Incorporating hard constraints into non-rigid registration via nonlinear programming

Non-rigid image registration is a key technique in medical image analysis. In conventional non-rigid registration, the whole image is deformed in a non-rigid fashion. However, in some clinical applications, the registration process is required to maintain rigidity in some parts of the image (e.g. bones) while other parts of the image (e.g. soft tissues) can deform in a non-rigid fashion. In this paper, we employ nonlinear programming techniques to solve the registration problem efficiently while ensuring feasibility of the solution with respect to rigidity constraints. Our approach differs from others from an optimization perspective: Unlike the frequently used regularization formulation that incorporates soft constraints into energy function, we impose the local rigidity requirements as hard constraints. The constrained optimization problem is solved by nonlinear programming. The nonlinear programming formulations allow us to exploit the constraints in order to reduce the dimensionality of the optimization problem. In addition, we use dense registration framework to control the deformation at every voxel explicitly. Therefore, unconstrained voxels are not affected by the method. Experimental results from synthetic and MR images of the knee show that our method converges to the optimal solution faster and satisfies the rigidity constraints of the transformation during registration process. The result is a more realistic estimation of rigid and non-rigid deformations.