Optimal regularization parameter in approximate TPS interpolation

The thin plate splines (TPS) has been applied to landmark-based elastic image registration. However, TPS forces the corresponding landmarks to exactly match each other, which is problematic when the localization of landmarks is prone to some error. Approximating TPS (ATPS) has been proposed to weak the interpolation condition. In ATPS, the regularization parameter plays an important role. It controls the smoothness of the transformation. Unfortunately, how to estimate is not solved. In this paper, estimation of the optimal regularization parameter has been proposed. It combines two evaluation factors, smoothness and location error hypothesis testing, to evaluate transformation results using fuzzy integral. The optimal regularization parameter is the best value maximizing the evaluation function. Experiments of the artificial grids and medial images show that our technique is feasible.