Magnetic resonance (MR) images often exhibit grayscale nonuniformities, caused by radio frequency (RF) coil design or acquisition sequences. Many algorithms to remove these nonuniformities have been proposed in the past decade. However, only minor attention has been given to the performance evaluation of existing methods. We derive a link between the estimation performance and underlying image structure. For a piecewise constant 1D signal model with equal size regions we demonstrate that the variance in estimation grows as M/sup 2/ , where M is the number of regions. In 2D case the growth becomes linear in M.