Hi folks, I want to signal you this new publication that just came out.
There we present a complete theory about the threefold decomposition of deformation (homothetic, affine and non affine components) as well as new methods to perform it in the Thin Plate Spline space (Varano et al 2017). Moreover, some new efforts are present: We unify in a unique formalism the Procrustes metric and the bending energy metric (that is a pseudo-distance vanishing on affine transformations). We also introduce two new types of energies: the stretching energy that deals with affine transformations and the gamma energy (depending on two source-dependent constants) that unifies affine and non affine energetics in a given transformation. We also introduce the decay factor rho that relates the strain energy (calculated on the body only) and the bending energy (calculated on the whole R^m). We unify in a unique formalism the Ordinary Procrustes Analysis and the Modified Ordinary Procrustes Analysis (Varano et al., 2017). One key aspect is to consider the concept of orthogonality between components non-strictly depending from the Euclidean metric. Our new methods deal also with the m-Volume size definition, that has a more physical meaning ,in place of Centroid Size. We demonstrate the usefulness of all of this using both simulated examples (in both 2D and 3D) and using a real clinical example. This is inserted in a long term project aimed at bridging Geometric Morphometrics and Continuum Mechanics. Varano V., *Piras P.,* Gabriele S., Teresi L., Nardinocchi L., Dryden I.L., Torromeo C., Puddu P.E. 2018. The Decomposition of Deformation: new metrics to enhance shape analysis in medical imaging. *Medical Image Analysis*, 46: 35-56.Doi:https://doi.org/10.1016/j.media.2018.02.005 A complete set of R functions for all of this is available upon request. All the best Paolo -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org.
