CADER: CAD-constrained elastic registration for voxel-accurate sparse-view 3D surface reconstruction in minutes

Computed tomography (CT) is a standard for high-precision metrology in industrial non-destructive testing (NDT), enabling sub-voxel reconstruction of internal geometries in complex aerospace and biomedical components. However, attaining such accuracy typically requires thousands of X-ray projections and long acquisition and reconstruction times, particularly for high-attenuation materials such as nickel alloys. This work presents a computationally efficient alternative to volumetric CT reconstruction based on projection-space 3D–2D elastic registration of a prior CAD model to sparse CT projections. The voxel-wise reconstruction and segmentation steps are replaced by a hierarchical surface deformation model that morphs a CAD mesh using multi-scale radial basis functions (RBFs) followed by constrained vertex-level refinement (texture fitting). A differentiable X-ray renderer based on soft rasterization simulates forward projections and provides analytical gradients of mutual-information and edge-based objectives for gradient-based optimization with stochastic batching and sub-image sampling. A geometry-driven view-optimization heuristic further improves sparse-view performance using only the rigidly registered CAD input. Across representative industrial datasets, measurement accuracy is equivalent to CT reconstruction and segmentation using filtered back projection while using only 12–20 projections. Wall thickness measurements relative to microCT segmentation (filtered back projection) deviate by less than 1 voxel for simple parts, though both methods measure thickness within one voxel compared to coordinate-measuring-machine (CMM) measurements. For complex industrial components such as a turbine blade, mean wall thickness deviation is ∼1 voxel vs. conventional microCT segmentation. The proposed framework reduces image acquisition time to as little as 22 s with total processing time less than five minutes (a hundred-fold improvement relative to conventional microCT for the same accuracy), establishing a realistic pathway toward high-throughput CT metrology without requiring full CT reconstruction.