The name is absent

vi

1.4 Three-dimensional comparison of methods, (a) is the input of a
sphere-like segment, (b) is rendered using Tiede et al.’s classification
scheme [27]. Note that it produces a bumpy surface, (c) is our
representation for the segment contour. Details for constructing (c)
from the segment (a) is described in Section 3.4............ 5

1.5 The GroEL molecular structure and an engine block. 1.5(a) shows
the raw density map, and 1.5(b) is the result of its segmentation into
14 subunits using our tool. 1.5(c) shows the raw engine data and

1.5(d) shows the result of the segmentation with transparency. ...    7

2.1 Two material example. 2.1(a) shows the bilinear function of a single
cell. Red represents the parts of the cell that has positive values in
the bilinear evaluation, and green represents the negative values. The
arrows indicate the direction of the gradient. 2.1(b) is the plot of the
bilinear function in 3D with the same color representation...... 11

2.2 2 material example continued. 2.2(a) is the plot of the function in

2.1 by replacing the negative voxels (coefficients of the bilinear) with
O’s. 2.2(b) is the plot of the same function by replacing the positive
voxels with O’s and taking the absolute value of the coefficients.

2.2(c) is the maximum of the functions in 2.2(a) and 2.2(b)...... 12

2.3 3 material example. 2.3(a) is the classification of the bi-linear
function under our scheme. The arrows denote the gradient. 2.3(b)
is the plot of 3 functions that are created under our evaluation

scheme. 2.3(c) is the maximum plot of the three functions...... 12

2.4 The perspective view of a multi-material volume of size 33³ rendered
using GPU tri-linear contouring (a) and as polygonal contours
generated by Dual Contouring (b), showing the grid structure (c). (d)
depicts the mesh generated from Dual Contouring without the letters. 15

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