I have a circular label pasted on a cylindrical object. In the image, this circle looks like a asymmetrical ellipse. I know the radius of the cylinder and that of the label. What mapping do I need to do to "stretch" this ellipse onto a circle? 
This image shows mapping of the ellipse onto a circle
If we assume for simplicity that the picture is straight on (i.e. tha axis of the cylinder is vertical) and the distance camera-object is much larger than the bending (no perspective idstortion), you can, for each $x$, measure the height $h$ of the vertical line through it and shift the line to its correct place, i.e. to $x'$ where $x'^2+(h/2)^2=r^2$, where $r$ is half the maximal height.