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We propose an unsupervised image fusion architecture for multiple application scenarios based on the combination of multi-scale discrete wavelet transform through regional energy and deep learning. To our best knowledge, this is the first…
This paper surveys results found by the authors in the previous papers (see for example, A. Duyunova, V. Lychagin, S. Tychkov, Differential invariants for spherical layer flows of a viscid fluid, Journal of Geometry and Physics, 130,…
Dense image correspondence is central to many applications, such as visual odometry, 3D reconstruction, object association, and re-identification. Historically, dense correspondence has been tackled separately for wide-baseline scenarios…
Advection is believed to be the dominant cooling mechanism in optically thin advection-dominated accretion flows (ADAF's). When outflow is considered, however, the first impression is that advection should be of opposite sign in the inflow…
Conformal Field Theories (CFTs) are special classes of quantum field theories that find applications ranging from critical phenomena to theories of quantum gravity via holography. Understanding thermal effects in CFTs is crucial:…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
We establish basic properties of the heat flow on entire holomorphic functions that have order at most 2. We then look specifically at the action of the heat flow on the Gaussian analytic function (GAF). We show that applying the heat flow…
The detection of moving infrared dim-small targets has been a challenging and prevalent research topic. The current state-of-the-art methods are mainly based on ConvLSTM to aggregate information from adjacent frames to facilitate the…
Why has SIFT been so successful? Why its extension, DSP-SIFT, can further improve SIFT? Is there a theory that can explain both? How can such theory benefit real applications? Can it suggest new algorithms with reduced computational…
In this thesis we deal with spectral invariants for polygons and closed orbisurfaces of constant Gaussian curvature. In each case our method is to study the heat kernel and the asymptotic expansion of the heat trace. First, we investigate…
Image-conditioned Video diffusion models achieve impressive visual realism but often suffer from weakened motion fidelity, e.g., reduced motion dynamics or degraded long-term temporal coherence, especially after fine-tuning. We study the…
Intrinsic image decomposition aims to factorize an image into albedo (reflectance) and shading (illumination) sub-components. Being ill-posed and under-constrained, it is a very challenging computer vision problem. There are infinite pairs…
In this paper, flows of a viscid fluids on curves are considered. Symmetry algebras and the corresponding fields of differential invariants are found. We study their dependence on thermodynamic states of media, and provide classification of…
Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop…
We introduce and study the flow of metrics on a foliated Riemannian manifold $(M,g)$, whose velocity along the orthogonal distribution is proportional to the mixed scalar curvature, $\Sc_{\,\rm mix}$. The flow is used to examine the…
In this paper we present a general, axiomatical framework for the rigorous approximation of invariant densities and other important statistical features of dynamics. We approximate the system trough a finite element reduction, by composing…
In this study, a novel feature coding method that exploits invariance for transformations represented by a finite group of orthogonal matrices is proposed. We prove that the group-invariant feature vector contains sufficient discriminative…
Recent numerical work has shown that high-speed confined granular flows down inclines exhibit a rich variety of flow patterns, including dense unidirectional flows, flows with longitudinal vortices and supported flows characterized by a…
Recent success in contrastive learning has sparked growing interest in more effectively leveraging multiple augmented views of data. While prior methods incorporate multiple views at the loss or feature level, they primarily capture…
We discuss various issues related to the understanding of the conformal anomaly matching in CFT from the dual holographic viewpoint. First, we act with a PBH diffeomorphism on a generic 5D RG flow geometry and show that the corresponding…