registrationdiffer

Registrationdiffer is a term used in registration science to denote a quantitative measure of the discrepancy between two registered states of a dataset or image. It captures how much the underlying alignment differs when comparing two registration results or methods, after both have been transformed into a common coordinate system.

Formally, suppose two datasets A and B are each registered to a reference space by transformations T_A and T_B, with parameter vectors p_A and p_B. The registrationdiffer D is defined as a distance metric d(p_A, p_B) in the transformation parameter space. Common choices include the L2 (Euclidean) distance d(p_A, p_B) = ||p_A - p_B||_2 or an L1 variant. More sophisticated versions measure geodesic distance on the manifold of admissible transformations or use a weighted combination of weight differences.

Calculation involves: choosing a parameterization for the registration (rigid, affine, nonrigid), computing registration results for each dataset, extracting parameter vectors, and applying the distance metric. In practice, registrationdiffer serves as a quick proxy for alignment quality between methods or as a criterion to compare iterative refinements.

Applications are common in medical imaging, remote sensing, and multimodal data fusion, where comparing registration outcomes helps assess robustness and reproducibility. Limitations include dependence on the chosen parameterization and metric, and the possibility that a small parameter difference does not always correspond to meaningful image alignment. In reporting, it is best paired with direct alignment errors such as target registration error.