptimal connectivity encoding of 2-manifold polygon meshes, Graphical Models 64
- Khodakovsky, Alliez, et al.
- 2002
(Show Context)
Citation Context ...developed a method to compress quadrilateral meshes. Methods to encode the connectivity of polygon meshes were introduced by Isenburg and Snoeyink [6], Konrod and Gotsman [13], and Khodakovsky et.al. =-=[10]-=-. These algorithms focus on compressing the connectivity information very efficiently, and are all based on a traversal of the primal or dual graph of the mesh. Some of them compress connectivity of v... |

45 | Constrained elastic surface nets: generating smooth surfaces from binary segmented data
- Gibson
- 1998
(Show Context)
Citation Context ... in the primal mesh specify the location of the face centroids of the Cuberille mesh. The location of the cuberille vertices can then be computed by local averaging, or by using more accurate schemes =-=[4, 27]-=-. In addition, the client can apply a number of subsequent smoothing algorithms to improve the mesh appearance [26, 28]. The situation is similar for normals. If computed in the server as the gradient... |

38 | A comparison of normal estimation schemes
- Möller, Machiraju, et al.
- 1997
(Show Context)
Citation Context ...nt smoothing algorithms to improve the mesh appearance [26, 28]. The situation is similar for normals. If computed in the server as the gradient of the scalar function at the edge intersection points =-=[36, 16, 19]-=-, and included in the compressed data, the Marching Cubes decoder will treat them as vertex normals, and the Cuberille decoder as face normals. If the normals are not included in the compressed data, ... |

35 |
Geometry compression through topological surgery
- Taubin, Rossignac
- 1996
(Show Context)
Citation Context ...ing A number of general purpose polygon mesh compression algorithms have been proposed in recent years. Deering [3] developed a mesh compression scheme for hardware acceleration. Taubin and Rossignac =-=[30]-=-, Touma and Gotsman [31], Rossignac [21], Gumhold and Strasser [5], and others, introduced methods to encode the connectivity of triangle meshes with no loss of information. King et. al. [12] develope... |

33 | Gradient estimation in volume data using 4D linear regression
- Neumann, Csébfalvi, et al.
- 2000
(Show Context)
Citation Context ...nt smoothing algorithms to improve the mesh appearance [26, 28]. The situation is similar for normals. If computed in the server as the gradient of the scalar function at the edge intersection points =-=[36, 16, 19]-=-, and included in the compressed data, the Marching Cubes decoder will treat them as vertex normals, and the Cuberille decoder as face normals. If the normals are not included in the compressed data, ... |

32 | A.: Connectivity compression for irregular quadrilateral meshes
- KING, ROSSIGNAC, et al.
- 1999
(Show Context)
Citation Context ...ossignac [30], Touma and Gotsman [31], Rossignac [21], Gumhold and Strasser [5], and others, introduced methods to encode the connectivity of triangle meshes with no loss of information. King et. al. =-=[12]-=- developed a method to compress quadrilateral meshes. Methods to encode the connectivity of polygon meshes were introduced by Isenburg and Snoeyink [6], Konrod and Gotsman [13], and Khodakovsky et.al.... |

31 | Linear anisotropic mesh filtering
- Taubin
- 2001
(Show Context)
Citation Context ...rtices can then be computed by local averaging, or by using more accurate schemes [4, 27]. In addition, the client can apply a number of subsequent smoothing algorithms to improve the mesh appearance =-=[26, 28]-=-. The situation is similar for normals. If computed in the server as the gradient of the scalar function at the edge intersection points [36, 16, 19], and included in the compressed data, the Marching... |

22 | Rapid high quality compression of volume data for visualization
- Nguyen, Saupe
(Show Context)
Citation Context ...tific visualization and medical applications, and their very large size, special purpose algorithms to compress them for efficient storage and fast download have not been proposed until very recently =-=[24, 18, 38, 20, 37]-=-. We compare our new algorithm with these recent approaches in section 8, after the relevant concepts are introduced. Polygon Mesh Coding A number of general purpose polygon mesh compression algorithm... |

21 | Scalable isosurface visualization of massive data sets on cots clusters
- Zhang, Bajaj, et al.
- 2001
(Show Context)
Citation Context ...tific visualization and medical applications, and their very large size, special purpose algorithms to compress them for efficient storage and fast download have not been proposed until very recently =-=[24, 18, 38, 20, 37]-=-. We compare our new algorithm with these recent approaches in section 8, after the relevant concepts are introduced. Polygon Mesh Coding A number of general purpose polygon mesh compression algorithm... |

20 |
Surface Shading in the Cuberille Environment
- Chen, Herman, et al.
- 1985
(Show Context)
Citation Context ... extraction algorithms construct polygon mesh approximations to level sets of scalar functions specified at the vertices of a 3D regular grid. The most popular isosurface algorithms [9] are Cuberille =-=[1]-=- and Marching Cubes [14]. In this paper we refer to the polygon meshes produced by these and related algorithms as isosurface meshes. Despite the widespread use of these meshes in scientific visualiza... |

16 |
A survey of algorithms for constructing surfaces from 3D volume data. Research report rc 17600
- Kalvin
- 1992
(Show Context)
Citation Context ...DUCTION Isosurface extraction algorithms construct polygon mesh approximations to level sets of scalar functions specified at the vertices of a 3D regular grid. The most popular isosurface algorithms =-=[9]-=- are Cuberille [1] and Marching Cubes [14]. In this paper we refer to the polygon meshes produced by these and related algorithms as isosurface meshes. Despite the widespread use of these meshes in sc... |

13 |
Efficient coding of nontriangular meshes
- Kronrod, Gotsman
- 2000
(Show Context)
Citation Context ...formation. King et. al. [12] developed a method to compress quadrilateral meshes. Methods to encode the connectivity of polygon meshes were introduced by Isenburg and Snoeyink [6], Konrod and Gotsman =-=[13]-=-, and Khodakovsky et.al. [10]. These algorithms focus on compressing the connectivity information very efficiently, and are all based on a traversal of the primal or dual graph of the mesh. Some of th... |

13 |
A.E.: Normal estimation in 3d discrete space. The Visual Computer 8(5&6
- Yagel, Cohen, et al.
- 1992
(Show Context)
Citation Context ...nt smoothing algorithms to improve the mesh appearance [26, 28]. The situation is similar for normals. If computed in the server as the gradient of the scalar function at the edge intersection points =-=[36, 16, 19]-=-, and included in the compressed data, the Marching Cubes decoder will treat them as vertex normals, and the Cuberille decoder as face normals. If the normals are not included in the compressed data, ... |

12 |
Dual mesh resampling
- Taubin
- 2002
(Show Context)
Citation Context ... in the primal mesh specify the location of the face centroids of the Cuberille mesh. The location of the cuberille vertices can then be computed by local averaging, or by using more accurate schemes =-=[4, 27]-=-. In addition, the client can apply a number of subsequent smoothing algorithms to improve the mesh appearance [26, 28]. The situation is similar for normals. If computed in the server as the gradient... |

7 |
Segmentation and surface-based modeling of objects in three-dimensional biomedical images
- Kalvin
- 1991
(Show Context)
Citation Context ...at the isosurface algorithm generates a mesh with the same characteristics. This property is guaranteed when the mesh is the boundary of a regular solid (without self intersections). Cuberille Kalvin =-=[8]-=- proposed one way to resolve this inconsistency problem by observing that the polygon mesh generated by Marching Cubes is the dual mesh of the quadrilateral mesh generated by the Cuberille algorithm [... |

5 | Space-efficient boundary representation of volumetric objects. Accepted for publication
- Mroz, Hauser
- 2001
(Show Context)
Citation Context ...tific visualization and medical applications, and their very large size, special purpose algorithms to compress them for efficient storage and fast download have not been proposed until very recently =-=[24, 18, 38, 20, 37]-=-. We compare our new algorithm with these recent approaches in section 8, after the relevant concepts are introduced. Polygon Mesh Coding A number of general purpose polygon mesh compression algorithm... |

5 |
The Qx-coder
- Slattery, Mitchell
- 1998
(Show Context)
Citation Context ...ropy. Arithmetic coding is used as the basis of many image and data compression schemes and applications [15], very good public domain software implementations [33], and even hardware implementations =-=[25]-=- are available. To deal with the lack of stationary distribution of symbols in the sequence, adaptive models are used. In arithmetic coding with an adaptive model the encoder updates the alphabet prob... |

5 |
Compressing isosurfaces generated with marching cubes, Vis
- Yang, Wu
- 2002
(Show Context)
Citation Context |

4 |
A JBIG-ABIC compression engine for digital document processing
- Marks
- 1998
(Show Context)
Citation Context ...iven by the entropy [23]. In practice the arithmetic coder [34] asymptotically achieves the entropy. Arithmetic coding is used as the basis of many image and data compression schemes and applications =-=[15]-=-, very good public domain software implementations [33], and even hardware implementations [25] are available. To deal with the lack of stationary distribution of symbols in the sequence, adaptive mod... |

3 |
Compression of isosurfaces
- Saupe, Kuska
- 2001
(Show Context)
Citation Context |

1 |
Arithmetic coding package. http://www.cipr.rpi.edu/wheeler/ac
- Wheeler
- 1996
(Show Context)
Citation Context ...der [34] asymptotically achieves the entropy. Arithmetic coding is used as the basis of many image and data compression schemes and applications [15], very good public domain software implementations =-=[33]-=-, and even hardware implementations [25] are available. To deal with the lack of stationary distribution of symbols in the sequence, adaptive models are used. In arithmetic coding with an adaptive mod... |