### Table 2: Iso-surface extraction for the MRI-heads and CAT- abdomens in Fig.7,

in The Multilevel Finite Element Method for Adaptive Mesh Optimization and Visualization of Volume Data

1997

"... In PAGE 6: ... Extraction time, generated triangles and image quality will be of interest. Considering the triangle generation speed with respect to the number of tetrahedra shown in Table2 , we see that the extraction time is nearly constant. An optimal algorithm would just inspect those tetrahedra, that contribute to the iso-surface.... In PAGE 6: ...7, Threshold = 0:2 exhibit constant behavior, but the decay is quite low which means, that the triangulation of the volume implicitly results in an effective processing of the generated tetrahedra. As we can see in Table2 the time needed to generate the tri- angles is decreasing significantly compared to the standard march- ing cubes algorithm. Looking especially at Head 1 we see, that the number of triangles is about a half and the processing time is about 6 times faster.... ..."

Cited by 37

### Table 2: Results for the iso-surfaces of the MRI-heads in Fig.8 (iso-value 2926)

1996

"... In PAGE 10: ... Our algorithm does not exhibit constant behavior, but especially for the L2 norm the decay is quite low which means, that the triangulation of the volume implicitly results in an effective processing of the generated tetrahedra. As we can see in Table2 the time needed to generate the triangles is decreasing dramatically compared to the standard marching cubes algorithm. Looking at a special case we see, that in the first H1 image the number of triangles is less than one third and the processing time is about 9 times faster.... ..."

Cited by 3

### Table 1: Experiments for tissue transformation: real volume variations ( Vth), spheres method( Vsphere), iso-surfaces method ( Viso) and segmen- tation ( Vseg).

### Table 2: Iso-surface of unstructured grids currently outperforms software implementations. For iso- surfaces, the Klein et al. extraction algorithm was used, while for the direct volume rendering Weiler et al. GPU ray caster was used.

"... In PAGE 6: ...The GPU implementation is faster in more than one order of magnitude (see Table2 ). However, the 1Rendered only with diffuse shading.... ..."

### Table 1: The performance of full extraction and rendering of iso-surfaces, measured in million MC cells processed per second, with frames per second given in parentheses. The algorithms measured were HistoPyramid extraction in the vertex shader (HP- VS), extraction in the geometry shader (HP-GS), and the Marching Tetrahedra implementation of the NVidia OpenGL SDK10 (NV-SDK10).

2007

### Table 2: Number of points on the iso-surface (subdivision parameters, measure and estimation) from synthetic 3D images given by relation (4). Our estimation is very accurate since the maximal relative error is about 2%. These experiments validate our statistical study, which can predict precisely the memory space and the computing time associated to particular subdivision parame- ters.

### Table 4: Iso-surface refinement and extraction times (in sec.) and triangle count for the abdomen data set

"... In PAGE 9: ... Together with the time informa- tion we include the number of triangles in the iso-surface at each level of resolution. In Table4 the corresponding per- formance results for the abdomen data set are presented. These numbers demonstrate how fast iso-surfaces can be ex- tracted from the compressed meshes.... ..."

### Table 3: Iso-surface refinement and extraction times (in sec.) and triangle count for the spherical harmonics

"... In PAGE 9: ...(a) Level 6, 58,491 vertices (b) Level 7, 80,111 vertices (c) Level 8, 89,505 vertices Figure 2: Mesh of an iso-surface from the spherical harmonic data set at different levels of resolution in the images appearing as shadows, because the normals used for shading do not correspond to the normals of the tri- angles at coarser levels. In Table3 we give timing results for the iso-surface ex- traction and for the iso-surface refinement algorithm for the spherical harmonic data set. Together with the time informa- tion we include the number of triangles in the iso-surface at each level of resolution.... ..."