DM-Count reduced the error of the state-of-the-art published result by approximately16%.

Eq. 6 in our paper is Lemma 2.1, pg 84. We will cite and clarify.

In crowd counting, each training image contains multiple people, where each person is annotated by a dot. Existing crowd counting methods need to use a Gaussian to smooth each annotated dot or to estimate the likelihood of every pixel given the annotated point. In this paper, we show that imposing Gaussians to annotations hurts generalization performance. Instead, we propose to use Distribution Matching for crowd COUNTing (DM-Count). In DM-Count, we use Optimal Transport (OT) to measure the similarity between the normalized predicted density map and the normalized ground truth density map. To stabilize OT computation, we include a Total Variation loss in our model. We show that the generalization error bound of DM-Count is tighter than that of the Gaussian smoothed methods. In terms of Mean Absolute Error, DM-Count outperforms the previous state-of-the-art methods by a large margin on two large-scale counting datasets, UCF-QNRF and NWPU, and achieves the state-of-the-art results on the ShanghaiTech and UCF-CC50 datasets. DM-Count reduced the error of the state-of-the-art published result by approximately 16%.

DM-Count and investigate the robustness of different methods to noisy annotations. Assume for all x D and g G we have |g ( x) | B . We propose the following five lemmas which are essential for proving the proposed theorems. Lemmas A, B, C and D give the Lipschitz constants of different loss functions. Consider the dual form of Eq. (15) W ( µ, ν) = max α The first inequality in Eq. (20) is achieved because The second equality in Eq. (20) is achieved because We restate Theorem 1 in the main paper below.

Instead, we propose to use Distribution Matching for crowd COUNTing (DM-Count).

Eq. 6 in our paper is Lemma 2.1, pg 84. We will cite and clarify.

In crowd counting, each training image contains multiple people, where each person is annotated by a dot. Existing crowd counting methods need to use a Gaussian to smooth each annotated dot or to estimate the likelihood of every pixel given the annotated point. In this paper, we show that imposing Gaussians to annotations hurts generalization performance. Instead, we propose to use Distribution Matching for crowd COUNTing (DM-Count). In DM-Count, we use Optimal Transport (OT) to measure the similarity between the normalized predicted density map and the normalized ground truth density map.