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Considering there is a 2-dimensional array $A$ consisting of point coordinates in two dimension space (as shown in image).

enter image description here

There is another array 2-dimension array $B$ also representing the position of points in similar fashion as that of $A$. $B$ may also represent the position of points with some rotation of $A$. In this case I would like to compare the position of points in both arrays if they overlap or not. One option is to apply Procrustes analysis. When I tried, it provided good result when the arrays have equal size i.e. goodness of fit is high when $A$ and $B$ represent the distribution of same points. However, I cannot figure how to apply the Procrustes analysis for unequal sized arrays. I have tried to add numbers to equalize the array but the goodness of fit deteriorate significantly.

Can anyone suggest me a methodology which can be applied to solve the above-mentioned issue i.e. comparison of point distributions of unequal size.

Thanks in advance.

user3563929
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  • only rotation, or also a shift (translation)? – G Cab Jun 24 '17 at 13:03
  • @GCab thanks for your comment. Presently the issue is limited to rotation only. – user3563929 Jun 24 '17 at 13:44
  • If limited to rotation only, about the origin (or any other point, e.g. the barycenter), what about to plot both sets in polar coordinates, cut out the points falling in the "less" overlapping anuli, and in the "more" distant from average sectors, as to leave the same number and then proceed with Procrustes analysis? – G Cab Jun 24 '17 at 14:55

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