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Related papers: Nonlinear Diffusion equations in image processing

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In recent years, partial differential equation (PDE) systems have been successfully applied to the binarization of text images, achieving promising results. Inspired by the DH model and incorporating a novel image modeling approach, this…

Computer Vision and Pattern Recognition · Computer Science 2025-03-12 Youjin Liu , Yu Wang

Many important applications are available for nonlinear reaction-diffusion equation especially in the area of biology and engineering. Therefore a mathematical model for Lie symmetry reduction of system of nonlinear reaction-diffusion…

Mathematical Physics · Physics 2007-05-23 Sanjeev Kumar , Ravendra Singh

The aim of this paper is to discuss potential advances in PET kinetic models and direct reconstruction of kinetic parameters. As a prominent example we focus on a typical task in perfusion imaging and derive a system of…

Optimization and Control · Mathematics 2014-11-20 Louise Reips , Martin Burger , Ralf Engbers

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

Diffusion models can be used as learned priors for solving various inverse problems. However, most existing approaches are restricted to linear inverse problems, limiting their applicability to more general cases. In this paper, we build…

Image and Video Processing · Electrical Eng. & Systems 2022-11-28 Bahjat Kawar , Jiaming Song , Stefano Ermon , Michael Elad

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…

Numerical Analysis · Mathematics 2025-05-14 Maria Vasilyeva , Aleksei Krasnikov , Kelum Gajamannage , Mehrube Mehrubeoglu

This paper deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. We first show an intrinsic formulation for the nonlinear diffusion equation to…

Computer Vision and Pattern Recognition · Computer Science 2026-04-24 Javier Sanguino , Carlos Platero , Olga Velasco

The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…

Mathematical Physics · Physics 2020-01-07 Andrei D. Polyanin

The use of cross-diffusion systems as mathematical models of different image processes is investigated. The present paper is concerned with linear filtering. First, those systems satisfying the most important scale-space properties are…

Analysis of PDEs · Mathematics 2017-02-21 A. Araujo , S. Barbeiro , E. Cuesta , A. Duran

We introduce a general framework for solving partial differential equations (PDEs) using generative diffusion models. In particular, we focus on the scenarios where we do not have the full knowledge of the scene necessary to apply classical…

Machine Learning · Computer Science 2024-11-04 Jiahe Huang , Guandao Yang , Zichen Wang , Jeong Joon Park

This paper explores the use of score-based diffusion models for Bayesian image reconstruction. Diffusion models are an efficient tool for generative modeling. Diffusion models can also be used for solving image reconstruction problems. We…

Image and Video Processing · Electrical Eng. & Systems 2025-10-06 Michael T. McCann , Hyungjin Chung , Jong Chul Ye , Marc L. Klasky

In this report, we present and compare the results of an improved fractional and integer order partial differential equation (PDE)-based binarization scheme. The improved model incorporates a diffusion term in addition to the edge and…

Computer Vision and Pattern Recognition · Computer Science 2021-11-24 Uche A. Nnolim

Image restoration is a long-standing problem in low-level computer vision with many interesting applications. We describe a flexible learning framework based on the concept of nonlinear reaction diffusion models for various image…

Computer Vision and Pattern Recognition · Computer Science 2016-08-23 Yunjin Chen , Thomas Pock

This report presents the results of a partial differential equation (PDE)-based image enhancement algorithm, for dynamic range compression and illumination correction in the absence of the logarithmic function. The proposed algorithm…

Computer Vision and Pattern Recognition · Computer Science 2018-01-23 U. A. Nnolim

In this work, we propose a telegraph coupled partial differential equation (TCPDE) based model for image restoration. New framework interpolates between a couple of non-linear telegraph equation and a parabolic equation. Proposed strategy…

Analysis of PDEs · Mathematics 2019-09-12 Sudeb Majee , Subit K. Jain , Rajendra K. Ray , Ananta K. Majee

Diffusion Probabilistic Models (DPMs) have recently shown remarkable performance in image generation tasks, which are capable of generating highly realistic images. When adopting DPMs for image restoration tasks, the crucial aspect lies in…

Computer Vision and Pattern Recognition · Computer Science 2023-06-01 Yi Zhang , Xiaoyu Shi , Dasong Li , Xiaogang Wang , Jian Wang , Hongsheng Li

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…

Numerical Analysis · Mathematics 2014-04-08 Emma Naden , Thomas März , Colin B. Macdonald

We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under…

Machine Learning · Computer Science 2025-06-18 Edward Li , Zichen Wang , Jiahe Huang , Jeong Joon Park

Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which…

Machine Learning · Computer Science 2022-03-21 Tobias Alt , Karl Schrader , Joachim Weickert , Pascal Peter , Matthias Augustin

A multitude of imaging and vision tasks have seen recently a major transformation by deep learning methods and in particular by the application of convolutional neural networks. These methods achieve impressive results, even for…

Computer Vision and Pattern Recognition · Computer Science 2018-11-30 Simon Arridge , Andreas Hauptmann