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Haoyuan Xu

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3 publications

preprint2026arXiv

Uncertainty-aware Spatial-Frequency Registration and Fusion for Infrared and Visible Images

Infrared and Visible Image Fusion (IVIF) has shown promise in visual tasks under challenging environments, but fusion under unregistered conditions faces inherent misalignments. Current studies to solve them either predict the deformation parameters coarse-to-fine (i.e., coarse registration and fine registration) or estimate the deformation fields in multi-scales for registration. Though straightforward, they overlook the cumulative errors in registration, which contaminate the fusion stage and severely deteriorate the resulting images. We introduce the Spatial-Frequency Registration and Fusion (SFRF) framework, which incorporates uncertainty estimation and infrared thermal radiation distribution consistency into a unified pipeline to handle the error accumulation for robust registration and fusion across both spatial and frequency domains. Specifically, SFRF constructs a Multi-scale Iterative Registration (MIR) framework that iteratively refines the deformation field across scales, leveraging uncertainty estimation at each stage to mitigate error accumulation and enhance alignment accuracy dynamically. To ensure the accurate alignment of infrared thermal distributions during registration, thermal radiation distribution consistency is employed as a frequency-domain supervisory signal, promoting global consistency in the frequency domain. Based on the spatial-frequency alignment, SFRF further adopts a Dual-branch Spatial-Frequency Fusion (DSFF) module, which incorporates spatial geometric features and frequency distribution information to reconstruct visually appealing images. SFRF achieves impressive performance across diverse datasets.

preprint2020arXiv

Normalized solutions for a coupled fractional schrodinger system in low dimensions

We consider the following coupled fractional Schrödinger system: \begin{equation*} \left\{ \begin{aligned} &(-Δ)^su+λ_1u=μ_1|u|^{2p-2}u+β|v|^p|u|^{p-2}u\\ &(-Δ)^sv+λ_2v=μ_2|v|^{2p-2}v+β|u|^p|v|^{p-2}v\\ \end{aligned} \right.\quad\text{in}~{\mathbb{R}^N}, \end{equation*} with 0<s<10<s<1, 2s<N≤4s2s<N\le 4s and 1+2sN<p<NN−2s1+\frac{2s}{N}<p<\frac{N}{N-2s}, under the following constraint \begin{align*} \int_{\mathbb{R}^N}|u|^2dx=a_1^2\quad\text{and}\quad \int_{\mathbb{R}^N}|v|^2dx=a_2^2. \end{align*} Assuming that the parameters μ1,μ2,a1,a2μ_1,μ_2,a_1, a_2 are fixed quantities, we prove the existence of normalized solution for different ranges of the coupling parameter β>0β>0 .

preprint2015arXiv

Multi-bump solutions of −Δu=K(x)un+2n−2-Δu=K(x)u^{\frac{n+2}{n-2}} on lattices in RnR^n

We consider critical exponent semi-linear elliptic equation with coefficient K(x) periodic in its first k variables, with 2k smaller than n-2. Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in Rk, including infinite lattices. We also show that for 2k greater than or equal to n-2, no such solutions exist.

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