Browsing by Author "Martin G"

Now showing 1 - 3 of 3
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    Extremal mappings of finite distortion and the Radon–Riesz property
    (EMS Press, 2022-12-23) Martin G; Yao C
    We consider Sobolev mappings f ∈ W 1;q(Ω; C), 1 < q < ∞, between planar domains Ω ⊂ ℂ. We analyse the Radon–Riesz property for polyconvex functionals of the form (Formula presented) and show that under certain criteria, which hold in important cases, weak convergence in Wloc1;q.(Ω) of (for instance) a minimising sequence can be improved to strong convergence. This finds important applications in the minimisation problems for mappings of finite distortion and the Lp and Exp-Teichmüller theories.
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    Local-enhanced representation for text-based person search
    (Elsevier B.V., 2024-12-12) Zhang G; Chen Y; Zheng Y; Martin G; Wang R
    Text-based person search is a critical task in intelligent security, designed to locate a person of interest by text descriptions. The primary challenge in this task is to effectively bridge the significant gap between the text and image domains while simultaneously extracting the discriminative features that are crucial for the accurate identification of individuals. Existing methods have made some effective attempts by conducting cross-modal matching at the fine-grained representation level. However, these approaches frequently overlook two crucial factors: (i) the presence of noise in the local features during information fusion, and (ii) the lack of intra-modal matching when measuring feature similarity. To address the above issues, we propose a novel local-enhanced representation framework in this paper. Specifically, to restrain noises in local features, we design a Relation-based cross-modal local-enhanced fusion module, which can filter out weak related information by relation assessment. In addition, we explore an intra-cross modal projection strategy to overcome the limitations of existing cross-modal projection methods. This strategy jointly applies the intra-modal and cross-modal matching constrains in feature distribution. Finally, experiments on three mainstream datasets verify the performance superiority of our proposed method compared to existing state-of-the-art methods.
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    Topological Regularity for Solutions to the Generalised Hopf Equation
    (Springer Nature, 2023-08-02) Martin G; Yao C
    The generalised Hopf equation is the first order nonlinear equation defined on a planar domain Ω ⊂ C , with data Φ a holomorphic function and η≥ 1 a positive weight on Ω , hwhw¯¯η(w)=Φ. The Hopf equation is the special case η(w) = η~ (h(w)) and reflects that h is harmonic with respect to the conformal metric η~(z)|dz| , usually η is the hyperbolic metric. This article obtains conditions on the data to ensure that a solution is open and discrete. We also prove a strong uniqueness result.