-------- Original Message --------
Subject: RE: Simulating naturally occurring human craniofacial variation
Date: Fri, 4 Feb 2011 11:39:11 -0500
From: F. James Rohlf <[email protected]>
Reply-To: [email protected]
Organization: Stony Brook University
To: [email protected]
Perhaps you mean to generate a normally distributed random sample of
specimens with the same mean and covariance structure as that of a given
sample? That is easy to do. Procedure is that same as to generate any
multivariate normal sample with a specified true mean and covariance
matrix. First generate a data matrix for a random normal sample with
mean zero and identity covariance matrix of the proper number of
dimensions and observations. Then multiply that matrix by the weighted
eigenvectors of the desired covariance matrix and then add on the
desired mean vector. This yields a sample of data in the tangent space.
If the original covariance matrix was based on aligned specimens then
you need only scale specimens to unit centroid size. If the covariance
matrix was based on partial warps then you will need to back transform
to coordinates and then scale to unit centroid size.
----------------------
F. James Rohlf, John S. Toll Professor
Dept. Ecology and Evolution, Stony Brook University, NY 11794-5245
Please consider the environment before printing this email
-----Original Message-----
From: morphmet [mailto:[email protected]]
Sent: Thursday, February 03, 2011 12:25 PM
To: morphmet
Subject: Simulating naturally occurring human craniofacial variation
-------- Original Message --------
Subject: Simulating naturally occurring human craniofacial variation
Date: Mon, 31 Jan 2011 16:49:44 -0500
From: Hans Wellens <[email protected]>
To: <[email protected]>
Dear all,
For an ongoing research project, I would need to “simulate” (within
reasonable limits) naturally occurring human craniofacial variation.
More precisely, I was hoping to apply principal component analysis to a
relatively large patient sample, to then “randomly” vary/modify a consensus
configuration while respecting the underlying population’s covariation
structure. Simply generating Gaussian scatter around the consensus
configuration’s landmarks won’t cut it, since it neglects this underlying
covariation structure. The goal would understandably be to limit the random
variation around the consensus configuration to what’s clinically (naturally)
possible.
Although I understand in broad terms how principal component analysis
decomposes the variance-covariance matrix into eigenvectors and
eigenvalues, and I can program it in R, I keep struggling somewhat with the
required mathematical operations (for instance the ones to visualize the
information contained in the principal components). I know there are
programs out there that will do the latter for you (like MorphoJ), but I cannot
change these to suit my specific research purpose. Therefore I thought it
would probably be preferable to program these visualizations in R, which also
contains packages to perform PC analysis.
Does anyone know whether this would be possible and if so, could you give
me some clues as to how I should proceed?
Thanks!
With kind regards,
Hans
Hans Wellens, DDS
Orthodontist
Groene-Poortdreef 16
8200 Sint-Michiels
Tel: 050/39.68.36
[email protected]
