Parametric estimation of 2-D motion field on ultrasonic images using spatially smoothed regression model and respiration

An extension of a previously presented algorithm for estimating instantaneous 2-D motion fields in the ultrasonography of internal organs is proposed. In the previous algorithm, the motion field was modeled as a regression random process with respect to the respiratory signal, and utilized spatially independent unknown coefficients. However, the value of these coefficients should vary with spatial smoothness, which enables a spatial constraint to be applied. In the proposed extension, the regression coefficients are defined as random variables, i.e. Gaussian-Markov random field (GMRF), with unknown scale factors, allowing a computationally stable estimation algorithm to be constructed.