Due to the finite size of the probe tip, atomic force microscopy (AFM) images of biomolecules, and other structures similar in size, are laterally enlarged. We use mathematical morphology, a non-linear image processing method, to model the interaction between probe tip and sample. Zn a typical imaging situation, baseline dimensions are most affected by the probe and widths can be 80% tip and 20% molecule. Using the morphological model and a known tip, we can restore the image so that it more closely resembles the actual surface. Morphological restoration is ideal in some regions, giving the exact sample surface, and improved in others. In the case of a carbon probe, restoration increases the perfectly obtained surface area by as much as 160 times. Following restoration, lateral widths at fixed heights are improved by as much as 75%. Restoration greatly improves image resolution even if one uses probes consisting of very small candidate structures, e.g., nanotubes and Bucky balls. The tip imaging process is also modeled, and we find that calibration spheres should be larger than the molecules of interest and that for many tips, there is little or no advantage to using smaller spheres. A blood plasma protein, fibrinogen, is modeled, and AFM and restored images of single molecules are computed.