用于深度弱监督图像分割的统一变分框架

中文摘要 AI 辅助

我们提出了一种用于稀疏像素级监督下图像分割的统一变分框架。该方法基于具有平滑周长正则化器的单纯形约束Potts模型，产生一个凸的、平滑的能量泛函，可作为弱监督深度学习范式中的训练损失或用迭代方法有效优化。通过在再生核希尔伯特空间（RKHS）中构建模糊隶属函数将稀疏标签纳入数据保真项，能有效捕获不均匀强度统计。实验表明，训练标准网络的离散损失比非训练和部分交叉熵（PCE）基线更稳健且持续改进，无需真实分割图像即可实现可比性能。

英文摘要

We propose a unified variational framework for image segmentation under sparse pixel-level supervision. Our method is based on a simplex-constrained Potts model with a smooth perimeter regularizer, yielding a convex, smooth energy functional that can be used as a training loss in weakly supervised deep learning paradigms or optimized efficiently using iterative methods. Sparse labels are incorporated into the data fidelity term by constructing a fuzzy membership function via a function extension problem in a Reproducing Kernel Hilbert Space (RKHS), which can effectively capture inhomogeneous intensity statistics. The derived discrete loss for training standard networks demonstrates robustness and consistent improvements over non-training and partial cross-entropy (PCE) baselines in experiments, achieving comparable performance without requiring ground-truth segmentation images.

发表机构

• The Hong Kong University of Science and Technology（香港科技大学）
• Hetao Institute of Mathematics and Interdisciplinary Sciences（河套数学与交叉科学研究所）
• Georgia Institute of Technology（佐治亚理工学院）
• Xiangtan University（湘潭大学）
• Norwegian Research Center（挪威研究中心）

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