Purpose: Landmark point-based registration is an important tool in medical image analysis and applications. An efficient and robust new method is sought that does not require optimization and is less susceptible to noise. Methods: A new quaternion-based affine registration algorithm for matching 3D point sets, a generalization of a previously reported method for 2D point sets, was developed. The new algorithm computes the exact affine transformation and the unknown correspondence between two 3D point sets but does not require any optimization. The method performs robustly in the presence of noise for non-degenerate cases. The method performs a reduction of general affine case to an orthogonal case, and then computes the unknown rotation using the quaternion representation of the 3D points. The method assumes no prior knowledge of point-wise correspondence between the two point sets. The algebraic and geometric concepts underlying the method are shown to be both clear and intuitive. Results: Experimental evaluation of the method was performed using both randomly generated synthetic 3D point sets and Stanford Bunny dataset. The algorithm performed well even for noisy data. A feasibility test was performed with medical MR scans showing promising results. Conclusion: The algorithm for point-based correspondence registration demonstrated robust results, even in noisy cases, and was shown to be feasible for use with medical images. © CARS 2010.