The Herculaneum scrolls were buried and carbonized by the eruption of Mount Vesuvius in A.D. 79 and represent the only classical library discovered in situ. Charred by the heat of the eruption, the scrolls are extremely fragile. Since their discovery two centuries ago, some scrolls have been physically opened, leading to some textual recovery but also widespread damage. Many other scrolls remain in rolled form, with unknown contents. More recently, various noninvasive methods have been attempted to reveal the hidden contents of these scrolls using advanced imaging. Unfortunately, their complex internal structure and lack of clear ink contrast has prevented these efforts from successfully revealing their contents. This work presents a machine learning-based method to reveal the hidden contents of the Herculaneum scrolls, trained using a novel geometric framework linking 3D X-ray CT images with 2D surface imagery of scroll fragments. The method is verified against known ground truth using scroll fragments with exposed text. Some results are also presented of hidden characters revealed using this method, the first to be revealed noninvasively from this collection. Extensions to the method, generalizing the machine learning component to other multimodal transformations, are presented. These are capable not only of revealing the hidden ink, but also of generating rendered images of scroll interiors as if they were photographed in color prior to their damage two thousand years ago. The application of these methods to other domains is discussed, and an additional chapter discusses the Vesuvius Challenge, a $1,000,000+ open research contest based on the dataset built as a part of this work
