A Statistical Framework for Elastic Shape Analysis of Spatio-Temporal Evolutions of Planar Closed Curves

We propose a new statistical framework for spatiotemporal modeling of elastic planar, closed curves. This approach combines two recent frameworks for elastic functional data analysis and elastic shape analysis. The proposed trajectory registration framework enables matching and averaging to quantify spatio-temporal deformations while taking into account their dynamic specificities. A key ingredient of this framework is a tracking method that optimizes the evolution of curves extracted from sequences of consecutive images to estimate the spatio-temporal deformation fields. Automatic estimation of such deformations including spatial changes (strain) and dynamic temporal changes (phase) was tested on simulated examples and real myocardial trajectories. Experimental results show significant improvements in the spatio-temporal structure of trajectory comparisons and averages using the proposed framework.