Constrained registration is an active area of research and is the focus of this work. This note describes a non-rigid image registration framework for incorporating landmark constraints. Points that must remain stationary are selected, the user chooses the spatial extent of the inputs, and an automatic step computes the deformable registration, respecting the constraints. Parametrization of the deformation field is by an additive composition of a similarity transformation and a set of Gaussian radial basis functions. The bases' centers, variances, and weights are determined with a global optimization approach that is introduced. This approach is based on the particle filter for performing constrained optimization; it explores a series of states defining a deformation field that is physically meaningful (i.e., invertible) and prevents chosen points from moving. Results on synthetic two dimensional images are presented.