We present a generative document-specific approach to character analysis and recognition in text lines. Our main idea is to build on unsupervised multi-object segmentation methods and in particular those that reconstruct images based on a limited amount of visual elements, called sprites. Our approach can learn a large number of different characters and leverage line-level annotations when available. Our contribution is twofold. First, we provide the first adaptation and evaluation of a deep unsupervised multi-object segmentation approach for text line analysis. Since these methods have mainly been evaluated on synthetic data in a completely unsupervised setting, demonstrating that they can be adapted and quantitatively evaluated on real text images and that they can be trained using weak supervision are significant progresses. Second, we demonstrate the potential of our method for new applications, more specifically in the field of paleography, which studies the history and variations of handwriting, and for cipher analysis. We evaluate our approach on three very different datasets: a printed volume of the Google1000 dataset [19,46], the Copiale cipher [2, 27] and historical handwritten charters from the 12th and early 13th century [6,44].