The extraction of 3D dimensional measurements based on a limited number of 2D X-ray radiographs of a part would offer a significant speed-up of quality control procedures in industry. However, there are challenges with respect to both measurements and uncertainties. This work addresses these challenges by creating an estimated numerical model of the imaged part on which dimensional measurements can be made. The numerical model is chosen as a parametric deformable model that encodes the expected shape variability of the parts resulting from the manufacturing process. The parameters and uncertainties of the numerical model of the imaged part are estimated by the registration of the computed projections of the model and the observed radiographs without the need of any segmentation. The registration requires the model, the initial parameters, and the observed radiographs. The proposed approach is applied to the inspection of turbine blades manufactured by investment casting, and in particular to the measurement of their wall thickness, which is a critical control. The deformable model consists in partitioning the inner ceramic core into multiple subparts, which may undergo a rigid body motion with respect to the master die. Wall thickness measurements are determined from the estimation of these rigid body motions. To assess the reliability of the proposed procedure, a repeatability study is performed. In addition, wall thickness measurements were compared to corresponding measurements from the surface of the metal boundary obtained by X-ray computed tomography. This surface was determined from a reconstructed tomogram using commercial software. Both analyses show that such measurements are reliable and efficient. Furthermore, residual differences between captured and computed projections reveal localized shape deviations from the CAD model, meaning that despite localized model errors, the approach is operable.