New loss functions for medical image registration based on VoxelMorph

Optimization of loss function is one of the research directions in medical image registration. A loss function of registration is the sum of two terms: a similarity term Lsim (Φ) and a smoothing term Lsmooth(Φ). From variational method in differential geometry, control function is essential to generate better registration field Φ. Here, we propose a new registration loss function with novel smoothing terms using VoxelMorph based on control function and Laplacian operator. We divide the process into two steps. The first step is based on Laplacian operator. We replace the gradient of registration field Φ in Lsmooth (Φ) by the Laplacian of Φ. In the second step, we add the term control function F to the Lsmooth (Φ) in the first step, which is the key contribution of our method. We verify our method on two datasets including ADNI and IBSR, and obtain excellent improvement on MR image registration, with better convergence and gets higher average Dice and lower percentage of non-positive Jacobian locations compared with original loss function.