On 10/09/2018 03:06, Pablo Fisichella wrote:

Dear morphometriciansI am interested to obtain linear measurements from 3D models of humanfossil teeth.

Dear Paolo,

`in addition to the very informative reply by Murat, I have a couple of`

`further suggestions/alternatives`

Given that I don’t have more access to the fossils now Iam planning to use the 3D length tool in Avizo to obtain themeasurements that I need.

`Another option could simply be to collect points (that is`

`(semi)landmarks) on the tooth and then compute linear distances among`

`them using their XYZ coordinates. If you have a substantial number of`

`measurement and some proficiency in R/Matlab/similar, this might be`

`faster (and easier to retrieve in the future what you have done).`

My question is if the measurements obtainedfrom the 3D models are a good proxy of those obtained directly fromfossil teeth using a caliper and if such 3D measurements can be actuallyused to perform statistical analyses.

`If you had access to caliper measurements on the same specimens (or a`

`subset), you could also test for this rather than relying on expert`

`opinions. See:`

`Arnqvist G, Mårtensson T. 1998. Measurement error in geometric`

`morphometrics: empirical strategies to assess and reduce its impact on`

`measures of shape. Acta Zoologica Academiae Scientiarum Hungaricae 44:73-96.`

`Fruciano C. 2016. Measurement error in geometric morphometrics.`

`Development Genes and Evolution 226:139-158.`

In addition, I need to perform 2Dgeometric morphometric analyses in some teeth (molars) where the use of3D landmarks/semilandmarks is not very useful. So, I want to know ifthere exists a way to obtain standardized 2D pictures using Avizo oranother software which can be used to carry out 2D GM analyses.

`One thing that you may try if you can place some points to define your`

`plane in a reliable fashion as the two main axes is to perform a`

`principal component analysis (on the covariance matrix) using each`

`individual point as observation and x,y,z as variables, then retain the`

`first two principal components (eigenvectors), center (using the mean of`

`the points mentioned above) and project your true (semi)landmarks onto`

`these two principal components. If most of the variation in your true`

`(semi)landmarks is already along the two directions which identify your`

`plane of interest, you might even do this in a single step (i.e.,`

`perform a PCA for each individual using points as observations, x,y,z as`

`variables and then retain the scores along the first two principal`

`components for 2D geometric morphometric analyses).`

`Obviously, you'd still have the potential issue with projection of a 3D`

`structure on a 2D plane. For that, in addition to my review cited above,`

`you might want to check`

`Cardini A. 2014. Missing the third dimension in geometric morphometrics:`

`how to assess if 2D images really are a good proxy for 3D structures?`

`Hystrix, the Italian Journal of Mammalogy 25:73-81.`

`This paper suggest an approach you can use to quantify how well your 2D`

`data approximate the 3D data. As you would have both, it could be a good`

`way to check whether the projection you are choosing gives you`

`appropriate results.`

I hope this helps, Carmelo -- ================== Carmelo Fruciano Institute of Biology Ecole Normale Superieure - Paris CNRS http://www.fruciano.it/research/ -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org

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