Nucleus segmentation is fundamental for interpreting biomedical images, which further enables the analysis of cell structures and disease recognition. In this research, we pro pose Fourier Residual UNet m (FRunetm), an enhanced version of the Fourier Residual UNet (FRunet) architecture enhanced with the Convolutional Block Attention Module Squeeze and excitation attention (CBAM-SE) attention mechanism, for improving segmentation precision on complex biomedical images. The FRunetm model was compared with three other deep learning models, which are Classic U-Net, SE U-Net, FRunet with a classic attention mechanism. All models were evaluated based on a spectrum of performance metrics, including accuracy, Dice coefficient, F1 score, loss, mean intersect over union (IoU), precision, and recall. Results show a marked segmentation performance improvement with the U-Net based architecture that employs the sophisticated attention mechanism (CBAM-SE). The current work outlines the performance of several models and the potential impact on the segmentation of medical images.