Medical ultrasound is a non-invasive low-cost image modality used in diagnostic applications. It has become the preferred modality in cardiology. Motion estimation techniques may be applied to the echocardiographic images to estimate 2D blood motion and measure myocardial strain. Optical flow techniques may be used, but the choice of algorithm need to be carefully selected to achieve the required robustness and accuracy. This thesis compares the performance of structure tensor based methods for calculating the optical flow motion estimation in synthetic and optical images, as well as in realistic synthetic echocardiographic image sequences. The methods for calculating the structure tensor are gradients, Riesz transform and quadrature filters. Estimation of optical flow from the structure tensors is done by Lucas-Kanade and the eigenvector method. The Riesz transform is an extension of the Hilbert transform to higher dimensions. It is shown that it extracts the same information as the gradient, but without the high frequency amplification. Experiments are performed on a synthetic no-noise images, the Middlebury dataset containing both synthetic and optical images, and on realistic synthetic echocardiographic images. The Riesz and quadrature tensor are found to outperform the gradient in homogeneous regions in low-noise images. However, on the realistic synthetic echocardiographic images they perform equal with the gradient. Thus no significant evidence for replacing the gradient with the Riesz transform or quadrature filters for motion estimation in echocardiography are found.