Topological Noise Removal
- Quantification of
Complementary Space Topology
Topological complexity is
measured by Betti numbers. While the 1st and
3rd Betti numbers denote the number of
connected components and voids, the 2nd Betti
number denotes the number of through holes. Each of these topological features
can be captured by approximating them with the stable manifolds of critical
points (of suitable indices) of the distance function. The estimated features
are then augmented with suitable geometrical attributes (volume, area etc.) and
ranked. The low-ranked features are considered as Topological Noise and are selectively
removed.
- Sample Results:
On Free-form Objects
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On Molecular Imaging Data (cryo-EM maps)
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- References: