The registration of free-form shapes by the iterative closest point algorithm (ICP) has attracted much attention from the computer vision and image-processing community since it was first proposed in 1992. Many methods, mainly based on incorporating invariants described in a single coordinate frame have been devised to improve the accuracy and efficiency of the algorithm. In this paper, a novel method to improve image registration is proposed based on rigid constraints derived from geometric properties of correspondence vectors synthesized into a singe coordinate frame. False matches, which occur in almost every iteration of the ICP algorithm, are eliminated through properties of the motion. For an accurate estimation of the geometric parameters of the motion, the Monte Carlo method is used in con-junction with a median filter. Experimental results based on both synthetic data and real images show that the improved method can effectively eliminate false matches, is accurate, robust, and efficient for the registration of free-form shapes with small motions.