1. A method for obtaining an image of a smoothed-out document from an image of this document when it is crumpled, said method comprising: determining a three-dimensional geometric model of the surface of the crumpled document by triangulation of three-dimensional points defined from the pattern of a target extracted from the image of this document when it is crumpled, determining a projection of the three-dimensional geometric model on a so-called acquisition plane including: defining a polygon that defines the contour of the projected surface of smoothed-out document, identifying points of the three-dimensional geometric model among all the three-dimensional points as being points of the polygon when these points define edges that belong to only one triangle of the three-dimensional geometric model, defining for each point of the geometric model internal to the closed polygon a weighted linear combination of their neighbours, and minimizing of error of this projection under constraints of preservation of the distances between the three-dimensional points of the three-dimensional geometric model and preservation of the angles between the various edges that connect these three-dimensional points by decreasing the divergence between the weighted linear combination of the neighbours of said internal points of the three-dimensional geometric model and linear combinations of the points of the projection.