Shin Kim | Searcharxiv

arXiv2026

Orbifold Bergman Kernels

Let $({X}, \omega)$ be a compact $n$-dimensional K\"ahler orbifold, the stabilizer groups of which are abelian and have rank at most two. Let ${E}$ be an orbi-ample vector bundle of rank $2$ over ${X}$ and let $H$ be a Hermitian metric on ${E}$ such that the curvature form of $\det H$ is $-2\pi \sqrt{-1} \omega$. We show that a certain weighted sum of Bergman kernels for ${Sym}^i {E} \otimes \det({E})^{k+j}$ as $i$ and $j$ vary over a finite set admit an asymptotic expansion. This extends a similar result for cyclic K\"ahler orbifolds.

math.DG↗

arXiv2025

Higher Rank Bergman Kernels on Compact Riemann Surfaces

Let X be a compact Riemann surface equipped with a real-analytic K\"ahler form $\omega$ and let E be a holomorphic vector bundle over $X$ equipped with a real-analytic Hermitian metric $h$. Suppose that the curvature of $h$ is Griffiths-positive. We prove the existence of a global asymptotic expansion in powers of $k$ of the Bergman kernel associated to $(S^k E, S^k h)$ and $\omega$.

math.CV↗

arXiv2024

Fan-Beam CT Reconstruction for Unaligned Sparse-View X-ray Baggage Dataset

Computed Tomography (CT) is a technology that reconstructs cross-sectional images using X-ray images taken from multiple directions. In CT, hundreds of X-ray images acquired as the X-ray source and detector rotate around a central axis, are used for precise reconstruction. In security baggage inspection, X-ray imaging is also widely used; however, unlike the rotating systems in medical CT, stationary X-ray systems are more common, and publicly available reconstructed data are limited. This makes it challenging to obtain large-scale 3D labeled data and voxel representations essential for training. To address these limitations, our study presents a calibration and reconstruction method using an unaligned sparse multi-view X-ray baggage dataset, which has extensive 2D labeling. Our approach integrates multi-spectral neural attenuation field reconstruction with Linear pushbroom (LPB) camera model pose optimization, enhancing rendering consistency for novel views through color coding network. Our method aims to improve generalization within the security baggage inspection domain, where generalization is particularly challenging.

eess.IV↗