A Riemannian Framework for the Elastic Analysis of the Spatiotemporal Variability in the Shape and Structure of Tree-like 4D Objects

metric. By solving spatial registration in the ESRVF space, analyzing tree-like 4D objects can be reformulated as the problem of analyzing elastic trajectories in the ESRVF space. Based on this formulation, we develop a comprehensive framework for analyzing the spatiotemporal dynamics of tree-like objects, including registration and geodesic computation under large deformations and topological differences, statistical summarization through mean trajectories and modes of variation, and the synthesis of new, random tree-like 4D shapes. We demonstrate the effectiveness of the proposed framework on both synthetic 4D botanical tree models and real plant data, illustrating its robustness and practical applicability in capturing complex spatiotemporal shape evolution.