Image reconstruction from an elastically distorted scan

Abstract We consider the problem of inverting the artifacts associated with scanning a page from an open book, i.e. ’xeroxing’. The process typically leads to a non-uniform combination of distortion, blurring and darkening owing to the fact that the page is bound to a stiff spine that causes the sheet of paper to be bent inhomogeneously. Complementing purely data-driven approaches, we use knowledge about the geometry and elasticity of the curved sheet to pose and solve a minimal physically consistent inverse problem to reconstruct the image. Our result relies on three dimensionless parameters, all of which can be measured for a scanner and show that we can improve on the data-driven approaches. More broadly, our results might serve as a ‘textbook’ example and a tutorial of how knowledge of generative mechanisms can speed up the solution of inverse problems.