In the context of document image analysis, image binarization is an important preprocessing step for other document analysis algorithms, but also relevant on its own by improving the readability of images of historical documents. While historical document image binarization is challenging due to common image degradations, such as bleedthrough, faded ink or stains, achieving good binarization performance in a timely manner is a worthwhile goal to facilitate efficient information extraction from historical documents. In this paper, we propose a recurrent neural network based algorithm using Grid Long Short-Term Memory cells for image binarization, as well as a pseudo F-Measure based weighted loss function. We evaluate the binarization and execution performance of our algorithm for different choices of footprint size, scale factor and loss function. Our experiments show a significant trade-off between binarization time and quality for different footprint sizes. However, we see no statistically significant difference when using different scale factors and only limited differences for different loss functions. Lastly, we compare the binarization performance of our approach with the best performing algorithm in the 2016 handwritten document image binarization contest and show that both algorithms perform equally well.