Strain alignment: toward assessing mechanical plausibility of predicted displacement fields

Commonly used accuracy metrics for non-rigid registration such as target registration error (TRE) do not assess the mechanical plausibility of predicted deformations. We introduce a metric to quantify local coherence of deformation and complement existing measures of physical validity.

We propose the strain alignment metric, which evaluates local directional consistency of deformation by analyzing the principal directions and magnitudes of the Green strain tensor. The metric combines three components: (i) a sign term penalizing local flips between compression and extension, (ii) a magnitude term capturing relative variation in principal strain magnitude within a neighborhood and (iii) an angular term measuring non-directional alignment of principal strain directions. The metric is computed locally and summarized over the mesh. We compare it to the Jacobian determinant and strain norm on synthetic liver deformations registered using a deep learning-based method and a fast biomechanical FEM approach.

While both methods achieve comparable TRE, the proposed metric captures substantial differences in deformation coherence on the sample level that the Jacobian determinant and strain norm only show upon single mesh inspection. It is able to clearly differentiate the largely coherent deformation despite volume changes of the biomechanical method from the local inconsistencies of the learning-based method, including alternating compression and extension patterns.

Strain alignment provides complementary, interpretable information about the mechanical plausibility of predicted displacement fields. It enables quantitative assessment of local deformation coherence without requiring material assumptions and further highlights limitations of accuracy-only evaluation in non-rigid registration.