Unwanted motion of the probe with respect to the sample is a ubiquitous problem in scanning probe and scanning transmission electron microscopies, causing both linear and nonlinear artifacts in experimental images. We have designed a procedure to correct these artifacts by using orthogonal scan pairs to align each measurement line-by-line along the slow scan direction, by fitting contrast variation along the lines. We demonstrate the accuracy of our algorithm on both synthetic and experimental data and provide an implementation of our method.