Crowd Counting in the Frequency Domain

This paper investigates crowd counting in the frequency domain, which is a novel direction compared to the traditional view in the spatial domain. By transforming the density map into the frequency domain and using the properties of the characteristic function, we propose a novel method that is simple, effective, and efficient. The solid theoretical analysis ends up as an implementation-friendly loss function, which requires only standard tensor operations in the training process. We prove that our loss function is an upper bound of the pseudo sup norm metric between the ground truth and the prediction density map (over all of their sub-regions), and demonstrate its efficacy and efficiency versus other loss functions. The experimental results also show its competitiveness to the state-of-the-art on five benchmark data sets: ShanghaiTech A & B, UCF-QNRF, JHU++, and NWPU. Our codes will be available at: wbshu/Crowd Counting in the Frequency Domain DNN Ground truth density map Predicted density map 𝑙𝑜𝑠𝑠 = න ℝ 2 |𝜑 𝑔 𝒕 -𝜑 𝑝 𝒕 |𝑑𝒕 Backpropagation Characteristic function Characteristic function 𝜑 𝑔 𝜑 𝑝