This work proposes an image segmentation model based on active contours. For a better handling of regions where anatomical structures are poorly contrasted and/or missing, we propose to incorporate a priori shape information in a variational formulation. Based on a level set approach, the proposed functional is composed of four terms. The first one makes the level set keep the important signed distance function property, which is necessary to guarantee the good level set evolution. Doing so results in avoiding the classical re-initialization process, contrary to most existing works where a partial differential equation is used instead. The second energy term contains the a priori information about admissible shapes of the target object, the latter being integrated in the level set evolution. An energy that drives rapidly the level set towards objects of interest is defined in the third term. A last term is defined on prior shapes thanks to a complete and modified Mumford-Shah model. The segmentation model is derived by solving the Euler-Lagrange equations associated to the functional minimization. Efficiency and robustness of our segmentation model are validated on synthetic images, digitally reconstructed images, and real image radiographs. Quantitative evaluations of segmentation results are also provided, which also show the importance of prior shapes in the context of image segmentation.