Understanding the behaviour of cells is an important problem for biologists. Significant research has been done to facilitate this by automating the segmentation of microscopic cellular images. Bright-field images of cells prove to be particularly difficult to segment due to features such as low contrast, missing boundaries and broken halos. In this paper, we present two algorithms for automated segmentation of cellular images. These algorithms are based on a graph-partitioning approach where each pixel is modelled as a node of a weighted graph. The method combines an effective Region Force with the Laplacian and the Total Variation boundary forces, respectively, to give the two models. This region force can be interpreted as a conditional probability of a pixel belonging to a certain class (cell or background) given a small set of already labelled pixels. For practicality, we use a small set of only background pixels from the border of cell images as the labelled set. Both algorithms are tested on bright-field images to give good results. Due to faster performance, the Laplacian-based algorithm is also tested on a variety of other datasets including fluorescent images, phase-contrast images and 2- and 3-D simulated images. The results show that the algorithm performs well and consistently across a range of various cell image features such as the cell shape, size, contrast and noise levels.