中文摘要：

随着图像采集设备的发展和对图像分辨率要求的提高,人们对图像处理算法在收敛速度和鲁棒性方面提出了更高的要求.从优化的角度对Chan-Vese模型进行算法上的改进,即将共轭梯度法应用到该模型中,使得新算法有更快的收敛速度.首先,简单介绍了Chan-Vese模型的变分水平集方法的理论框架;其次,将共轭梯度算法引入到该模型的求解,得到了模型的新的数值解方法;最后,将得到的算法与传统求解Chan-Vese模型的最速下降法进行了比较.数值实验表明,提出的共轭梯度算法在保持精度的前提下有更快的收敛速度.

英文摘要：

As the development of the image acquisition device and the high re- quirements, people require more advanced image processing algorithms in terms of convergence rate and robustness. This paper improves the Chan-Vese model from the optimization aspect. The conjugate gradient method to the model is used, and thus the new algorithm has a better convergence rate. First, a brief introduction to the theoretical frame of the level set formulation of the Chan-Vese model is given. Secondly, the conjugate gradient method to the Chan-Vese model is intro- duced, and the new numerical solution is implemented. Finally, the algorithm with the gradient descent method is compared, which is the traditional solution for the Chan-Vese model. Numerical experiment shows that the proposed conjugate gra- dient method has a faster convergent rate on the premise that the same accuracy is preserved.