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Optimal Transport Minimization: Crowd Localization on Density Maps for Semi-Supervised Counting

Wei Lin · Antoni B. Chan

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The accuracy of crowd counting in images has improved greatly in recent years due to the development of deep neural networks for predicting crowd density maps. However, most methods do not further explore the ability to localize people in the density map, with those few works adopting simple methods, like finding the local peaks in the density map. In this paper, we propose the optimal transport minimization (OT-M) algorithm for crowd localization with density maps. The objective of OT-M is to find a target point map that has the minimal Sinkhorn distance with the input density map, and we propose an iterative algorithm to compute the solution. We then apply OT-M to generate hard pseudo-labels (point maps) for semi-supervised counting, rather than the soft pseudo-labels (density maps) used in previous methods. Our hard pseudo-labels provide stronger supervision, and also enable the use of recent density-to-point loss functions for training. We also propose a confidence weighting strategy to give higher weight to the more reliable unlabeled data. Extensive experiments show that our methods achieve outstanding performance on both crowd localization and semi-supervised counting. Code is available at

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