.png){kind=icon}
.png){kind=icon}
Return
Hierarchical Geodesic Models in Diffeomorphisms
.png){kind=icon}
PRE
AI
DOI：10.1007/s11263-015-0849-2.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
Hierarchical linear models (HLMs) are a standard approach for analyzing data where individuals are measured repeatedly over time. However, such models are only applicable to longitudinal studies of Euclidean data. This paper develops the theory of hierarchical geodesic models (HGMs), which generalize HLMs to the manifold setting. Our proposed model quantifies longitudinal trends in shapes as a hierarchy of geodesics in the group of diffeomorphisms. First, individuallevel geodesics represent the trajectory of shape changes within individuals. Second, a grouplevel geodesic represents the average trajectory of shape changes for the population. Our proposed HGM is applicable to longitudinal data from unbalanced designs, i.e., varying numbers of timepoints for individuals, which is typical in medical studies. We derive the solution of HGMs on diffeomorphisms to estimate individuallevel geodesics, the group geodesic, and the residual diffeomorphisms. We also propose an efficient parallel algorithm that easily scales to solve HGMs on a large collection of 3D images of several individuals. Finally, we present an effective model selection procedure based on cross validation. We demonstrate the effectiveness of HGMs for longitudinal analysis of synthetically generated shapes and 3D MRI brain scans.
Keywords:
Longitudinal modeling
Diffeomorphisms
Mixed-effects modeling
LDDMM
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
9.3
Papers:
3.9K
Citations:
2.8W