arXiv subjects

Aleksei Zhuravlev

Publications and source records attributed to Aleksei Zhuravlev.

4 recordsLinked to original sources

arXiv2026

Non-Rigid 3D Shape Correspondences: From Foundations to Open Challenges and Opportunities

Estimating correspondences between deformed shape instances is a long-standing problem in computer graphics; numerous applications, from texture transfer to statistical modelling, rely on recovering an accurate correspondence map. Many methods have thus been proposed to tackle this challenging problem from varying perspectives, depending on the downstream application. This state-of-the-art report is geared towards researchers, practitioners, and students seeking to understand recent trends and advances in the field. We categorise developments into three paradigms: spectral methods based on functional maps, combinatorial formulations that impose discrete constraints, and deformation-based methods that directly recover a global alignment. Each school of thought offers different advantages and disadvantages, which we discuss throughout the report. Meanwhile, we highlight the latest developments in each area and suggest new potential research directions. Finally, we provide an overview of emerging challenges and opportunities in this growing field, including the recent use of vision foundation models for zero-shot correspondence and the particularly challenging task of matching partial shapes.

cs.GR↗

arXiv2025

Denoising Functional Maps: Diffusion Models for Shape Correspondence

Estimating correspondences between pairs of deformable shapes remains a challenging problem. Despite substantial progress, existing methods lack broad generalization capabilities and require category-specific training data. To address these limitations, we propose a fundamentally new approach to shape correspondence based on denoising diffusion models. In our method, a diffusion model learns to directly predict the functional map, a low-dimensional representation of a point-wise map between shapes. We use a large dataset of synthetic human meshes for training and employ two steps to reduce the number of functional maps that need to be learned. First, the maps refer to a template rather than shape pairs. Second, the functional map is defined in a basis of eigenvectors of the Laplacian, which is not unique due to sign ambiguity. Therefore, we introduce an unsupervised approach to select a specific basis by correcting the signs of eigenvectors based on surface features. Our model achieves competitive performance on standard human datasets, meshes with anisotropic connectivity, non-isometric humanoid shapes, as well as animals compared to existing descriptor-based and large-scale shape deformation methods. See our project page for the source code and the datasets.

cs.CV↗

arXiv2021

Towards constraining axions with polarimetric observations of the isolated neutron star RX J1856.5-3754

Photon-axion mixing can create observable signatures in thermal spectra of isolated, cooling neutron stars. Their shape depends on the polarization properties of the radiation, which, in turn, are determined by the structure of stellar outermost layers. Here we investigate the effect of mixing on the spectrum and polarimetric observables, polarization fraction and polarization angle, using realistic models of surface emission. We focus on RX J1856.5-3754, the only source among the X-ray dim isolated neutron stars for which polarimetric measurements in the optical band were performed. Our results show that in the case of a condensed surface in both fixed and free-ion limits, the mixing can significantly limit the geometric configurations which reproduce the observed linear polarization fraction of 16.43%. In the case of an atmosphere, the mixing does not create any noticeable signatures. Complementing our approach with the data from upcoming soft X-ray polarimetry missions will allow to obtain constraints on $g_{γa} \sim 10^{-11}$ GeV$^{-1}$ and $m_a \lesssim 10^{-6}$ eV, improving the present experimental and astrophysical limits.

astro-ph.HE↗

arXiv2021

Photon-axion mixing in thermal emission of isolated neutron stars

Thermally emitting neutron stars represent a promising environment for probing the properties of axion-like particles. Due to the strong magnetic fields of these sources, surface photons may partially convert into such particles in the large magnetospheric region surrounding the stars, which will result in distinctive signatures in their spectra. However, the interaction depends on the polarization state of the radiation and is rather weak due to the low experimentally allowed values of the coupling constant $g_{γa}$. In this work, we compute the degree of photon-axion transition in the case of 100% O-mode polarization and spectral energy distribution of an isotropic blackbody with uniform surface temperature. The stellar magnetic field is assumed to be dipolar. We show that with the maximum effect reached for the magnetic fields $\sim10^{13}$ - $10^{14}$ G (typical for X-ray dim isolated neutron stars) and $g_{γa} = 2 \times 10^{-11}$ GeV$^{-1}$, the optical flux is reduced by 30 - 40%, while the high-energy part of the spectrum is not affected. The low-energy decrease exceeds 5% at $g_{γa} \geq 2 \times 10^{-12}$ GeV$^{-1}$ and $m_a \leq 2\times 10^{-6}$ eV, which is below the present experimental and astrophysical limits on axion parameters. To obtain the actual observational constraints, rigorous treatment of the radiative surface layers is required.

astro-ph.HE↗