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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).…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…