Binarization is an important step in reading text documents automatically through optical character recognition. Old document images often suffer from degradations that make their binarization a challenging task. In this paper, a new binarization technique for degraded document images is presented. The proposed technique is based on active contours evolving according to intrinsic geometric measures of the document image. The image contrast that is defined by the local image maximum and minimum is used to automatically generate the initialization map of our active contour model; an average thresholding is also used to produce the final delineation and binarization. The proposed implementation benefits from the level set framework, which allows the simultaneous application of a large variety of forces at the stroke–background interface. Our binarization method involves the combination of those forces in a specific way. The efficiency of the proposed method is shown on both recent and historical document images of the Document Image Binarization Contest (DIBCO) datasets that include different types of degradations. The results are compared to a number of known techniques from the literature.