Abstract: We present an interactive method to restore severely damaged historical parchments. When damaged by heat in a fire, such manuscripts undergo a complex deformation and contain various geometric distortions such as wrinkling, buckling, and shrinking, rendering them nearly illegible. They cannot be physically flattened due to the risk of further damage. We propose a virtual restoration framework to estimate the non-rigid deformation the parchment underwent and to revert it, making reading the text significantly easier whilst maintaining the veracity of the textual content. We estimate the deformation by combining automatically extracted constraints with user-provided hints informed by domain knowledge. We demonstrate that our method successfully flattens and straightens the text on a variety of pages scanned from a 17th century document which fell victim to fire damage.