This paper considers the termination criterion problem in curve evolution methods. First, we investigate the general scheme of curve evolution methods by analysing energy variation. Then, conventional termination criteria are discussed and some drawbacks are identified. Furthermore, the relationship between stability and convergence is discussed based on the Lax equivalence theorem. We then propose a new termination criterion based on a Bayesian approach and the use of global image information. The application of the proposed criterion in a given curve evolution scheme is presented. Experimental results show that the proposed termination criterion is effective and accurate compared to conventional criteria. In addition, it is successful in alleviating typical difficulties such as premature termination and weak edge leakage because of the use of global information in controlling the termination process.