A systematic method for the detection and segmentation of microcalcifications in mammograms is presented. It is important to preserve size and shape of the individual calcifications as exactly as possible. A reliable diagnosis requires both rates of false positives as well as false negatives to be extremely low. The proposed approach uses a two-stage algorithm for spot detection and shape extraction. The first stage applies a weighted difference of Gaussians filter for the noise-invariant and size-specific detection of spots. A morphological filter reproduces the shape of the spots. The results of both filters are combined with a conditional thickening operation. The topology and the number of the spots are determined with the first filter, and the shape by means of the second. The algorithm is tested with a series of real mammograms, using identical parameter values for all images. The results are compared with the judgement of radiological experts, and they are very encouraging. The described approach opens up the possibility of a reproducible segmentation of microcalcifications, which is a necessary precondition for an efficient screening program.