Cardiac motion assessment from echocardiographic image sequences by means of the structure multivector

We recently contributed an algorithm for the estimation of cardiac deformation from echocardiographic image sequences based on the monogenic signal. By exploiting the phase information instead of the pixel intensity, the algorithm was robust to the temporal contrast variations normally encountered in cardiac ultrasound. In this paper we propose an improvement of that framework making use of an extension of the monogenic signal formalism, called structure multivector. The structure multivector models the image as the superposition of two perpendicular waves with associated amplitude, phase and orientation. Such a model is well adapted to describe the granular pattern of the characteristic speckle noise. The displacement is computed by solving the optical flow equation jointly for the two image phases. A local affine model accounts for typical cardiac motions as contraction/expansion and shearing; a coarse-to-fine B-spline scheme allows for a robust and effective computation of the model parameters and a pyramidal refinement scheme helps deal with large motions. Performance was evaluated on realistic simulated cardiac ultrasound sequences and compared to our previous monogenic-based algorithm and classical speckle tracking. Endpoint-error was used as accuracy metric. With respect to them we achieved error reductions of 13% and 30% respectively.