The concept of tension is introduced in the framework of active contours with prior shape information, and it is used to improve image segmentation. In particular, two properties of this new quantity are shown: 1) high values of the tension correspond to undesired equilibrium points of the cost function under minimization and 2) tension decreases if a curve is split into two or more parts. Based on these ideas, a tree is generated whose nodes are different local minima of the cost function. Deeper nodes in the tree are expected to correspond to lower values of the cost function. In this way, the search for the global optimum is reduced to visiting and pruning a binary tree. The proposed method has been applied to the problem of fish segmentation from low quality underwater images. Qualitative and quantitative comparison with existing algorithms based on the Euler-Lagrange diffusion equations shows the superiority of the proposed approach in avoiding undesired local minima.