1. An apparatus for generating a mosaic picture of an object plane, comprising: a capturing device for portion-by-portion capturing of the object plane at a two-dimensional distribution of capturing positions by sequentially moving to the capturing positions along a capturing path using a motor, so as to acquire subimages which represent pictures of portions of the object plane which overlap, while allocating the capturing positions to the subimages, the capturing positions allocated to the subimages deviate from actual capturing positions in accordance with inaccuracies of the motor; and a processor for determining offset vectors between pairs of overlapping subimages by a similarity analysis of the overlapping subimages and for solving an optimization problem for finding an optimum set of capturing position variables for the subimages for minimizing a measure of a deviation between the offset vectors of the pairs of overlapping subimages and differences of the capturing position variables of the pairs of overlapping subimages, while complying with a secondary constraint for the capturing position variables which depends on error statistics statistically describing a distribution of a deviation between offsets between pairs of capturing positions allocated to the subimages, to which the motor moves immediately following each other, and actual offsets between corresponding pairs of actual capturing positions, wherein the secondary constraint limits, in dependence on the error statistics, the difference of capturing position variables for pairs of subimages which immediately follow one another along the capturing path.