1. A cell image segmentation method, as performed by a processor of a computer system, comprising: receiving a cell image; performing a nuclei initialization step to find an internal marker and an external marker to obtain a potential nuclei and a potential cell boundary corresponding to the potential nuclei; calculating a gradient map of the received cell image; performing a filtering step on the gradient map to generate a filtered gradient map according to the potential nuclei and the potential cell boundary; performing a nuclei detection step by calculating watersheds of the filtered gradient map to obtain a segmented nuclei; performing a nuclei validation step by preserving a part of the segmented nuclei with relatively higher compactness and excluding another part of the segmented nuclei with relatively lower compactness to obtain a valid nuclei, wherein the nuclei initialization step comprises: performing a blob detection step to obtain a nuclei candidate; performing an outlier removal step to exclude an outlier of the nuclei candidate to obtain the internal marker; performing a distance transform step of the internal marker to obtain a distance map; and performing a cell boundary initialization step to obtain the external marker from the distance map.