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3. Molecular Signatures
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 are equally important to characterize surfaces, particularly isosurfaces extracted from volume data sets.
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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