beta-FFT: Nonlinear Interpolation and Differentiated Training Strategies for Semi-Supervised Medical Image Segmentation

Ming Hu, Jianfu Yin, Zhuangzhuang Ma, Jianheng Ma, Feiyu Zhu, Bingbing Wu, Ya Wen, Meng Wu, Cong Hu, Bingliang Hu, Quan Wang; Proceedings of the Computer Vision and Pattern Recognition Conference (CVPR), 2025, pp. 30839-30849

Co-training has achieved significant success in the field of semi-supervised learning; however, the *homogenization phenomenon*, which arises from multiple models tending towards similar decision boundaries, remains inadequately addressed. To tackle this issue, we propose a novel algorithm called **β-FFT** from the perspectives of data diversity and training structure.First, from the perspective of data diversity, we introduce a nonlinear interpolation method based on the **Fast Fourier Transform (FFT)**. This method generates more diverse training samples by swapping low-frequency components between pairs of images, thereby enhancing the model's generalization capability. Second, from the structural perspective, we propose a differentiated training strategy to alleviate the homogenization issue in co-training. In this strategy, we apply additional training with labeled data to one model in the co-training framework, while employing linear interpolation based on the **Beta (β)** distribution for the unlabeled data as a regularization term for the additional training. This approach enables us to effectively utilize the limited labeled data while simultaneously improving the model's performance on unlabeled data, ultimately enhancing the overall performance of the system.Experimental results demonstrate that **β-FFT** outperforms current state-of-the-art (SOTA) methods on three public medical image datasets.