Karyotype analysis is a widespread procedure in cytogenetics to assess the possible presence of genetics defects. The procedure is lengthy and repetitive, so that an automatic analysis would greatly help the cytogeneticist routine work. Still, automatic segmentation and full disentangling of chromosomes are open issues. We propose an automatic procedure to obtain the separated chromosomes, which are then ready for a subsequent classification step. The segmentation is carried out by means of a space variant thresholding scheme, which proved to be successful even in presence of hyper- or hypo-fluorescent regions in the image. Then a greedy approach is used to identify and resolve touching and overlapping chromosomes, based on geometric evidence and image information. We show the effectiveness of the proposed method on routine data: 90% of the overlaps and 92% of the adjacencies are resolved, resulting in a correct segmentation of 96% of the chromosomes.