  We discuss a method to reconstruct two-dimensional proton bunch densities
using vertex distributions accumulated during LHC beam-beam scans. The $x$-$y$
correlations in the beam shapes are studied and an alternative luminosity
calibration technique is introduced. We demonstrate the method on simulated
beam-beam scans and estimate the uncertainty on the luminosity calibration
associated to the beam-shape reconstruction to be below 1\%.
