ESTIMATION OF THE VELOCITY-FIELD OF 2-DIMENSIONAL DEFORMABLE MOTION

For a deformable motion, the velocities of neighboring points are different in general. The traditional smoothness constraints which minimize the spatial derivatives of the velocity are not applicable. A new way is proposed to integrate the motion fundamental constraint and the deformation linear constraint. An iterative algorithm based on the maximum a posteriori (MAP) estimation criterion is proposed to estimate the velocity field of a two-dimensional (2D) deformable motion. Based on the statistical approach, the relative weights of the two constraints used in the estimation process can be represented by a single parameter. Methods to avoid the critical problem of determining the region size for which the linear constraint holds are discussed. The constraint propagation property is also used to overcome this problem by assuming that the flow field is analytic. A promising application for optical flow techniques is to visualize the 2D heart motion quantitatively. The 2D echocardiographic images taken by the short-axis view are used in the experiments to study the performance of the proposed algorithm. The results of using the method proposed by Horn and Schunck are also given for comparison.