arXiv subjects

Xin Zhan

Publications and source records attributed to Xin Zhan.

21 records · Page 2Linked to original sources

arXiv2022

Ret3D: Rethinking Object Relations for Efficient 3D Object Detection in Driving Scenes

Current efficient LiDAR-based detection frameworks are lacking in exploiting object relations, which naturally present in both spatial and temporal manners. To this end, we introduce a simple, efficient, and effective two-stage detector, termed as Ret3D. At the core of Ret3D is the utilization of novel intra-frame and inter-frame relation modules to capture the spatial and temporal relations accordingly. More Specifically, intra-frame relation module (IntraRM) encapsulates the intra-frame objects into a sparse graph and thus allows us to refine the object features through efficient message passing. On the other hand, inter-frame relation module (InterRM) densely connects each object in its corresponding tracked sequences dynamically, and leverages such temporal information to further enhance its representations efficiently through a lightweight transformer network. We instantiate our novel designs of IntraRM and InterRM with general center-based or anchor-based detectors and evaluate them on Waymo Open Dataset (WOD). With negligible extra overhead, Ret3D achieves the state-of-the-art performance, being 5.5% and 3.2% higher than the recent competitor in terms of the LEVEL 1 and LEVEL 2 mAPH metrics on vehicle detection, respectively.

cs.CV↗

arXiv2021

Biconservative hypersurfaces with constant scalar curvature in space forms

Biconservative hypersurfaces are hypersurfaces which have conservative stress-energy tensor with respect to the bienergy, containing all minimal and constant mean curvature hypersurfaces. The purpose of this paper is to study biconservative hypersurfaces $M^n$ with constant scalar curvature in a space form $N^{n+1}(c)$. We prove that every biconservative hypersurface with constant scalar curvature in $N^4(c)$ has constant mean curvature. Moreover, we prove that any biconservative hypersurface with constant scalar curvature in $N^5(c)$ is ether an open part of a certain rotational hypersurface or a constant mean curvature hypersurface. These solve an open problem proposed recently by D. Fetcu and C. Oniciuc for $n\leq4$.

math.DG↗

arXiv2020

On Chen's biharmonic conjecture for hypersurfaces in $\mathbb R^5$

A longstanding conjecture on biharmonic submanifolds, proposed by Chen in 1991, is that {\it any biharmonic submanifold in a Euclidean space is minimal}. In the case of a hypersurface $M^n$ in $\mathbb R^{n+1}$, Chen's conjecture was settled in the case of $n=2$ by Chen and Jiang around 1987 independently. Hasanis and Vlachos in 1995 settled Chen's conjecture for a hypersurface with $n=3$. However, the general Chen's conjecture on a hypersurface $M^n$ remains open for $n> 3$. In this paper, we settle Chen's conjecture for hypersurfaces in $\mathbb R^{5}$ for $n=4$.

math.DG↗