Motion Analysis of Echocardiograms Using a Local-Affine, Spatio-Temporal Model

We present a new method for estimating heart motion from two-dimensional (2D) echocardiographic sequences. It is inspired by the Lucas-Kanade algorithm for optical flow which estimates motion parameters over a sliding window. However, instead of assuming that the motion is constant within the analysis window, we consider a model that is locally affine and can account for typical heart motions such as dilation/contraction and shear. Another refinement is spatial adaptivity which is achieved by estimating displacement vectors at multiple scales and selecting the most promising fit. The affine parameters are estimated in the least squares sense using a separable spatial (resp., spatio-temporal) B-spline window. This particular choice is motivated by the fact that the B-splines are nearly isotropic (Gaussian-like) and that they satisfy a two-scale equation. We use this latter property to derive a wavelet-like algorithm that leads to a fast computation of B-spline-weighted inner products and moments at dyadic scales, which speeds up our method considerably. We test the algorithm on synthetic and real ultrasound sequences and show that it compares favorably with other methods, such as Lucas-Kanade and Horn-Schunk.