The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B6b. Beijing 2008 
Y ex PHI v, ~v|| 2 /(2cr : )] 
where <7 is the standard deviation of the Gaussian filter. For all 
the results in this paper we have used seven 
scales a e {If, 2e,3s,4s,5s,6s, le) , where £ is defined 
as 0.3% of the length of the diagonal of the bounding box of the 
model (Lee et al., 2005). 
In our method, we assigned a weight to each vertex according 
to the relationship between it and the global topographic 
features. Let the topographic feature map W define a mapping 
from each vertex of a TIN model to its feature. As shown in 
Figure 4 (b), the mean curvature map may have far too many 
“bumpy” being flagged as features. However, we can promote 
salience maps with a small number of high values by 
calculating Gaussian-weighted mean curvature in large scale. 
One can see that the topographic features are more coherent in 
the large-scales. Figure 4(c)-(f) gives an overview of 
topographic feature map such as peak, pit, ridge, channel and 
pass in different scales. We use pseudo-colours to texture the 
surface according to the feature weights: warmer colours (reds 
and yellows) show high weights, cooler colours (greens) show 
low weights, and blues show zero-feature. We guide the order 
of iterative half-edge collapses using a weight map CO derived 
from the topographic feature map W . In our algorithm, we use 
values of Gaussian-weighted mean curvature to evaluate the 
point to the extent of topographic feature. In order to improve 
the speed of processing, we don’t classify different features, 
such as peak, pit, ridge, channel and pass in our algorithm. 
However, the feature classification can easily be achieved 
according to the rules of Wood (1996). 
RESULTS AND DISCUSSION 
Among previous simplification methods, the QEM-based 
method holds much promise in terms of its time efficiency and 
relatively high quality of approximations. Garland and Zhou 
(2005) extended the QEM-based algorithm to simplify 
simplicial complexes of any type embedded in Euclidean spaces 
of any dimension and based on this, developed new GSlim 
software. However, the performance of their newer GSlim 
system on triangulated models is essentially identical to that of 
the earlier QSlim 2.0. 
Surazhsky and Gotsman (2005) have tested nine softwares for 
mesh simplification, including both commercial (Geomagic 
Studio 5.0 , Rapidform 2004 , 3ds max 7 , Maya 5.0 , 
Action3D Reducer 1.1, SIM Rational Reducer 3.1 and VizUp 
Professional 1.5) and academic offerings (QSlim 2.0 and 
Memoryless Simplification). They examined these software 
packages on the seven models of different sizes, properties and 
acquisition sources. According to their experiment results, they 
concluded the Hausdorff distance reflects visual fidelity better 
than the average distance. The possible reason is that a large 
deviation from the original surface even at just a small localized 
feature of the mesh can significantly affect the visual perception 
of the model, and this will be reflected in the Hausdorff 
distance even if the rest of the simplified mesh is very close to 
the original. In their experiments, Geomagic Studio was the 
leader with respect to the Hausdorff distance. 
Therefore, in the experiments, we use “Crater” model to 
compare our scheme with QSlim 2.0, which use area-based 
weights and optimizes vertex locations, and Geomagic Studio 8, 
which is the latest version of Geomagic Studio, for generating 
multi-resolution models in terms of visual performance, 
geometric errors (RMS), Hausdorff- distance and time 
performance. Our approach was implemented in C++ language 
on Windows XP operation system platform. The experiment 
was undertaken in a 3.0GHz Intel Pentium IV machine with 512 
MB of main memory. Figure 5 shows the “peak” in multi 
resolution “Crater” model generated by QSlim 2.0, Geomagic 
Studio 8 and our scheme (8 = 3s ) from 199,114 triangular 
faces to 4,000, 2000, and 300 triangular faces, respectively. One 
can see that our new algorithm has better performance in terms 
of the preservation the topographic features.