Proximal Mapping Loss: Understanding Loss Functions in Crowd Counting & Localization

Crowd counting and localization involve extracting the number and distribution of crowds from images or videos using computer vision techniques. Most counting methods are based on density regression and are based on an ``intersection'' hypothesis, i.e., one pixel is influenced by multiple points in the ground truth, which is inconsistent with reality since one pixel would not contain two objects. This paper proposes Proximal Mapping Loss (PML), a density regression method that eliminates this hypothesis. {PML} divides the predicted density map into multiple point-neighbor cases through the nearest neighbor, and then dynamically constructs a learning target for each sub-case via proximal mapping, leading to more robust and accurate training. {Furthermore}, PML is theoretically linked to various existing loss functions, such as Gaussian-blurred L2 loss, Bayesian loss, and the training schemes in P2PNet and DMC, demonstrating its versatility and adaptability. Experimentally, PML significantly improves the performance of crowd counting and localization, and illustrates the robustness against annotation noise. The code is available at https://github.com/Elin24/pml.