On Biases in Displacement Estimation for Image Registration, with a Focus on Photomechanics

Image registration under small displacements is the keystone of several image analysis tasks such as optical flow estimation, stereoscopic imaging, or full-field displacement estimation in photomechanics. A popular approach consists in locally modeling the displacement field between two images by a parametric transformation and performing least-squares estimation afterward. This procedure is known as digital image correlation in several domains as in photomechanics. The present article is part of this approach. First, the estimated displacement is shown to be impaired by biases related to the interpolation scheme needed to reach subpixel accuracy, the image gradient distribution, as well as the difference between the hypothesized parametric transformation and the true displacement. A quantitative estimation of the difference between the estimated value and the actual one is of importance in application domains such as stereoscopy or photomechanics, which have metrological concerns. Second, we question the extent to which these biases could be eliminated or reduced. We also present numerical assessments of our predictive formula in the context of photomechanics. Software codes are freely available to reproduce our results. Although this paper is focused on a particular application field, namely photomechanics, it is relevant to various scientific areas concerned by image registration.

Automated summary

The article discusses the importance and limitations of image registration under small displacements in tasks such as optical flow estimation, stereoscopic imaging, and photomechanics. It highlights the significance of quantitatively evaluating the estimation biases and questions the potential for eliminating or reducing these biases. Additionally, numerical assessments of the predictive formula in the context of photomechanics are presented, with freely available software codes to reproduce the results.