An improved SIMPLEC scheme for fluid registration

The image registration is always a strongly ill-posed problem, a stable numerical approach is then desired to better approximate the deformation vectors. This paper introduces an efficient numerical implementation of the Navier Stokes equation in the fluid image registration context. Although fluid registration approaches have succeeded in handling large image deformations, the numerical results are sometimes inconsistent and unexpected. This is related, in fact, to the used numerical scheme which does not take into consideration the different properties of the continuous operators. To take into account these properties, we use a robust numerical scheme based on finite volume with pressure correction. This scheme, which is called by the Semi-Implicit Method for Pressure-Linked Equation-Consistent (SIMPLEC), is known for its stability and consistency in fluid dynamics context. The experimental results demonstrate that the proposed method is more efficient and stable, visually and quantitatively, compared to some classical registration methods

An improved PDE-constrained optimization fluid registration for image multi-frame super resolution

The main idea of multi-frame super resolution (SR) algorithms is to recover a single high-resolution image from a sequence of low resolution ones of the same object. The success of the SR approaches is often related to a well registration and restoration steps. Therefore, we propose a new approach based on a partial differential equation (PDE)-constrained optimization fluid image registration and we use a fourth order PDE to treat both the registration and restoration steps that guarantee the success of SR algorithms. Since the registration step is usually a variational ill-posed model, a mathematical study is needed to check the existence of the solution to the regularized problem. Thus, we prove the existence and of the well posed fluid image registration and assure also the existence of the used second order PDE in the restoration step. The results show that the proposed method is competitive with the existing methods

Analysis of the nonlocal wave propagation problem with volume constraints

International audienceIn the current paper, we investigate a nonlocal hyperbolic problem with volume constraints. The main motivation of this work is to apply the nonlocal vector calculus, introduced and developed by DU et al. [3] to such problem. Moreover, based on some density arguments, some a priori estimates and using the Galerkin approach, we prove existence and uniqueness of a weak solution to the nonlocal wave equation. 1. Introduction. The study of nonlocal problems has gained great attention over the last two decades. Nonlocal models involve integral equations and fractional derivatives allowing nonlocal interactions, that is to say, the interaction may occur even when the closures of two domains have an empty intersection. Such models are effective in modeling material singularities and are widely considered in a variety of applications, including image analyses [6]-[10], phase transition [4][11], machine learning [12] and obstacle problem [5]... In a major advance in 2013, Du et al. [3] introduced nonlocal vector calculus as a nonlocal framework to understand and analyze nonlocal problems. It defines non-local fluxes , nonlocal analogues of the gradient, divergence, and curl operators, and presentes some basic nonlocal integral theorems that mimic the classical integral theorems of the vector calculus for differential operators, the authors have also provided connection between the nonlocal operators and their usual differential counterparts in a distributional sense then in a weak sense by introducing nonlocal weighted operators. The present paper was motivated by [2], where the authors threw light on the analogy between nonlocal and local diffusion problems with a convincing explanation of the usefulness, in the nonlocal case, of volume constraints which represent the nonlocal analogue of the boundary conditions of the classical theory. Our purpos

Reduction of the non-uniform illumination using nonlocal variational models for document image analysis

International audienceIn this paper, we investigate two new reflectance and illumination decomposition models based on a nonlocal partial differential equation (PDE) applied to text images. Taking into consideration the higher regularity level of the illumination compared to the reflectance, we propose a nonlocal PDE which deals with repetitive structures and textures that characterize the text image much better compared to the classical local PDEs. The aim of this approach is to use the repetitive features of the reflectance to efficiently extract it from the nonuniform illumination. This idea is motivated by extending the range of application of the nonlocal operators to such problem. Numerical experiments on both grayscale and color text images show the performance and strength of the proposed nonlocal PDE

A new denoising model for multi-frame super-resolution image reconstruction

International audienceMulti-frame image super-resolution (SR) aims to combine the sub-pixel information from a sequence of low-resolution (LR) images to build a high-resolution (HR) one. SR techniques usually suffers from annoying restoration artifacts such as noise, jagged edges, and staircasing effect. In this paper, we aim to increase the performance of SR reconstitution under a variational framework using adaptive diffusion-based regularization term. We propose a new tensor based diffusion regularization that takes the benefit from the diffusion model of Perona–Malik in the flat regions and use a nonlinear tensor derived from the diffusion process of Weickert filter near boundaries. Thus, the proposed SR approach can preserve important image features (sharp edges and corners) much better while avoiding artifacts. The synthetic and real experimental results show the effectiveness of the proposed regularisation compared to other methods in both quantitatively and visually

Simultaneous deconvolution and denoising using a second order variational approach applied to image super resolution

International audienceThe aim of a Super Resolution (SR) technique is to construct a high-resolution image from a sequence of observed low-resolution ones of the same scene. One major roadblock of an SR reconstitution is removing noise and blur without destroying edges. We propose a novel multiframe image SR algorithm based on a convex combination of Bilateral Total Variation and a non-smooth second order variational regulariza-tion, using a controlled weighting parameter. We prove the existence of a minimizer of the proposed SR model in the space of functions of bounded Hessian, and we confirm the success of this approach in avoiding undesirable artifacts. The simulation results show the efficient performance of the proposed algorithm compared to other methods in the literature using two criteria, PSNR and SSIM