Minimal time problem for discrete crowd models with a localized vector field

In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localized on a fixed control set. We characterize the minimal time for a discrete crowd model, both for exact and approximate controllability. This leads to an algorithm that computes the control and the minimal time. We finally present a numerical simulation

Ambient Sound Helps: Audiovisual Crowd Counting in Extreme Conditions

Visual crowd counting has been recently studied as a way to enable people counting in crowd scenes from images. Albeit successful, vision-based crowd counting approaches could fail to capture informative features in extreme conditions, e.g., imaging at night and occlusion. In this work, we introduce a novel task of audiovisual crowd counting, in which visual and auditory information are integrated for counting purposes. We collect a large-scale benchmark, named auDiovISual Crowd cOunting (DISCO) dataset, consisting of 1,935 images and the corresponding audio clips, and 170,270 annotated instances. In order to fuse the two modalities, we make use of a linear feature-wise fusion module that carries out an affine transformation on visual and auditory features. Finally, we conduct extensive experiments using the proposed dataset and approach. Experimental results show that introducing auditory information can benefit crowd counting under different illumination, noise, and occlusion conditions. The dataset and code will be released. Code and data have been made availabl