Three-dimensional coordinate subset correlation method based on tangent-plane constrained gradients for high-precision deformation measurement.

Conventional three-dimensional digital image correlation (3D-DIC) reconstructs deformation through image-domain stereo-temporal correlation and is susceptible to perspective-induced shape-function mismatch under complex surface geometry or significant deformation. This study extends three-dimensional coordinate subset correlation (3D-CSC) to stereo-DIC-based deformation measurement by establishing correspondence directly between reference and deformed object surfaces in 3D physical space. A tangent-plane-constrained surface-gradient reconstruction strategy and a 3D physical-space inverse compositional Gauss-Newton formulation are developed for efficient nonlinear optimization while preserving the constant-Hessian property. Numerical simulations and experimental results demonstrate that this method improves the measurement accuracy of displacement and strain and effectively suppresses deformation artifacts caused by projection effects.