Gross - 8 
f(x,y,z): volume intensity function, 
r: threshold. 
Let f(x,y,z) be given in a wavelet basis, it is straightforward to approximate the implicit 
isosurface using different levels—of-detail, just by filtering on the coefficients of the WT. 
This process is further displayed in fig. 5, where the shape of a human scull was extracted 
from volume data using a marching cubes algorithm. The number of coefficients and, 
hence, the accuracy of the approximation was dropped from left to right. 
Fig. 5 Isosurfaces of a human scull extracted from a CT volume data set and expanded with a 
B-spline wavelet basis: 
a) 16 % of the coefficients, 
b) 7.5 % of the coefficients, 
c) l % of the coefficients. 
(data source: courtesy University of North Carolina, from [11]) 
Unfortunately, the topology of 3D isosurfaces is usually non-2-manifold and thus the 
above meshing strategies for the 2-manifold case cannot be applied. However, due to the 
immense energy concentration, the coding gain of 3D data sets is even more striking than 
in 2D. 
In summary, wavelets have come in fashion in graphics and visualization, because hier 
archical data approximation and coding will help us to handle very large data sets. Special 
emphasis is given to the biorthogonal B-spline wavelets, which are derived from a 
B-spline scaling function. They can be employed for a multiresolution extension of the 
parametric curve and surface methods, as explained in section 2.