A scalar function formulation for optical flow: applications to X-ray imaging

The author presents results from a new formulation for determining velocities from a time-sequence of X-ray projection images of an incompressible fluid. Starting with the conservation of mass principle, and physics of X-ray projection, the author derives a motion constraint equation for projection imaging, a practical special case of which is shown to be the Horn and Schunck´s optical flow constraint. The formulation is particularly efficient, as the flow field is obtained from a 90 degrees rotation applied to the gradient of a scalar function. It is shown that if specific criteria are met, in addition to normal flow which is commonly recoverable, the tangential component of optical flow is also recoverable, without the need for smoothness. An algorithm is presented to illustrate this. Preliminary results from the optical flow formulation applied to synthetic images, as well as contrast-injected X-ray images of flowing fluid, in a cylindrical phantom are presented