Dear Andrea, > I'd like to ask your advice on a couple of issues: > 1) What can be done (if anything) when the tangent space approximation > of the shape space is bad? I am not talking about small problems due to > outliers. I am considering a case when the approximation is bad because > the biological variation in the sample is really large.
I would be interested to see an example of such data before offering any definitive advice. > 2) It is often difficult to sample landmarks all over a structure > (unless using semilandmark on curves etc.). Often, landmarks tend to be > more dense in some anatomical regions and less in others. Is there any > risk of 'overfitting' the regions with more landmarks during the > Procrustes superimposition? Are there other issues that may be related > to large differences in landmark density in a structure? > Thanks a lot for your help. There are (at least) two answers. (a) There is a version of Procrustes analysis in which weights are given to the landmarks. Your example, with a large number of tightly clustered landmarks, is a bit like using a smaller number of landmarks, but with differential weights. Bookstein coordinates are an extreme example of this in which two landmarks each have weight one, and the rest weight 0. But again, it would be helpful to see an example before offering definitive advice in your situation. (b) When using the thin-plate spline bending energy metric to compare different shapes, the presence of a dense set of landmarks in a small region is a bonus because it enables you to detect fine-scale differences between configurations which would be invisible if you only had a smaller set of landmarks. > Cheers > Andrea Best wishes, John Professor John T. Kent tel (direct) (44) 113-343-5103 Department of Statistics tel(secretary) (44) 113-343-5101 University of Leeds fax (44) 113-343-5090 Leeds LS2 9JT, England e-mail: [EMAIL PROTECTED] -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
