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Stickness, plateness and ballness

  1. nslay
    nslay
    Imagine you're given a point cloud and you want to measure how "stick"-like, "plate"-like or "ball"-like the point cloud is.

    That is, if your point cloud just happens to be a line (maybe with some perturbations), then the "stick"-like measurement should large while the "plate"-like and "ball"-like measurements should be small. How does one go about measuring the likeness of a point cloud?

    It's actually quite simple. I found this Masters thesis that shows a clever rewrite of the eigendecomposition on page 28. Rewriting the eigendecomposition of the covariance matrix of your point cloud gives the following



    How intuitive and convenient!

    If you like sharing math, you can easily make nice pictures like the above here.
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