4D Continuous Medial Representation Trajectory Estimation for Longitudinal Shape Analysis

Morphological change of anatomy over time has been of great interest for tracking disease progression, aging, and growth. Shape regression methods have shown great success to model the shape changes over time to create a smooth and representative shape trajectory of sparsely scanned medical images. Shape changes modeled by shape regression methods can be affected by pose changes of shapes caused by neighboring anatomies. Such pose changes can cause informative local shape changes to be obscured and neglected in longitudinal shape analysis. In this paper, we propose a method that estimates a continuous trajectory of medial surfaces with correspondence over time to track longitudinal pose changes and local thickness changes separately. A spatiotemporally continuous medial surface trajectory is estimated by integrating velocity fields from a series of continuous medial representations individually estimated for each shape in a continuous 3D shape trajectory. The proposed method enables straightforward analysis on continuous local thickness changes and pose changes of a continuous multi-object shape trajectory. Longitudinal shape analysis which makes use of correspondence and temporal coherence of the estimated continuous medial surface trajectory is demonstrated with experiments on synthetic examples and real anatomical shape complexes.