  Crowd counting is usually handled in a density map regression fashion, which
is supervised via a L2 loss between the predicted density map and ground truth.
To effectively regulate models, various improved L2 loss functions have been
proposed to find a better correspondence between predicted density and
annotation positions. In this paper, we propose to predict the density map at
one resolution but measure the density map at multiple resolutions. By
maximizing the posterior probability in such a setting, we obtain a log-formed
multi-resolution L2-difference loss, where the traditional single-resolution L2
loss is its particular case. We mathematically prove it is superior to a
single-resolution L2 loss. Without bells and whistles, the proposed loss
substantially improves several baselines and performs favorably compared to
state-of-the-art methods on four crowd counting datasets, ShanghaiTech A & B,
UCF-QNRF, and JHU-Crowd++.
