Giang Hoang | Searcharxiv

arXiv2022

F2SD: A dataset for end-to-end group detection algorithms

The lack of large-scale datasets has been impeding the advance of deep learning approaches to the problem of F-formation detection. Moreover, most research works on this problem rely on input sensor signals of object location and orientation rather than image signals. To address this, we develop a new, large-scale dataset of simulated images for F-formation detection, called F-formation Simulation Dataset (F2SD). F2SD contains nearly 60,000 images simulated from GTA-5, with bounding boxes and orientation information on images, making it useful for a wide variety of modelling approaches. It is also closer to practical scenarios, where three-dimensional location and orientation information are costly to record. It is challenging to construct such a large-scale simulated dataset while keeping it realistic. Furthermore, the available research utilizes conventional methods to detect groups. They do not detect groups directly from the image. In this work, we propose (1) a large-scale simulation dataset F2SD and a pipeline for F-formation simulation, (2) a first-ever end-to-end baseline model for the task, and experiments on our simulation dataset.

cs.CV↗

arXiv2015

An elliptic semilinear equation with source term and boundary measure data: the supercritical case

We give new criteria for the existence of weak solutions to an equation with a super linear source term \begin{align*}-Δu = u^q ~~\text{in}~Ω,~~u=σ~~\text{on }~\partialΩ\end{align*}where $Ω$ is a either a bounded smooth domain or $\mathbb{R}\_+^{N}$, $q\textgreater{}1$ and $σ\in \mathfrak{M}^+(\partialΩ)$ is a nonnegative Radon measure on $\partialΩ$. One of the criteria we obtain is expressed in terms of some Bessel capacities on $\partialΩ$. We also give a sufficient condition for the existence of weak solutions to equation with source mixed terms. \begin{align*} -Δu = |u|^{q\_1-1}u|\nabla u|^{q\_2} ~~\text{in}~Ω,~~u=σ~~\text{on }~\partialΩ\end{align*} where $q\_1,q\_2\geq 0, q\_1+q\_2\textgreater{}1, q\_2\textless{}2$, $σ\in \mathfrak{M}(\partialΩ)$ is a Radon measure on $\partialΩ$.

math.AP↗