The use of tools from algebraic topology to study simplicial complexes coming from point cloud data has been thoroughly discussed in the papers of Carlsson, Zomorodian, Ghrist, Edelsbrunner, Harer and more. Computing homology can be achieved in cubic time (in simplicies) and using persistent homology one can make an educated guess on which non-zero homology groups are noise and which represent n-dimensional holes in the point cloud.
In smooth theory one can use Morse theory to compute the homology of a closed manifold. One can also give a description of the cells in a CW complex which is homotopy equivalent to the manifold as well as computing the cohomology ring. I wonder what other "properties" of the manifold one can find using Morse theory.
The idea is to use Forman's discrete Morse theory to calculate properties of simplicial complexes. Since it is computationally expensive to define a discrete Morse function - it has to be something else than homology.