Non-stationary modeling for the separation of overlapped texts in documents

In this paper, we address the removal of severe back-to-front interferences in archival documents, when recto and verso images of the page are available. The problem is approached from a modeling point of view, considering the ideal images of the two separated texts as individual source patterns that overlap in the observed images through some parametric mixing operator. Earlier approaches were based on linear mixtures of the ideal reflectance maps, or of the ideal optical densities and absorptance maps, through unknown coefficients or blur kernels. Some approximations and/or partial user supervision were then adopted to jointly estimate the sources and the model parameters. Nevertheless, a feasible and reliable data model for this problem should at least be non-linear and space-variant, to cope with occlusions, ink saturation, and large variability of the mixing level. This is especially true for ancient documents affected by ink seeping (bleed-through). The search for such a model is still far from being concluded, or even impossible to pursue, due to the unavailability of information about the chemical and physical processes at the origin of the phenomenon. Hence, here, we propose the use of pixel-dependent parameters, within a model additive in the optical densities, to compensate not only for non-stationarity, but also for the lack or the imprecise knowledge of the non-linearity, and for modeling errors more in general.