We study the ground-state (T = 0) morphologies in the d = 3 random-field Ising model (RFIM) using a computationally efficient graph-cut method. We focus on ground states which arise for disorder strengths lower or higher than the critical disorder strength at T = 0. These states consist of correlated “domains” of up and down spins which are separated by rough, fractal interfaces. They show novel scattering properties with a cusp singularity in the correlation function at short distances.