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In this study, the authors propose an iterative registration algorithm with point-based representation. The task is to geometrically transform a mobile object to a stationary object. Without a good initial position for two shapes with high-curvature features, traditional point-based algorithms have many challenges, such as suffering from slow convergence or divergence. For these problems, the authors define a new distance function to describe the point-surface distance, where the point-surface shortest distance is considered. Then, a non-linear optimisation model is established to calculate the optimal transformation. Moreover, the convergence of the proposed algorithm is derived and analysed from the viewpoint of geometrical optimisation. The proposed method does not require surface representation, feature extraction, curvature computation and is more applicable when initial position is rough. Its efficiency and robustness are verified by a series of experiments.