Magnetic resonance imaging (MRI) of pediatric brain provides invaluable information for early normal and abnormal brain development. Longitudinal neuroimaging has spanned various research works on examining infant brain development patterns. However, studies on predicting postnatal brain image evolution remain scarce, which is very challenging due to the dynamic tissue contrast change and even inversion in postnatal brains. In this paper, we unprecedentedly propose a dual image intensity and anatomical structure (label) prediction framework that nicely links the geodesic image metamorphosis model with sparse patch-based image representation, thereby defining spatiotemporal metamorphic patches encoding both image photometric and geometric deformation. In the training stage, we learn the 4D metamorphosis trajectories for each training subject. In the prediction stage, we define various strategies to sparsely represent each patch in the testing image using the training metamorphosis patches; while progressively incrementing the richness of the patch (from appearance-based to multimodal kinetic patches). We used the proposed framework to predict 6, 9 and 12-month brain MR image intensity and structure (white and gray matter maps) from 3 months in 10 infants. The proposed framework showed promising preliminary prediction results for the spatiotemporally complex, drastically changing brain images.