Noninvasive multilevel geometric regularization of mesh-based three-dimensional shape measurement

Finite element stereo digital image correlation (FE-SDIC) requires a crucial calibration phase in which the initial CAD needs to be updated to fit the actual shape of the specimen. On the one hand, the use of a FE mesh facilitates the coupling of measurements with simulation tools, while on the other hand, it provides a unique, fine description of both the geometry and the displacement, which often makes the shape measurement problem highly ill-posed. As a remedy, we propose a hybrid isogeometric-FE strategy that can measure a shape in terms of spline functions while considering as an input and output the analysis-suitable FE mesh. Making use of the appealing spline refinement procedures and of Bezier-based operators, multilevel smooth spline discretizations are built concurrently with the initial FE subspace and related to the multiscale images used for the initialization of the shape measurement. It results in a geometrically sound regularization which provides a spline parametrization of the optimal shape along with its FE twin. A noninvasive implementation from an existing FE-SDIC code is also detailed. The performance of the proposed method is assessed on real images and comparisons are made with other published techniques to prove its efficiency.