Two novel computational techniques, harmonic cut and regularized centroid transform, are developed for segmentation of cells and their corresponding substructures observed with an epi-fluorescence microscope. Harmonic cut detects small regions that correspond to small subcellular structures. These regions also affect the accuracy of the overall segmentation. They are detected, removed, and interpolated to ensure continuity within each region. We show that interpolation within each region (subcellular compartment) is equivalent to solving the Laplace equation on a multi-connected domain with irregular boundaries. The second technique, referred to as the regularized centroid transform, aims to separate touching compartments. This is achieved by adopting a quadratic model for the shape of the object and relaxing it for final segmentation.