to perform a topological analysis after Surface reconstruction from point cloud, yet it appears that it is computationally expensive to define a discrete Morse function "it has to be something else than homology".
James F Peters
This is a good question with many possible answers.
A good introduction to defining discrete morse functions on point cloud data is given in
J. Curry, R. Ghrist, V. Nanda, Discrete morse theory for computing cellular sheaf cohomology:
http://www.math.upenn.edu/~ghrist/preprints/computationalsheafcohom.pdf
See Section 2.2, starting on page 4.
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