The segmentation of white blood cells and their nuclei is still difficult and challenging for many reasons, including the differences in their colour, shape, background and staining techniques, the overlapping of cells, and changing cell topologies. This paper shows how these challenges can be addressed by using level set forces via edge-based geometric active contours. In this work, three level set forces-based (curvature, normal direction, and vector field) are comprehensively studied in the context of the problem of segmenting white blood cell nuclei based on geometric flows. Cell images are first pre-processed, using contrast stretching and morphological opening and closing in order to standardise the image colour intensity, to create an initial estimate of the cell foreground and to remove the narrow links between lobes and cell bulges. Next, segmentation is conducted to prune out the white blood cell nucleus region from the cell wall and cytoplasm by combining the theory of curve evolution using curvature, normal direction, and vector field-based level set forces and edge-based geometric active contours. The overall performance of the proposed segmentation method is compared and benchmarked against existing techniques for nucleus shape detection, using the same databases. The three level set forces studied here (curvature, normal direction, and vector field) via edge-based geometric active contours achieve F-index values of 92.09%, 91.13%, and 90.76%, respectively, and the proposed segmentation method results in better performance than all other techniques for all indices, including Jaccard distance, boundary displacement error, and Rand index.