We propose a novel variational approach based on a level set formulation of the Mumford-Shah functional and shape priors. We extend the functional by a labeling function which indicates image regions in which the shape prior is enforced. By minimizing the proposed functional with respect to both the level set function and the labeling function, the algorithm selects image regions where it is favorable to enforce the shape prior. By this, the approach permits to segment multiple independent objects in an image, and to discriminate familiar objects from unfamiliar ones by means of the labeling function. Numerical results demonstrate the performance of our approach.