Closed-form, engine-portable uncertainty prediction of deformable image registration for dose accumulation in adaptive radiotherapy

Objective. Voxel-level uncertainty estimates of the deformation vector field (DVF) produced by commercial deformable image registration (DIR) engines are flagged as an open issue by AAPM TG-132 but seldom available, preventing principled propagation into accumulated dose-volume histograms (DVHs). We propose and validate an engine-portable per-voxel σ predictor for the DVF (μ) of a deterministic DIR, calibrated by one scalar f against landmark Target Registration Error (TRE), with no access to the engine's internals. Approach. The framework combines (i) an anisotropic Gaussian correlation kernel, longer along the cranio-caudal axis, generalising the isotropic kernel of Smolders et al. (2023); and (ii) a heuristic-residual σ_h=f[wR̃+(1−w)d̃] (default w=0.7), where R̃ combines a self-similarity descriptor residual with an image-gradient suppression factor and d̃ is |Jacobian determinant−1|, both normalised to [0,1]; σ_h is closed-form, computed from the image pair and the DVF without optimisation or training. For each combination of dataset and DIR engine (a cell), f is calibrated against TRE via grid search minimising the Landmark Expected Calibration Error (LECE). Main results. Across 4 publicly annotated computed tomography datasets (Lung-, Abdominal- and Liver-DIR-QA and DIR-LAB Castillo; 44,778 landmarks) and 4 DIR engines (ANTs SyNRA, ConvexAdam, uniGradICON, Elastix), with f fitted on other patients (5-fold cross-validation), the calibrated σ_h achieves, in the per-direction convention of Smolders et al., LECE within or below their 0.41–1.34mm range in all 16 cells (cases with final root-mean-square TRE ≤10mm retained). A constant σ calibrated likewise also meets this range, but the variation of σ_h raises the held-out log-likelihood in 13 cells; σ_h ranks landmarks by error only weakly (Spearman ρ=−0.11 to +0.34). Significance. A one-scalar, post-hoc calibration yields voxel-level DVF uncertainty for any deterministic DIR that exports its DVF, partly addressing the AAPM TG-132 gap; propagation into accumulated DVH bands is illustrated on one lung stereotactic body radiotherapy case.