A novel

robust algorithm for solving the non-rigid matching between two images is proposed.This method represents the image by sets of feature points.Due to a special characteristic of the thin-plate spline(TPS)—it can decompose a deformation into the affine and non-affine components.TPS for non-rigid spatial mapping is chosen.A convex TPS bending energy function describing the problem is derived and a one-to-one two-way matching constraint on the match matrix is enforced.By minimizing the above bending energy

we can jointly estimate the TPS mapping parameters and match matrix between the two feature point-sets of the images.We utilize the deterministic annealing which emerged from the statistical physics to solve the optimization problem.Embedded within a deterministic annealing framework

and by introducing an annealing temperature to control the degree of fuzziness of the match matrix

the algorithm not only improves the robustness but also reduces the chances of getting trapped in local minima.We compare our method with the polynomial quasi-exhaustive exploration (PQEE) algorithm proposed by Michigan University

and the results show that PQEE's performance deteriorates much faster with the increase of degrees of deformation

amounts of noise and percentage of outliers.We also conduct experiments on matching of hand-shapes images and registration of anatomical brain MR images.The experimental results demonstrate the validation and robustness of the algorithm.