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

We propose a new method to estimate a rigid transform from a set of 3-D matched points or matched frames, and we concentrate on the analysis of the uncertainty of the estimated transform. The theoretical contributions are an intrinsic model of noise for transformations based on composition rather than addition, a unified formalism for the estimation of both the rigid transform and its covariance matrix for points or frames correspondences, and also a statistical validation method to verify the error estimation, which applies even when no "ground truth" is available. The practical contribution is the validation of our transform estimation method in the case of 3-D medical images, which shows that a precision of the registration, far below the size of a voxel, can be achieved.<<ETX>>

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