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Quantitative Metrics
Quantitative metrics can be computed for isosurface representations of molecules.
The quantitative metrics include the area of the surfaces, the volume enclosed by
the surfaces and the gradient integral on the surfaces.
Topological Metrics
Topological metrics are equally important to characterize surfaces, particularly
isosurfaces extracted from volume data sets.
Betti Number
Each isosurface has an associated triple of Betti numbers.
The kth Betti number of a simplicial complex is the rank of
its k-dimensional homology group. In the case of isosurfaces
for 3D molecular data sets, only the first three Betti numbers
are non-zero.
Contour Tree(CT)
Contour Tree is a tree with (V,E).
- Vertex 'V': Critical Points(CP)
(points where contour topology changes)
- Edge 'E':
- connecting CP where an infinite contour class
is created and CP where the infinite contour
class is destroyed.
- contour class : maximal set of continuous
contours which don¡¯t contain critical points
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