Barycentric Subspace Analysis: A New Symmetric Group-Wise Paradigm for Cardiac Motion Tracking

In this paper, we propose a novel approach to study cardiac motion in 4D image sequences. Whereas traditional approaches rely on the registration of the whole sequence with respect to the first frame usually corresponding to the end-diastole (ED) image, we define a more generic basis using the barycentric subspace spanned by a number of references images of the sequence. These subspaces are implicitly defined as the locus of points which are weighted Karcher means of \(k+1\) references images. We build such subspace on the cardiac motion images, to get a Barycentric Template that is no longer defined by a single image but parametrized by coefficients: the barycentric coordinates. We first show that the barycentric coordinates - the coefficients of the projection of the motion during a cardiac sequence - define a meaningful signature for group-wise analysis of dynamics and can efficiently separate two populations. Then, we use the barycentric template as a prior for regularization in cardiac motion tracking, efficiently reducing the error of tracking between end-systole and end-diastole by almost 40 % as well as the error of the evaluation of the ejection fraction. Finally, to best exploit the fact that multiple reference images allow to reduce the registration displacement, we derived a symmetric and transitive registration that can be used both for frame-to-frame and frame-to-reference registration and further improves the accuracy of the registration.