Although essential in the medical domain, protecting patient privacy often restricts data sharing across institutions. Moreover, publicly available datasets often suffer from poor and inconsistent annotation-particularly for image segmentation that requires precise pixel- or voxel-level annotations. As a result, deep learning models are frequently trained on single-institution datasets that are small and lack the heterogeneity of broader patient populations, which limits their generalizability. Federated learning (FL) enables collaborative model training across institutions by sharing model parameters instead of raw medical data. However, it requires uniform model architectures, which may not align with local hardware or software, and still exposes privacy risks through parameter sharing. Further, coordination across institutions with varying data volumes and annotation standards remains challenging, and exchanging model weights-especially for large models-is costly and slow. To address these limitations, we propose DCFed, a data-centric, semi-supervised framework that avoids sharing private data and model parameters by leveraging pseudo-labeling and uncertainty estimation on publicly available unannotated datasets. In our experiments, we use a modified U-Net with residual blocks, atrous spatial pyramid pooling, and convolutional block attention modules at the client level. DCFed improves performance by up to 8.9% on a breast cancer ultrasound dataset and 3.7% on a skin cancer dermoscopy dataset over local training. Notably, DCFed outperforms conventional FL methods such as FedAvg and FedNova across multiple clients in both tasks. In conclusion, DCFed surpasses both centralized training on local datasets and parameter-sharing FL approaches across institutions, establishing a scalable and privacy-preserving solution for real-world medical image segmentation.