In this paper, we use partial-differential-equation-based filtering as a preprocessing and post processing strategy for computer-aided cytology. We wish to accurately extract and classify the shapes of nuclei from confocal microscopy images, which is a prerequisite to an accurate quantitative intranuclear (genotypic and phenotypic) and internuclear (tissue structure) analysis of tissue and cultured specimens. First, we study the use of a geometry-driven edge-preserving image smoothing mechanism before nuclear segmentation. We show how this filter outperforms other widely-used filters in that it provides higher edge fidelity. Then we apply the same filter, with a different initial condition, to smooth nuclear surfaces and obtain sub-pixel accuracy. Finally we use another instance of the geometrical filter to correct for misinterpretations of the nuclear surface by the segmentation algorithm. Our prefiltering and post filtering nicely complements our initial segmentation strategy, in that it provides substantial and measurable improvement in the definition of the nuclear surfaces.