Reduction of Noise‐Induced Bias in Displacement Estimation by Linear Off‐Pixel Digital Image Correlation

Abstract: A linear digital image correlation algorithm is proposed to eliminate noise‐induced bias in one‐dimensional translation estimation using noisy images. The algorithm uses linear interpolation for both initial and current images at off‐pixel positions and solves directly the displacement parameter by minimizing a sum‐of‐squared‐differences coefficient. Both analytical results and numerical simulations using synthetic image sets show that there is indeed no noise‐induced bias in the displacement estimation using the proposed algorithm if the off‐pixel positions in both images are chosen properly according to the relative displacement between two images. When the displacement is only known initially within a range of ±0.5 pixels from the actual displacement, an iterative procedure using the algorithm is able to obtain the displacement estimation with a residual bias that converges to the noiseless subpixel approximation bias. A further refinement of the off‐pixel analysis algorithm will be needed so the remaining residual bias due to subpixel approximation can also be significantly reduced.