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 using between 12-20 projections. Wall thickness measurements relative to micro CT 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 1̃ voxel vs conventional microCT segmentation. The proposed framework reduces image acquisition time to as little as 22 s with total processing time being 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 necessitating full CT reconstruction.