Robust Displacement Vector Estimation including a Statistical Error Analysis

The determination of displacement vectors is an important task in the context of temporal image sequence analysis, as well as in stereoscopic vision. The relations between images taken from an image sequence or a stereo pair are conceptually represented by a displacement vector field which establishes a pairwise correspondence between points in both regarded images. Most approaches for the determination of displacement vector fields include a first step, where individual measurements of local displacements are performed. Often these initial measurements are subsequently combined in a way that exploits a priori knowledge, e.g. using spatial smoothness constraints for the resulting vector field. However, the very first step, i.e. the determination of individual displacement vectors is a process whose results are in general afflicted by errors. The extent and specific type of error that is to be expected varies largely between the different displacement vectors, as the reliability is largely dependent on the local characteristics of the image signal. If reliability or accuracy measures can be assigned to these estimates, this is advantageous compared to the approach of detecting and suppressing erroneous measurements (’outliers’) in subsequent processing steps. The present contribution is oriented towards the joint estimation of individual displacement vectors and their corresponding reliability measures. Extending the results of Singh and Allen [1], these estimation theoretic relations can be fully derived from a statistical image model.