The current document is directed to methods and systems that acquire an image containing text with curved text lines to generate a corresponding corrected image in which the text lines are straightened and have a rectilinear organization. The method may include identifying a page sub-image within the text-containing image, generating a text-line-curvature model for the page sub-image that associates inclination angles with pixels in the page sub-image, generating local displacements, using the text-line-curvature model, for pixels in the page sub-image, and transferring pixels from the page sub-image to a corrected page-sub-image using the local displacements to construct a corrected page sub-image in which the text lines are straightened and in which the text characters and symbols have a rectilinear arrangement.