Elastic registration is a difficult problem in image registration technology. An elastic point registration method using the Hausdorff distance is presented in this paper. With B-splines as the deformation model, the proposed method is able to handle elastic deformations between the images to be registered. Since no correspondence is required to be established between two point sets, the method is robust to outliers. In addition, a sequential updating strategy is introduced to further speed up the elastic registration method by dividing the source image and the grid of control points into separate blocks. The performance of the proposed method is demonstrated and validated in three experiments, a synthetic image registration experiment, a hand-drawn character registration experiment, and a brain MRI image registration experiment. While these results are somewhat preliminary, they clearly demonstrate the applicability of our method to real world tasks involving feature-based elastic registration.