Accurate deflection measurement of plates using monocular vision and quadratic shape function-based homography

Abstract

Vision-based measurement methods have attracted increasing attention in the field of structural tests and health monitoring due to their non-contact nature and ability to capture full-field displacements. Typically, out-of-plane deflection measurement of plate structures requires two or more cameras, being costly and cumbersome to synchronize. To circumvent so, this paper proposes an accurate monocular vision-based method for measuring the out-of-plane deflection of plates using quadratic shape functions. The method employs quadratic polynomial functions to construct a homography matrix, enabling it to accommodate a wide range of out-of-plane deflection states—from rigid-body motion to complex nonlinear deformations—thus improving the accuracy and robustness of deflection measurements. The constructed homography matrix is solved iteratively using the classical digital image correlation algorithm, allowing for efficient estimation of the structure’s out-of-plane deflection field. The effectiveness of the proposed method is validated through both synthetic simulations and laboratory experiments on steel plates.