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

Chafik Samir, Sebastian Kurtek, Justin Strait, Shantanu H. Joshi; Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR) Workshops, 2016, pp. 10-18

We propose a new statistical framework for spatio-temporal 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 spatial-temporal deformation fields. Automatic estimation of such spatio-temporal deformations (including spatial changes or strain and dynamic temporal changes or phase) was tested on several simulated examples and real myocardial trajectories. Experimental results showed significant improvements in the spatio-temporal structure of trajectory comparisons and averages using the proposed framework.