My comments are inserted below. -------------------- F. James Rohlf - Dept. Ecology & Evolution SUNY, Stony Brook, NY 11794-5245
> -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of > [EMAIL PROTECTED] > Sent: Monday, February 09, 2004 11:14 AM > To: [EMAIL PROTECTED] > Subject: Re: Asking for advice > ... Deleted ... > Finally, I would like to make one question (or-better said- I > would like you to criticise what I think) about the overall > ,general (and-I > suppose-oversimplified) procedure that the program performs > to find the relative warps from the landmarks of the digital images: I assume that "the program" refers to tpsRelw. > -As far as I know, the first step is to find the consensus > configuration from the superimposition of a set of > configurations, which implies the use of the Generalized > procrustes analysis (GPA) (also called the Generalized least > squares (GLS)), the resistant fit or the use of other > algorithm. -Once this is obtained, it is computed the > "energy" needed to warp or deform landmarks of each > individual to the consensus configuration. From this it is > obtained the bending energy matrix. -The partial warps are > the eigenvectors of the bending energy matrix. -The relative > warps are the result of a PCA performed from the weight > matrix (the matrix of the partial warp scores and the uniform > component). Close but not quite correct. Details of what the program does are given in the help file for that program. In particular, the 'introduction' topic gives an overview of the computational steps. Notes: 1) Only the GPA method of superimposition is used to compute the consensus configuration and to align the specimens to the consensus. There are some options to modify how it is done but it is still just GPA not a resistant fit. 2) While the program does compute partial warps and partial warp scores, that fact is a bit of a distraction if you use the default option of alpha = 0 and include the uniform component. One gets the identical relative warps ordination plot and the same visualization of shape differences if you simply do a PCA on the GPA aligned specimens. This point is made in my paper Rohlf (1999) "Shape statistics: Procrustes superimpositions and tangent spaces". Journal of Classification, 16:197-223. Thus, one should not spend much time worrying about the meaning of bending energy for the interpretation of shape variation in your data. It is introduced as a clever mathematical trick to eliminate non-shape variation and to order shape variation according to spatial scale. 3) The tpsRelw program does have an option to use resistant fit in the visualization of an estimated shape in comparison to the consensus configuration. The option is just for visualization of the results - resistant fit is not used within any of the computations of the relative warps. > > Do I have guessed something right? Pretty close - I hope my comments are helpful. > > Javier Mariana > > Barcelona > (Spain) > == > Replies will be sent to list. > For more information see > http://life.bio.sunysb.edu/morph/morphmet.h> tml. > == Replies will be sent to list. For more information see http://life.bio.sunysb.edu/morph/morphmet.html.
