We introduce the term cosegmentation which denotes the task of segmenting simultaneously the common parts of an image pair. A generative model for cosegmentation is presented. Inference in the model leads to minimizing an energy with an MRF term encoding spatial coherency and a global constraint which attempts to match the appearance histograms of the common parts. This energy has not been proposed previously and its optimization is challenging and NP-hard. For this problem a novel optimization scheme which we call trust region graph cuts is presented. We demonstrate that this framework has the potential to improve a wide range of research: Object driven image retrieval, video tracking and segmentation, and interactive image editing. The power of the framework lies in its generality, the common part can be a rigid/non-rigid object (or scene), observed from different viewpoints or even similar objects of the same class.