In this paper, we address the segmentation of tumor subtypes in whole slide images (WSI) by utilizing incomplete label proportions. Specifically, we utilize `partial' label proportions, which give the proportions among tumor subtypes but do not give the proportion between tumor and non-tumor. Partial label proportions are recorded as the standard diagnostic information by pathologists, and we, therefore, want to use them for realizing the segmentation model that can classify each WSI patch into one of the tumor subtypes or non-tumor. We call this problem ``learning from partial label proportions (LPLP)'' and formulate the problem as a weakly supervised learning problem. Then, we propose an efficient algorithm for this challenging problem by decomposing it into two weakly supervised learning subproblems: multiple instance learning (MIL) and learning from label proportions (LLP). These subproblems are optimized efficiently in the end-to-end manner. The effectiveness of our algorithm is demonstrated through experiments conducted on two WSI datasets.

翻译：在本文中，我们通过利用不完整的标签比例来解决全切片图像中肿瘤亚型的分割问题。具体而言，我们使用“部分”标签比例，该比例给出了肿瘤亚型之间的比例，但未给出肿瘤与非肿瘤之间的比例。部分标签比例是病理学家记录的标准诊断信息，因此我们希望利用它们来实现能够将每个WSI块分类为肿瘤亚型或非肿瘤的分割模型。我们将这一问题称为“从部分标签比例中学习”，并将其形式化为一个弱监督学习问题。随后，我们通过将该问题分解为两个弱监督学习子问题：多实例学习和从标签比例中学习，提出了一种针对这一具有挑战性问题的有效算法。这些子问题以端到端的方式高效优化。通过在两个WSI数据集上进行的实验，证明了我们算法的有效性。