Abstract We present a new point matching algorithm for robust nonrigid registration. The method iteratively recovers the point correspondence and estimates the transformation between two point sets. In the fifirst step of the iteration, feature descriptors such as shape context are used to establish rough correspondence. In the second step, we estimate the transformation using a robust estimator called L2E. This is the main novelty of our approach and it enables us to deal with the noise and outliers which arise in the correspondence step. The transformation is specifified in a functional space, more specififically a reproducing kernel Hilbert space. We apply our method to nonrigid sparse image feature correspondence on 2D images and 3D surfaces. Our results quantitatively show that our approach outperforms state-ofthe-art methods, particularly when there are a large number of outliers. Moreover, our method of robustly estimating transformations from correspondences is general and has many other applications.