Quaternionic Spatiotemporal Filtering for Dense Motion Field Estimation in Ultrasound Imaging

Blood motion estimation provides fundamental clinical information to prevent and detect pathologies such as cancer. Ultrasound imaging associated with Doppler methods is often used for blood flow evaluation. However, Doppler methods suffer from shortcomings such as limited spatial resolution and the inability to estimate lateral motion. Numerous methods such as block matching and decorrelation-based techniques have been proposed to overcome these limitations. In this paper, we propose an original method to estimate dense fields of vector velocity from ultrasound image sequences. Our proposal is based on a spatiotemporal approach and considers 2D+t data as a 3D volume. Orientation of the texture within this volume is related to velocity. Thus, we designed a bank of 3D quaternionic filters to estimate local orientation and then calculate local velocities. The method was applied to a large set of experimental and simulated flow sequences with low motion (≈1 mm/s) within small vessels (≈1 mm). Evaluation was conducted with several quantitative criteria such as the normalized mean error or the estimated mean velocity. The results obtained show the good behaviour of our method, characterizing the flows studied.