On biases in displacement estimation for image registration, with a focus on photomechanics - Extended version

Image registration under small displacements is embodied in many image analysis tasks, such as optical flow estimation, stereoscopic imaging, or in photomechanics. A wide family of methods performs registration through local least-squares estimation of a parametric transformation. The present article is part of this approach. Its contribution is twofold. First, the estimated displacement is shown to be impaired by bias and uncertainty terms related to sensor noise, interpolation scheme needed to reach subpixel accuracy, image gradient distribution, as well as difference between the hypothesized parametric transformation and the true displacement. To this end, we generalize results from the literature on stereo-imaging, we reexamine the so-called fattening effect, and we present in a unified work several results from the photomechanics literature, in particular from the digital image correlation (DIC) community. We also establish the link with Savitzky-Golay filtering. Second, we question the extent to which these biases can be eliminated or reduced. We also present numerical assessments of our pre-dictive 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 interested in image registration.