中文摘要：

从最优化理论的角度来看, 目前求解图像分割的测地线活动轮廓（geodesic active contour, GAC）模型大多采用固定步长的最速下降算法. 而众所周知, 该算法收敛速度较慢, 这在能量泛函的梯度较小时尤为明显. 对求解GAC模型的快速算法进行了研究. 首先, 回顾了GAC模型的演化方程; 随后, 将共轭梯度（conjugate gradient, CG）算法引入到GAC模型的求解中, 形成一种新的求解图像分割问题的数值方法, 即GAC模型的CG算法; 最后, 通过试验对比传统的数值方法, 表明CG算法具有良好的收敛性.

英文摘要：

From the viewpoint of optimization, most methods to deal with the image segmentation problem based on the geodesic active contour （GAC） model adopt the steepest descent algorithm with constant step-size. It is well known that the steepest descent algorithm converges relatively slowly, especially when the gradient of the energy functional is small. The fast algorithm to solve the GAC model is studied. First, after recalling the GAC model and corresponding evolution equations, a discrete form of the evolution equations is proposed. Then, by introducing the conjugate gradient （CG） method to the model, a novel fast algorithm is proposed. Finally, several numerical experiments are conducted to compare with the traditional numerical method, which validates that the proposed CG algorithm has a better performance.