Robust Estimation of Transformation for Non-Rigid Registration

Abstract—We introduce a new transformation estimation algo-rithm using the estimator and apply it to non-rigid registra-tion for building robust sparse and dense correspondences. In the sparse point case, our method iteratively recovers the point cor-respondence and estimates the transformation between two point sets. Feature descriptors such as shape context are used to estab-lish rough correspondence. We then estimate the transformation using our robust algorithm. This enables us to deal with the noise and outliers which arise in the correspondence step. The transfor-mation is specified in a functional space, more specifically a re-producing kernel Hilbert space. In the dense point case for non-rigid image registration, our approach consists of matching both sparsely and densely sampled SIFT features, and it has particular advantages in handling significant scale changes and rotations. The experimental results show that our approach greatly outperforms state-of-the-art methods, particularly when the data contains se-vere outliers. Index Terms—Dense correspondence, estimator, non-rigid, outlier, registration, regularization