A Framework for Uncertainty and Validation of 3-D RegistrationMethods Based on Points and Frames

  • Authors:
  • Xavier Pennec;Jean-Philippe Thirion

  • Affiliations:
  • Inria, B.P. 93, 2004 route des Lucioles, 06902 Sophia Antipolis Cedex, France. E-mail: Xavier.Pennec@sophia.inria.fr;Inria, B.P. 93, 2004 route des Lucioles, 06902 Sophia Antipolis Cedex, France. E-mail: Xavier.Pennec@sophia.inria.fr

  • Venue:
  • International Journal of Computer Vision
  • Year:
  • 1997

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Abstract

In this paper, we propose and analyze several methods to estimate arigid transformation from a set of 3-D matched points or matchedframes, which are important features in geometric algorithms. Wealso develop tools to predict and verify the accuracy of theseestimations. The theoretical contributions are: an intrinsic model ofnoise for transformations based on composition rather than addition;a unified formalism for the estimation of both the rigidtransformation and its covariance matrix for points or framescorrespondences, and a statistical validation method to verify theerror estimation, which applies even when no “ground truth” isavailable. We analyze and demonstrate on synthetic data that ourscheme is well behaved. The practical contribution of the paper isthe validation of our transformation estimation method in the case of3-D medical images, which shows that an accuracy of the registrationfar below the size of a voxel can be achieved, and in the case ofprotein substructure matching, where frame features drasticallyimprove both selectivity and complexity.