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I'd like to find a method for scoring the difference in regularity of points in grids - there are two examples below (left) a relatively well ordered grid and (right) a relatively disordered grid.

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I have a brutish method which analyses nearest neighbours, finds approximate orientations (rotation and shear) and then attempts to fit a modelled grid (and computes the score of the model compared with the real data).

It seems that there must be a more elegant solution, maybe by calculating an entropic value for each grid (I only want to know which is more regular, and maybe by how much). Thanks in advance, Dan

danodonovan
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  • I would compute the mean-squared error (distance) of each point in the "disordered" grid from its corresponding point in the scaled, axes-aligned perfect grid. Mathematically, this would be the minimum mean-squared error of the "disordered" grid over all relative orientations, center positions and uniform scales of candidate "perfect" grids. – David G. Stork Nov 04 '15 at 17:52
  • @danodonovan Did you find a solution ? I have a similar problem and I'm looking for some ideas. – YeO Apr 18 '20 at 19:41
  • Sorry, no - the approximate score outlined in the question was good-enough. I'd be interested to hear of solutions if you find any though! – danodonovan Apr 18 '20 at 20:33
  • have you thought of using procrustes analysis ? it does give a measure of how similar shapes are (see the scipy docs) and could suit you maybe ? – YeO Apr 18 '20 at 21:09

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