Abstract: In the field of medical image processing，elastic registration based on Euler-Lagrange has a wide range of application and is central to many challenges.Traditional algorithm has low accuracy，because it uses difference to calculate the image gradients.In this paper，the Hermite difference operator is used to calculate the image gradients.Smooth constraints to outside force are utilized in every iteration.The experiment proves that this method not only has a high accuracy，but also high robustness.

Key words: elastic registration, Euler-Lagrange equation, difference, Hermite derivative operator

摘要： 基于Euler-Lagrange方程的医学图像弹性配准算法在临床中有着广泛的应用，它是医学图像处理的研究热点问题。传统算法采用差分近似计算图像的梯度误差较大，本文利用Hermite微分算子计算图像的梯度信息；并在迭代过程中对外力进行平滑约束。通过对模拟和真实数据的实验表明改进方法不仅具有较高的计算精度，而且具有很强的鲁棒性，适合于医学图像的弹性配准。

关键词: 弹性配准, Euler-Lagrange方程, 差分, Hermite微分算子