Distribution Matching for Crowd Counting Supplementary Material

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.