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Binarization is a well-known image processing task, whose objective is to separate the foreground of an image from the background. One of the many tasks for which it is useful is that of preprocessing document images in order to identify relevant information, such as text or symbols. The wide variety of document types, alphabets, and formats makes binarization challenging. There are multiple proposals with which to solve this problem, from classical manually-adjusted methods, to more recent approaches based on machine learning. The latter techniques require a large amount of training data in order to obtain good results; however, labeling a portion of each existing collection of documents is not feasible in practice. This is a common problem in supervised learning, which can be addressed by using the so-called Domain Adaptation (DA) techniques. These techniques take advantage of the knowledge learned in one domain, for which labeled data are available, to apply it to other domains for which there are no labeled data. This paper proposes a method that combines neural networks and DA in order to carry out unsupervised document binarization. However, when both the source and target domains are very similar, this adaptation could be detrimental. Our methodology, therefore, first measures the similarity between domains in an innovative manner in order to determine whether or not it is appropriate to apply the adaptation process. The results reported in the experimentation, when evaluating up to 20 possible combinations among five different domains, show that our proposal successfully deals with the binarization of new document domains without the need for labeled data.