Comments on: A locally constrained radial basis function for registration and warping of images

In a recent paper, Siddiqui et al. introduced a kernel function to be used as a radial basis function (RBF) in image registration tasks. This function is mainly designed so that the resulting deformation is fairly distributed inside its support. The important property of positive definiteness is checked in the paper erroneously, so that the conclusions inferred are wrong. In this communication, we discuss this point and some other methodological errors in the formulation. In addition, we provide some insights into the importance of positive definiteness, concluding that this property may not be critical, or may even be worthless, in certain interpolation problems.

Research highlights
► The RBF kernel proposed by Siddiqui et al. (2009) is not positive definite as claimed.
► A positive definite kernel always induces invertible interpolation matrices.
► For varying-width RBF kernels, positive definiteness does not assure invertibility.