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Texture analysis is an important field of investigation that has received a great deal of interest from computer vision community. In this paper, we propose a novel approach for texture modeling based on partial differential equation (PDE).…

Computer Vision and Pattern Recognition · Computer Science 2012-01-20 Bruno Brandoli Machado , Wesley Nunes Gonçalves , Odemir Martinez Bruno

Partial differential equations (PDEs) are typically used as models of physical processes but are also of great interest in PDE-based image processing. However, when it comes to their use in imaging, conventional numerical methods for…

Computer Vision and Pattern Recognition · Computer Science 2021-10-19 Pascal Tom Getreuer , Peyman Milanfar , Xiyang Luo

This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…

Methodology · Statistics 2017-07-12 Jon Cockayne , Chris Oates , Tim Sullivan , Mark Girolami

This report presents the results of a sky detection technique used to improve the performance of a previously developed partial differential equation (PDE)-based hazy image enhancement algorithm. Additionally, a proposed alternative method…

Computer Vision and Pattern Recognition · Computer Science 2018-03-13 Uche A. Nnolim

Data compression is a method of improving the efficiency of transmission and storage of images. Dithering, as a method of data compression, can be used to convert an 8-bit gray level image into a 1-bit / binary image. Undithering is the…

Computer Vision and Pattern Recognition · Computer Science 2011-08-17 V. Asha

We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…

Numerical Analysis · Mathematics 2020-08-28 Sana Keita , Abdelaziz Beljadid , Yves Bourgault

In this paper, we develop an analytical framework for the partial differential equation underlying the consensus-based optimization model. The main challenge arises from the nonlinear, nonlocal nature of the consensus point, coupled with a…

Analysis of PDEs · Mathematics 2025-04-16 Jinhuan Wang , Keyu Li , Hui Huang

Anisotropic diffusion is a well recognized tool in digital image processing, including edge detection and denoising. We present here a particular nonlinear time-dependent operator together with an appropriate high-order discretization for…

Numerical Analysis · Mathematics 2022-04-29 Lorella Fatone , Daniele Funaro

The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…

Numerical Analysis · Mathematics 2021-03-04 Alexander Hvatov

This paper introduces two key contributions aimed at improving the speed and quality of images generated through inverse diffusion processes. The first contribution involves reparameterizing the diffusion process in terms of the angle on a…

Machine Learning · Computer Science 2026-02-26 Zhenkai Zhang , Krista A. Ehinger , Tom Drummond

Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized…

Numerical Analysis · Mathematics 2021-09-09 Dominik Garmatter , Margherita Porcelli , Francesco Rinaldi , Martin Stoll

This report describes the experimental results obtained using a proposed variational Retinex algorithm for controlled illumination correction. Two colour restoration and enhancement schemes of the algorithm are presented for drastically…

Computer Vision and Pattern Recognition · Computer Science 2017-02-07 U. A. Nnolim

Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the…

Computer Vision and Pattern Recognition · Computer Science 2015-06-16 Laurent Hoeltgen , Markus Mainberger , Sebastian Hoffmann , Joachim Weickert , Ching Hoo Tang , Simon Setzer , Daniel Johannsen , Frank Neumann , Benjamin Doerr

This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We propose to represent the PDE in the form of a computational graph, facilitating the…

Numerical Analysis · Mathematics 2025-01-28 Zhanhong Ye , Xiang Huang , Leheng Chen , Hongsheng Liu , Zidong Wang , Bin Dong

In this paper, a new variational model with fractional-order regularization term arising in registration of diffusion tensor image(DTI) is presented. Moreover, the existence of its solution is proved to ensure that there is a regular…

Functional Analysis · Mathematics 2017-02-28 Huan Han

In this paper, we present a new numerical method to solve fractional differential equations. Given a fractional derivative of arbitrary real order, we present an approximation formula for the fractional operator that involves integer-order…

Numerical Analysis · Mathematics 2015-12-16 Ricardo Almeida , Nuno R. O. Bastos

Rendering highly scattering participating media using brute force path tracing is a challenge. The diffusion approximation reduces the problem to solving a simple linear partial differential equation. Flux-limited diffusion introduces…

Graphics · Computer Science 2018-07-03 David Koerner , Jamie Portsmouth , Wenzel Jakob

We present three schemes for the numerical approximation of fractional diffusion, which build on different definitions of such a non-local process. The first method is a PDE approach that applies to the spectral definition and exploits the…

Numerical Analysis · Mathematics 2019-02-05 Andrea Bonito , Juan Pablo Borthagaray , Ricardo H. Nochetto , Enrique Otarola , Abner J. Salgado

The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…

Numerical Analysis · Mathematics 2020-10-28 Zhengqi Zhang , Zhi Zhou

We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…