Optical flow restoration of X-ray images of the heart using the theory of convex projections

The authors propose a method for computing the interframe optical flow (OF) of digitized X-ray image sequence of the heart injected with radio-opaque dye. An OF equation which allows for brightness change is presented, and it is shown that it can be solved by the theory of projections onto convex sets by assuming that: (1) the OF field varies smoothly; (2) the rate of change of brightness is proportional to the image brightness; and (3) the OF is locally linear. This approach makes it possible to determine both the interframe OF and the brightness changes due to heart motion perpendicular to the image plane. The local linearity constraint makes it possible to measure the translational, rotational, divergent, and shear components of regional wall motions. These components are measured from the flow parameters of the linear equations and an be used as a feature set to characterize normal and abnormal motion