I would like to signal the following new contribution:
Valerio Varano, Stefano Gabriele, Luciano Teresi, Ian L. Dryden, Paolo E.
Puddu, Concetta Torromeo, Paolo Piras. 2017. *The TPS Direct Transport: A
New Method for Transporting Deformations in the Size-and-Shape Space*. Int J
Comput Vis. doi:10.1007/s11263-017-1031-9.
In this paper we do the following:
- we propose a type of Parallel Transport, namely the Direct
Transport, that has two properties: (i) it is independent from the path;
(ii) it is compatible with the affine/non affine decomposition. We couple
this strategy with a data-centering aimed at eliminating
and with a trajectory analysis aimed at recovering the original
deformational series, once shapes have been transported.
- we do it by introducing a new metric, i.e. TPS metric, and a new
Riemannian manifold i.e TPS space.
- we introduce a new kind of optimal rotation (deformation based), namely
MOPA: Modified Ordinary Procrustes Analysis.
- The last but not the least, we provide the derivation for the estimation
of the correct absolute value of the bending energy in both 2D and 3D.
I understand it is** very** technical but the arguments we propose there
could have important consequences for studies aimed at investigating the
deformative process behind shape differences such as in ontogeny, motion
attributes, soft tissue deformation, etc.
Moreover, we introduce there our package "deformetrics" available on github
where all example and mathematical procedures present in the paper have
been implemented. deformetrics includes also the linear shift Parallel
Transport (i.e. Euclidean) and many functions for visualizing deformations
in 2D and 3D (using the determinant of jacobian matrix deriving from the
1th derivative of Thin Plate Spline interpolant).
Specific functions visualize the morphological consequences of ontogenetic
trajectories and produce also the corresponding animations for that.
It would be great having some feedback from the community in order to
correct possible malfunctioning in the functions.
It can be installed in R by typing:
It is very probable that you will have to install manually many
dependencies to run the examples. Follow the messages.
All the best
MORPHMET may be accessed via its webpage at http://www.morphometrics.org
You received this message because you are subscribed to the Google Groups
To unsubscribe from this group and stop receiving emails from it, send an email