1. A machine-implemented method for reducing image distortion in magnetic resonance imaging (MRI), comprising: receiving a first MRI image and a second MRI image, wherein the first MRI image and the second MRI image were acquired using different gradient fields; estimating displacements of voxels between the first MRI image and the second MRI image by minimizing a cost function expressing a cost of the displacements; reducing distortion in an MRI image using the estimated displacements; and making the MRI image having reduced distortion available.