Thin electronic-packaging films can develop substantial warpage during heating. Three-dimensional digital image correlation (3D-DIC) reconstructs the full displacement field, yet displacement-plane fitting still introduces curvature-dependent projection errors into the calculated strain. The proposed estimator differentiates matched reference and heated surfaces in common material coordinates and compares their first fundamental forms. Directional Green–Lagrange strains are then averaged over a fixed region of interest before temperature regression. Both global-coordinate and local-plane DPF varied with curvature in the cylindrical benchmarks. The surface-metric CTE remained invariant at the reporting resolution across the tested bending directions and regions of interest. Coordinate-noise simulations quantified precision after field averaging and regression. In the reported copper-foil sequence, the surface metric gave an RMSE of $0.170$ $\mathrm{ppm}{\mathrm{K}}^{-1}$ relative to the NIST copper reference, which was lower than either DPF baseline. The method measures directional CTE during smooth developable warpage without prescribing its shape, curvature, or bending direction.