中文摘要：

三维超声心动图技术能使医生直观地看到心脏整体和各部分的运动，在临床得到重视。在三维超声心动图技术中，如何定量的描述心脏中某个组织的运动状况极具临床意义。本研究提出了一种基于椭圆偏微分方程的二尖瓣三维运动估计方法。该方法直接在三维超声图像的位移场上进行了运动估计，避免了传统运动估计方法，如光流法，需要标定的缺点。本研究首先建立一个二次误差指标函数，然后利用变分法导出了三维空间下的一组椭圆型偏微分方程。这类方程有着比较成熟的数值解法，利用了有限差分法，对多个三维超声数据立方体进行了计算，结果证明这类方法是有效的。

英文摘要：

Three-dimensional echocardiography is widely used because it can give images of part or whole heart motions and indicate the complex structure of hearts. In this technology how to describe the motion of some part of the heart quantitatively is meaningful for diagnosis. In this paper we proposed a method of 3D motion estimation based on elliptic partial differential equation. It was computed on the displacement fields instead of on the optical flow fields, which needs calibration. First a new quadratic error functional was proposed in this paper, then, a set of elliptic partial differential equations was deduced by various calculus and solved by finite difference method. Our experiments showed consistent results with the estimation of the motion of mitral valve.