On div-curl regularization for motion estimation in 3-D volumetric imaging

We consider the classical optical ow algorithm due to Horn and Schunck for estimating the motion of brightness patterns between image pairs. We use a modi-ed smoothness condition based on the divergence and curl of the velocity eld. In previous work, we have developed well-posed stochastic state-space models for these optical ow methods in two dimensions. This paper extends our results to 3-D. We rst show that by using the rst order DIV-CURL spline, it is not possible to obtain a rst order linear diierential well-posed model in 3-D. Next, we employ the second order DIV-CURL spline smoothness condition and develop well-posed state-space models.