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.<br> 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.<br> 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