Riemannian Nonlinear Mixed Effects Models: Analyzing Longitudinal Deformations in Neuroimaging

Area of Science:

• Machine Learning
• Statistics
• Medical Imaging

Background:

• Manifold-valued data analysis is crucial for computer vision tasks like activity recognition and medical imaging.
• Parametric models for manifold data are emerging, offering advantages in small sample sizes.
• Existing manifold regression models are limited to cross-sectional data, posing challenges for longitudinal studies.

Purpose of the Study:

• To generalize non-linear mixed effects models for manifold-valued responses in longitudinal data analysis.
• To develop computationally tractable estimation schemes for these models.
• To demonstrate the utility of the proposed model for both group and individual longitudinal analyses.

Main Methods:

• Generalization of non-linear mixed effects models to manifold-valued responses (f : R^d -> M).
• Derivation of underlying model formulations and estimation algorithms.
• Application and validation on longitudinal brain imaging data.

Main Results:

• Successful generalization of mixed effects models to manifold-valued longitudinal data.
• Demonstration of benefits for both group-level and individual-level analysis.
• Computationally tractable methods for analyzing longitudinal data on manifolds, especially Symmetric Positive Definite (SPD) manifolds.

Conclusions:

• The developed model effectively addresses the limitations of fixed-effects models in longitudinal manifold data analysis.
• This work provides a computationally efficient framework for longitudinal analysis of manifold-valued measurements.
• The approach is particularly beneficial for analyzing longitudinal data in medical imaging, such as SPD brain imaging data.