Robust variational model with weighted data term for degraded document binarization

Document image binarization remains a fundamental yet difficult issue, particularly when simultaneously facing multiple forms of degradations (e.g., noise, shadows, bleed-through and uneven background). This paper proposes a robust variational model for degraded document binarization, which consists of a weighted data term responsible for binarization, a robust regularization term accounting for character structure-preserving smoothness, and a penalty term ensuring the stable updating of the weight map toward the weight prior. In particular, the potential function for the data term is defined via local foreground/background centers of the input image. The regularization term is defined by gradient and a Huber loss weight function from robust statistics, where the scale parameter is estimated by the MAD estimator in robust regression. The weight prior is estimated from the input image, having the properties that it takes relatively large values around character borders and approaches to zero otherwise. The proposed variational model is proved to admit at least one solution within the space of functions of bounded variation. In the numerical implementation, the proposed model is split into two subproblems that are alternately solved via gradient descent and explicit finite differencing. Comprehensive experiments on nine public DIBCO datasets (2009 to 2014 and 2016 to 2018) show that the proposed model in general achieves higher binarization performance, in comparison to seven representative document binarization models based on partial differential equations/calculus of variations.