Vertex Proportion Loss for Multi-class Cell Detection from Label Proportions

Learning from label proportions (LLP) is a weakly supervised classification task in which training instances are grouped into bags annotated only with class proportions. While this task emerges naturally in many applications, its performance is often evaluated on bags generated artificially by sampling uniformly from balanced, annotated datasets. In contrast, we study the LLP task in multi-class blood cell detection, where each image can be seen as a “bag” of cells and class proportions can be obtained using a hematocytometer. This application introduces several challenges that are not appropriately captured by the usual LLP evaluation regime, including variable bag size, noisy proportion annotations, and inherent class imbalance. In this paper, we propose the Vertex Proportion loss, a new, principled loss for LLP, which uses optimal transport to infer instance labels from label proportions, and a Deep Sparse Detector that leverages the sparsity of the images to localize and learn a useful representation of the cells in a self-supervised way. We demonstrate the advantages of the proposed method over existing approaches when evaluated in real and synthetic white blood cell datasets.