Non-rigid curve correspondence for estimating heart motion

Abstract

The boundaries of many biological objects are two-dimensional curves which evolve non-rigidly with time. This paper contains a theory and experiments for estimating motion of such curves using local shape. Beginning from first principles, a symmetric and explicitly non-rigid formulation is developed. The formulation uses the topology of correspondences and its associated geometry. A numerical implementation of the resulting algorithm is also reported. The algorithm is used to estimate non-rigid motion of the endocardium in 21 MRI image sequences of normal and post-infarct dog hearts. Over 500 correspondences were computed. The measured average return error of the algorithm was less than 1 pixel.