Hi all- I'd just like to add a couple of comments about the reflection averaging discussion.
The paper by Mardia, Bookstein and Moreton provides an excellent approach to the problem, and for me is clearly the preferred approach. The BigFix program was intended primarily for use with paleontological specimens where we had substantial numbers of damaged trilobite specimens. Reflecting and averaging allowed use of some specimens where several landmarks were unavailable on one side (these points are simply reflected, not averaged of course). Mixing averaged and unaveraged data produces it's own set of problems of course, but it does allow use of damaged specimens potentially increasing your sample size. BigFix was not originally intended as a general solution to the issues related to bilateral symmetry. BigFix does orient the specimens with the axis horizontally, so you do not need to have digitized specimens in this orientation. After using BigFix to carry out the backreflection, you can use the Coordgen program to orient the specimens as desired, and many of the other IMP program allow you to rotate your specimens and reference form as desired. All of that said, I would urge you to use the approach outlined in Mardia, Bookstein and Moreton as long as you do not have damaged specimens. -Dave Sheets ---- Original message ---- >Date: Wed, 23 Mar 2005 18:32:55 -0500 >From: morphmet <[EMAIL PROTECTED]> >Subject: Symmetry-averaging landmarks and rotating axis >To: morphmet <[email protected]> > > >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 > -- Replies will be sent to the list. For more information visit http://www.morphometrics.org
