We propose a new method based on graph cuts for joint segmentation of monotonously growing or shrinking shapes in time series of noisy images. By introducing directed infinite links connecting pixels at the same spatial locations in successive image frames, we impose shape growth/shrinkage constraint in graph cuts. Minimization of energy computed on the resulting graph of the image sequence yields globally optimal segmentation. We validate the proposed approach on two applications: segmentation of melting sea ice floes from a time series of multimodal satellite images and segmentation of a growing brain tumor from sequences of 3D multimodal medical scans. In the latter application, we impose an additional inter-sequences inclusion constraint by adding directed infinite links between pixels of dependent image structures.