Algorithm 1: Fixed-Point Iteration Algorithm

Input: $I_1^l,I_2^l,U^{l-1}$, l is the current level. Output: $U^l$. Initialization: Upsample $U^{l-1}$ to the size in level l, then deform the moving image: $I_2^l\left(x\right)=I_2^l(x+U^{l-1}\left(x\right))$;