Tianyu Cai | Searcharxiv

arXiv2025

Inverse problem for fractional Schrödinger equations with drift on closed Riemannian manifolds

This paper is concerned about the inverse coefficient problems of variable-coefficient fractional Schrödinger equations with drift on connected closed Riemannian manifolds. We prove that the knowledge of the underlying equation of order $α\in (\frac{1}{2},1)$ on any non-empty open subset of the underlying manifold determines the Riemannian metric, the drift and the potential, simultaneously and uniquely, up to a gauge transformation, under the same geometric assumptions on the observation set as in \cite{feizmohammadi2024calderonproblemfractionalschrodinger}. The method of proof is based on that of \cite{feizmohammadi2024calderonproblemfractionalschrodinger} for fractional Schrödinger operators, with the incorporation of the Runge approximation to recover the drift term.

math.AP↗

arXiv2021

RaP-Net: A Region-wise and Point-wise Weighting Network to Extract Robust Features for Indoor Localization

Feature extraction plays an important role in visual localization. Unreliable features on dynamic objects or repetitive regions will interfere with feature matching and challenge indoor localization greatly. To address the problem, we propose a novel network, RaP-Net, to simultaneously predict region-wise invariability and point-wise reliability, and then extract features by considering both of them. We also introduce a new dataset, named OpenLORIS-Location, to train the proposed network. The dataset contains 1553 images from 93 indoor locations. Various appearance changes between images of the same location are included and can help the model to learn the invariability in typical indoor scenes. Experimental results show that the proposed RaP-Net trained with OpenLORIS-Location dataset achieves excellent performance in the feature matching task and significantly outperforms state-of-the-arts feature algorithms in indoor localization. The RaP-Net code and dataset are available at https://github.com/ivipsourcecode/RaP-Net.

cs.CV↗