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

I am interested to obtain linear measurements from 3D models of human fossil 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 I am planning to use the 3D length tool in Avizo to obtain the measurements 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 obtained from the 3D models are a good proxy of those obtained directly from fossil teeth using a caliper and if such 3D measurements can be actually used 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 2D geometric morphometric analyses in some teeth (molars) where the use of 3D landmarks/semilandmarks is not very useful. So, I want to know if there exists a way to obtain standardized 2D pictures using Avizo or another 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 Fruciano
Institute of Biology
Ecole Normale Superieure - Paris

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