3D displacement fields estimation of three-dimensional cardiac echocardiographic images based on elliptic partial differential equation

Three-dimensional echocardiography is a promising technique for quantitative analysis of heart functions because it can visualize the complex structure of the hearts intuitively. Within this new technical how to describe the motion of some part of the heart quantitatively is meaningful. This paper proposes a method of 3D motion estimation based on elliptic partial differential equation. It detects the displacement fields instead of the optical flow fields, which needs calibrated for. First a new quadratic error functional is proposed in this paper; then, it leads to a set of elliptic partial differential equations by variation calculus. Using finite difference method, this algorithm is possible to evaluation the motion of mitral valve.