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本数据集为基于Bône等人[1]提出的纵向微分同胚（diffeomorphic）模型构建的64×64分辨率星型人体合成纵向图像数据集。以给定的参考模板(y_0)为基础，群体的截面形态变异性通过四个定位控制点（头部、右臂及双腿）对应的微分同胚变换来表征；而统一的进展时间线则仅通过左臂的位移来生成。 如此一来，左臂抬起这一时间进展相关的效应（在空间上）与形态的个体间变异性相互独立。驱动各变形过程的速度场均为正交场，且每个个体的形态轨迹通过Deformetrica软件[2]的平行输运方案计算得到。换言之，所有个体均会执行左臂抬起的动作，但双腿与双臂的位置存在差异，从而呈现出不同的形态。 进展动力学通过对第(j)次访视时的年龄(t_{ij})进行仿射重参数化来定义，该参数化由个体起始时间( au_i)与加速因子(alpha_i)表征，真实疾病进展的表达式为(psi^{ast}_{ij}=t_{0}+alpha_{i}(t_{ij}- au_{i}-t_{0}))。我们采用与文献[1]类似的变量采样方式，最终构建得到包含(N=1000)名个体、每名个体拥有(n=10)次访视的数据集。 [1] A. Bône、O. Colliot与S. Durrleman，"从纵向数据集学习形态轨迹分布：微分同胚流形上的分层模型"，美国盐湖城，2018年6月。访问时间：2021年7月8日。[在线]。可获取：https://hal.archives-ouvertes.fr/hal-01744538 [2] A. Bône、M. Louis、B. Martin与S. Durrleman，"Deformetrica 4：一款用于统计形态分析的开源软件"，发表于2018年9月举办的ShapeMI @ MICCAI 2018。访问时间：2021年7月8日。[在线]。可获取：https://hal.inria.fr/hal-01874752