中文摘要：

作为经典Snake模型的一个变体，梯度矢量流（gradient vector flow，简称GVF）Snake在扩大Snake轮廓的捕捉范围和深度凹陷区域的收敛上具有卓越的性能，但GVF Snake在初始化时存在一个临界点问题：在目标内部的临界点必须在初始Snake轮廓的内部；在目标外部的临界点必须在Snake轮廓的外部。否则，Snake轮廓将不能收敛到正确的结果，对GVF Snake的临界点问题进行探讨，详细分析了临界点的影响因素，指出GVF场只有在合适的条件下才是有效的；证明了相关文献中从粘性流体力学的Navier-Stokes方程来解决临界点问题的理论基础是不对的：还给出了临界点问题的一个简单、有效的解决方案，并用实验证明了其有效性。

英文摘要：

Gradient vector flow （GVF） snake shows high performance at capture-range enlarging and boundary concavity convergence, however, the initial contours encounter a so-called critical point problem （CPP）. The initial contour must contain the critical points inside the object and exclude those outside the object, otherwise, the final result would be far from the expected. This paper investigates the CPP of the GVF snake and points out that, serving as an external force field for snake models, gradient vector flow could be effective only under some restrictions. Also, it is proved that the theoretical foundation, the Navier-Stokes equation for viscous fluid flow, for the solution to this CPP in literatures is incorrect. Finally, an empirical solution to the CPP is presented and its performance is validated by experiments.