On account of the dense distribution and blurred boundaries of nuclei in pathological images, nuclei instance segmentation remains a challenging task. Existing methods often fail to fully utilize information across points, lines, and regions. To fulfill the research gap, this paper proposes a novel multi-dimensional nuclei instance segmentation network (SES-Net). First, we introduce a three-branch network structure that includes a keypoint branch for precise localization of nuclei, an edge branch for describing the shape and contours of nuclei, and a mask branch for comprehensive characterization of nuclei regions. Next, we present a region optimization module (ROM) that effectively integrates keypoint and edge features to distinguish overlapping instances and refine segmentation masks. Finally, we describe a post-processing method that combines the ROM output with nuclei mask images to produce the final instance segmentation results. Extensive experiments validate the effectiveness of each component in SES-Net and demonstrate its promising performance on publicly available MoNuSeg, CoNSep and Kumar datasets.