Starmen longitudinal

Synthetic longitudinal dataset of starmen images (64x64), based on the longitudinal diffeomorphic model of Bône et al [1]. From a given reference template \(y_{0}\), the cross-sectional variability of the population is prescribed by a diffeomorphism localized at four control points: the head, right arm and legs. The common progression timeline, on the other hand, is generated through a displacement of the left arm only.
This way, the effects of time progression, raising the left arm, are (spatially) independent from the inter-variability of the shapes. The velocity fields driving each deformation are orthogonal and the trajectory of each individual is computed using a parallel transport scheme via Deformetrica software [2].

That is to say, all subjects raise the left arm but vary in shape with different position of their legs and arms.
The dynamics of progression is given by an affine reparametrization of the age \(t_{ij}\) at visit \(j
\), characterized by individual onset \(\tau_{i}\) and acceleration \(\alpha_{i}\) factors, such that the true disease progression is given by \(\psi^{\ast}_{ij}=t_{0}+\alpha_{i}(t_{ij}-\tau_{i}-t_{0})\). We sample variables in a similar fashion as in [1] to obtain a dataset of \(N=1000\) subjects, each with \(n=10
\) visits.

[1] A. Bône, O. Colliot, and S. Durrleman, “Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms,” Salt Lake City, United States, Jun. 2018. Accessed: Jul. 08, 2021. [Online]. Available: https://hal.archives-ouvertes.fr/hal-01744538

[2] A. Bône, M. Louis, B. Martin, and S. Durrleman, “Deformetrica 4: an open-source software for statistical shape analysis,” presented at the ShapeMI @ MICCAI 2018, Sep. 2018. Accessed: Jul. 08, 2021. [Online]. Available: https://hal.inria.fr/hal-01874752