Procrustes Analysis: Comparing multiple shapes to mean shape?

I am new to Procrustes Analysis, and can't seem to find anybody local that is more familiar with it. Any insight you wise forumites can offer is infinitely appreciated.

I am comparing the trajectories of finger movements during tapping. I want a measure of how similar the 2D trajectories are (in other words, how consistently the person is tapping). I am using the procrustes() function, and the dissimilarity measure d is great.

The issue is that I have multiple shapes. This idea has been visited before here, but I'm getting lost. Right now, my technique involves finding the mean procrustes shape via this file and using procrustes() to compare each shape to that mean. Basically this:

for n=1:number_shapes
    d(n)=procrustes(RawShapes(:,:,n), MeanShape)
end
result = mean(d)

Is this kosher? Today I was messing around with a Generalized Procrustes package in R, and the r.m.s. of full Procrustes distances to the mean shape here is different. I confused myself.

In short: I want a measure that will tell me how similar a bunch of shapes are. Finding the mean shape and comparing each shape to that mean makes intuitive sense to me.

Gosh, what a mess. Any help is much appreciated.

Answer 1

[Molly]

I'm going to try and answer my own question in case anybody ever comes across this in the future, because I think I figured out my issue.

The Procrustes dissimilarity measure that Matlab gives is the sum of squared errors between the corresponding landmarks of the shapes after the shapes are rotated, translated, and transformed. The square root of this is the partial procrustes distance measure.

The R.M.S of all full procrustes distances to the mean shape that I find with R (author Ian Dryden) is approximately the RMS of the partial procrustes distances in my case, since shapes were very similar sizes.

The RMS of all procrustes distances to the mean shape is a way to measure the variability of a series of shapes. (The full procrustes distance is found after re-sizing the shapes onto the unit space).

Of course, if somebody reading this knows that I'm off my rocker, please correct me.