Hi Pablo,
as far as the first one of your questions is concerned, I suspect that
you can easily rotate all specimens in order to have the axis of
symmetry in the direction of the x axis by superimposing specimens with
Morpheus and then restoring size. Prof. Slice can tell you more (if this
works). 
Also some older versions of Morphologika can do that (ask Paul
O'Higgins).
Otherwise, I guess it is just a simple matrix product (check on a matrix
algebra textbook and try with your statistical software - for instance,
SPSS does simple matrix operations - or use math software - SCILAB is
freeware).

About your second question, I am very interested too. I was waiting to
send a message on this issue because I am abroad for work and cannot
check e-mails often. However, since you asked it, I will take this
chance to send my message too (next e-mail).
Good luck with your work.
Cheers

Andrea





>
>Dear colleagues,
>
>I would like to thank Dr. Bameul and Dr. Reyment for their help regarding my  
>discriminant function question. However I will appreciate any advice regarding 
> 
>the following problem:
>
>It is customary to do systematic analyses on landmarks from half of the skull, 
> 
>considering at least two landmarks as midline points (at the axis of 
>symmetry).  
>Most of the recent studies work on the average of bilaterally homologous 
>landmarks, providing a single landmark representing any homologous character 
>in  
>half of the skull. The main reason for this is to avoid excess of degrees of  
>freedom in statistical contrasts. Many of you should know this better than me. 
>
>The only program I know that can provide the average for a set of symmetrical  
>landmarks is BigFix in the IMP package. The problem is that BigFix only works  
>with landmarks oriented in an X axis of symmetry. Unaware of this requirement 
>I  
>made a TPS landmark matrix from bat skulls having a Y axis of symmetry, which  
>wont work on BigFix. It will take me many days to remake this matrix if I do  
>not find an automated method to rotate the coordinates 90 degrees to either  
>side for having them aligned to an X axis of symmetry. 1) Is there any 
>application or method in which I can make this rotation? 2)Is there any 
>alternative tool to BigFix for obtaining the average from symmetrical 
>landmarks?
>
>Another unclear method is how if statistical analyses are based on half-skull  
>landmarks, it is possible to make the visual reconstructions of skull 
>variability on the full set of landmarks (after reflecting the average set on  
>the other side of the skull). This is usually done to avoid vectors of 
>variability along the axis of symmetry which can obscure the interpretation of 
> 
>results. The dimensionality of the data changes if using only half or the full 
>skull, and thus, any thin-plate spline application will be influenciated by 
>this. It  is unclear for me how then, one can obtain statistical estimates and 
>then make  the visualizations on the full skull, which will not accurately 
>represent those  estimates. Available literature is unclear about this topic, 
>and I will be  grateful if you can point towards a reference explaining this 
>method more 
>clearly.
>
>Thanks in advance for any advice you can provide me.
>
>Pablo
>
>Pablo Jarrin Grad. Student
>Department of Biology
>Boston University
>
> 
>-- 
>Replies will be sent to the list.
>For more information visit http://www.morphometrics.org
>
>
>

Dr. Andrea Cardini
Hull York Medical School
The University of York, Heslington, York YO10 5DD, UK
&
The University of Hull,Cottingham Road, Hull HU6 7RX, UK
tel. 01904 321752
fax 01904 321696
E-mail: [EMAIL PROTECTED]
http://www.york.ac.uk/res/fme/people/andrea.htm
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