De nition of a 4D continuous polar transformation for the tracking and the analysis of LV motion

A 4D polar transformation is de ned to describe the left ventricle (LV) motion and a method is presented to estimate it from sequences of 3D images. The transformation is de ned in 3D-planispheric coordinates by a small number of parameters involved in a set of simple linear equations. It is continuous and regular in time and space, periodicity in time can be imposed. The local motion can be easily decomposed into a few canonical motions (centripetal contraction, rotation around the long-axis, elevation). To recover the motion from original data, the 4D polar transformation is calculated using an adaptation of the Iterative Closest Point algorithm. We present the mathematical framework and a demonstration of its feasability on a gated SPECT sequence.