arXiv subjects

Kaiqiang Li

Publications and source records attributed to Kaiqiang Li.

4 recordsLinked to original sources

arXiv2026

Back to Point: Exploring Point-Language Models for Zero-Shot 3D Anomaly Detection

Zero-shot (ZS) 3D anomaly detection is crucial for reliable industrial inspection, as it enables detecting and localizing defects without requiring any target-category training data. Existing approaches render 3D point clouds into 2D images and leverage pre-trained Vision-Language Models (VLMs) for anomaly detection. However, such strategies inevitably discard geometric details and exhibit limited sensitivity to local anomalies. In this paper, we revisit intrinsic 3D representations and explore the potential of pre-trained Point-Language Models (PLMs) for ZS 3D anomaly detection. We propose BTP (Back To Point), a novel framework that effectively aligns 3D point cloud and textual embeddings. Specifically, BTP aligns multi-granularity patch features with textual representations for localized anomaly detection, while incorporating geometric descriptors to enhance sensitivity to structural anomalies. Furthermore, we introduce a joint representation learning strategy that leverages auxiliary point cloud data to improve robustness and enrich anomaly semantics. Extensive experiments on Real3D-AD and Anomaly-ShapeNet demonstrate that BTP achieves superior performance in ZS 3D anomaly detection. Code will be available at \href{https://github.com/wistful-8029/BTP-3DAD}{https://github.com/wistful-8029/BTP-3DAD}.

cs.CV↗

arXiv2024

Some further progress for existence and boundedness of solutions to a two-dimensional chemotaxis-(Navier-)Stokes system modeling coral fertilization

In this paper, we investigate the effects exerted by the interplay among Laplacian diffusion, chemotaxis cross diffusion and the fluid dynamic mechanism on global existence and boundedness of the solutions. The mathematical model considered herein appears as \begin{align}\left\{ \begin{array}{l} n_t+u\cdot\nabla n=Δn-\nabla\cdot( nS(n)\nabla c)-nm,\quad x\in Ω, t>0, \disp{ c_{ t}+u\cdot\nabla c=Δc-c+w},\quad x\in Ω, t>0, \disp{w_{t}+u\cdot\nabla w=Δw-nw},\quad x\in Ω, t>0,\\ u_t+κ(u \cdot \nabla)u+\nabla P=Δu+(n+m)\nabla ϕ,\quad x\in Ω, t>0,\\ \nabla\cdot u=0,\quad x\in Ω, t>0,\\ \end{array}\right.\eqno(KSNF) \end{align} in a bounded domain $Ω\subset \mathbb{R}^2$ with a smooth boundary, which describes the process of coral fertilization occurring in ocean flow. Here $κ\in \mathbb{R}$ is a given constant, $ϕ\in W^{2,\infty}(Ω)$and $S(n) $ is a scalar function satisfies $|S(n)|\leq C_S(1+n)^{-α}$ {for all} $n\geq 0$ with some $C_S>0$ and $α\in\mathbb{R}$. It is proved that if either $α>-1,κ=0$ or $α\geq-\frac{1}{2},κ\in\mathbb{R}$ is satisfied,then for any reasonably smooth initial data, the corresponding Neumann-Neumann-Neumann-Dirichlet initial-boundary problem $(KSNF)$ possesses a globally classical solution. In case of the stronger assumption $α>-1,κ= 0$ or $α>-\frac{1}{2},κ\in\mathbb{R},$ we moreover show that the corresponding initial-boundary problem admits a unique global classical solution which is uniformly bounded on $Ω\times(0,\infty)$.

math.AP↗

arXiv2024

Wellposedness of solution for an $N$-D chemotaxis-convection model during tumor angiogenesis

In this paper, we consider the following parabolic-parabolic-elliptic system } \begin{align*} \left\{\aligned & u_t=Δu-\nabla\cdot(u\nabla v)+ξ\nabla\cdot(u\nabla w)+au-μu^α, && x\inΩ, t>0,\\ & v_t=Δv+\nabla\cdot(v\nabla w)-v+u,&& x\inΩ, t>0,\\ & 0=Δw-w+u,&& x\inΩ, t>0\\ \endaligned\right. \end{align*} on a bounded domain $Ω\subset \mathbb{R}^{N}$ ($N\geq1$) with smooth boundary $\partial Ω$, where $μ$, $a$, $α$ are positive constants and $ξ\in\mathbb{R}$. If one of the following cases holds:\\ (i) $N\geq4$ and $α>\frac{4N-4+N\sqrt{2N^2-6N+8}}{2N}$;\\ (ii) $N=3$, $α>2$, for any $μ>0$ or $α=2$, the index $μ$ should be suitably big;\\ (iii) $N=2$, $α\geq2$, for any $μ>0$.\\ Without any restriction on the index $ξ$, for any given suitably regular initial data, the corresponding Neumann initial-boundary problem admits a unique global and bounded classical solution.

math.AP↗

arXiv2018

Decay of solutions to anisotropic conservation laws with large initial data

In this paper, we study the large time behavior of solutions to the Cauchy problem for the anisotropic conservation laws in two dimensional space. Without any smallness assumption on the initial data, the decay rates of solutions in $L^2$ space and homogeneous Sobolev space $\dot{H}^γ$ are obtained by using the method of time-frequency decomposition and the classical energy method.

math.AP↗