Segmenting individual cell nuclei from microscope images normally involves volume labelling of the nuclei with a DNA stain. However, this method often fails when the nuclei are tightly clustered in the tissue, because there is little evidence from the images on where the borders of the nuclei are. In this paper we present a method which solves this limitation and furthermore enables segmentation of whole cells. Instead of using volume stains, we used stains that specifically label the surface of nuclei or cells: lamins for the nuclear envelope and alpha-6 or beta-1 integrins for the cellular surface. The segmentation is performed by identifying unique seeds for each nucleus/cell and expanding the boundaries of the seeds until they reach the limits of the nucleus/cell, as delimited by the lamin or integrin staining, using gradient-curvature flow techniques. We tested the algorithm using computer-generated objects to evaluate its robustness against noise and applied it to cells in culture and to tissue specimens. In all the cases that we present the algorithm gave accurate results.