Seattle, March 12, 2024
Dear MorphMetters,
This email is to tell all of you about a new preprint that was
just posted today at the public biorXiv server: "Bridging geometric
morphometrics to medical anatomy: An example from an experimental
study of the human smile," by John Kent (Leeds), Balvinder
Khambay (Birmingham), Kanti Mardia (Leeds), and me. In its 61 pages and
25 figures, the article shows how to manipulate mostly standard
GMM tools in order to make explicit the match between a
physiological GMM data set (high-speed cinematography of
a ten-semilandmark configuration capturing two different types
of human smiles) and the different geometric actions of the two
main muscles that produce those two distinct expressions.
The presentation, a generous elaboration of
the summary in Section 5.6.9.2 of my 2018 textbook,
emphasizes how relying on partial warps
rather than principal components was crucial to a proper biological
understanding of the striking morphometric
contrast uncovered here. In this setting, the action of
the zygomaticus major muscle emerges as one varimax-rotated
factor of these data, while the action of the orbicularis
oris emerges as a different, distinct factor of the same
data. Of course this finding is not new as physiology.
The point of the manuscript is instead an intellectual
one: by deprecating Procrustes distance (in
particular, by eschewing principal components analysis),
GMM can help achieve D'Arcy Thompson's original purpose,
the "origins of form in force" -- the bridge between
arithmetic and understanding --
in a context where change in form is indeed produced
by physical force, the original mantra of DWT's 1917 method.
The preprint can be downloaded free of
charge as a .pdf by redirection from the following link:
https://doi.org/10.1101/2024.03.07.583999
It appears there under the rubric of "confirmatory results,
physiology."
Fred Bookstein (for the authors)
For those of you who like to decide in advance whether the full
61-page development is worth your time, here is the Abstract.
The method of Cartesian transformations
introduced by D'Arcy Thompson a century ago in his
celebrated book {\sl On Growth and Form}
precipitated an important development in 20th-century biometrics:
a fusion of the geometrical and biological approaches to
morphology. Some decades later this fusion, in turn,
spun off another multidisciplinary focus,
{\sl statistical shape analysis,} that bridges between
biostatistics and biomedical imaging. Our article is intended to
seed a complementary focus: a bridge between biostatistics and
medical anatomy, a field that has to this day remained mainly verbal
rather than quantitative.
Specifically, we are proposing a novel methodology for arriving at anatomical
interpretations of statistical findings about large-scale contrasts of
organismal morphology or its dynamics by combining
two toolkits hitherto separate in their
notation and their disciplinary housing: morphometrics and
psychometrics. A contemporary morphometric analysis
deals with patterns of shape coordinate covariation in terms
of their geometric adjacency; psychometric factor analysis, the same
patterns of covariation in terms of simplicity of interpretation.
By combining these tools we account for the dynamics of a
facial expression in terms of the actions of the
underlying muscles, thereby realizing Thompson's
original metaphor, the ``origins of form in force,''
for systems that ``vary in a more or less uniform manner.''
This paper reviews the history of Thompson's metaphor and then
the current literature quantifying smiles, in order to set the
stage for the combination of scaling analysis and factor analysis
that we are putting forward. We demonstrate the new approach
by reanalyzing a data set of ten landmarks around the vermilion
borders of the human lip contrasting the dynamics of two
socially stereotyped physiological cycles, the open-lip smile
and the closed-lip smile, over a sample of 14 normal faces.
Our analysis centers on just two dimensions of statistical shape
space, those of largest geometrical scale, which
can be identified with the action of two different
muscles, orbicularis oris and zygomaticus major.
The two smiles differ radically in their
achieved deformations. Furthermore, while the closed-lip smiles
arrived at their final forms along similar shape trajectories,
the open-lip smiles did not. Our closing discussion explores
some aspects of morphodynamics that are illuminated by
the example here.
~
~
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