提出统一变分框架，实现稀疏标注下的高效图像分割。
A Unified Variational Framework for Deep Weakly Supervised Image Segmentation
- 基于单纯形约束的Potts模型与光滑边界正则化构造凸平滑能量函数。
- 通过再生核希尔伯特空间构建模糊隶属度，有效捕捉强度分布差异。
- 在无需真实分割图情况下，性能优于基线方法，适合弱监督场景。
我们提出一种在稀疏像素级标注下进行图像分割的统一变分框架。该方法基于单纯形约束的Potts模型与光滑轮廓正则项，生成一个凸且平滑的能量泛函，可作为弱监督深度学习中的训练损失，或通过迭代方法高效优化。通过再生核希尔伯特空间（RKHS）中的函数延拓问题构建模糊隶属度函数，将稀疏标签融入数据保真项，有效建模非均匀强度统计特性。推导出的标准网络训练离散损失在实验中表现出鲁棒性，相比非训练和部分交叉熵（PCE）基线方法实现一致提升，在无需真实分割图的情况下达到相当性能。
原文摘要 · Abstract (English)
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.
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