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The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color…
This paper explores the concept of near-cloaking in the context of time-dependent heat propagation. We show that after the lapse of a certain threshold time instance, the boundary measurements for the homogeneous heat equation are close to…
Image inpainting methods have shown significant improvements by using deep neural networks recently. However, many of these techniques often create distorted structures or blurry textures inconsistent with surrounding areas. The problem is…
We present an algorithm to estimate fast and accurate depth maps from light fields via a sparse set of depth edges and gradients. Our proposed approach is based around the idea that true depth edges are more sensitive than texture edges to…
Krylov subspace methods are an essential building block in numerical simulation software. The efficient utilization of modern hardware is a challenging problem in the development of these methods. In this work, we develop Krylov subspace…
We present a multiscale finite element method for a diffusion problem with rough and high contrast coefficients. The construction of the multiscale finite element space is based on the localized orthogonal decomposition methodology and it…
Removing or repairing the imperfections of a digital images or videos is a very active and attractive field of research belonging to the image inpainting technique. This later has a wide range of applications, such as removing scratches in…
This paper presents a novel framework to accelerate score-based diffusion models. It first converts the standard stable diffusion model into the Fokker-Planck formulation which results in solving large linear systems for each image. For…
We consider image denoising using a nonlinear diffusion process, where we solve unsteady partial differential equations with nonlinear coefficients. The noised image is given as an initial condition, and nonlinear coefficients are used to…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature,…
We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each…
Decomposing a scene into its reflectance and shading is a challenge due to the lack of extensive ground-truth data for real-world scenes. We introduce a novel physics-based approach for intrinsic image decomposition using a pair of visible…
We demonstrate a method for filtering images defined on curved surfaces embedded in 3D. Applications are noise removal and the creation of artistic effects. Our approach relies on in-surface diffusion: we formulate Weickert's edge/coherence…
This paper proposes a non-computational method of counteracting the effect of image degradation introduced by the diffraction phenomenon in lensless microscopy. All the optical images (whether focused by lenses or not) are diffraction…
We give a decomposition expression for dissipative heat using the instantaneous diffusion coefficient in a nonequilibrium steady state. The dissipative heat can be expressed using three diffusion coefficients: instantaneous, equilibrium,…
Image compression technology eliminates redundant information to enable efficient transmission and storage of images, serving both machine vision and human visual perception. For years, image coding focused on human perception has been…
The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of…
A new technique for embedding data into an image coupled with compression has been proposed in this paper. A fast and efficient coding algorithms are needed for effective storage and transmission, due to the popularity of telemedicine and…
Transforming a thermal infrared image into a realistic RGB image is a challenging task. In this paper we propose a deep learning method to bridge this gap. We propose learning the transformation mapping using a coarse-to-fine generator that…