local refinement
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AbstractDeblurring images of dynamic scenes is a challenging task because blurring occurs due to a combination of many factors. In recent years, the use of multi-scale pyramid methods to recover high-resolution sharp images has been extensively studied. We have made improvements to the lack of detail recovery in the cascade structure through a network using progressive integration of data streams. Our new multi-scale structure and edge feature perception design deals with changes in blurring at different spatial scales and enhances the sensitivity of the network to blurred edges. The coarse-to-fine architecture restores the image structure, first performing global adjustments, and then performing local refinement. In this way, not only is global correlation considered, but also residual information is used to significantly improve image restoration and enhance texture details. Experimental results show quantitative and qualitative improvements over existing methods.

<div>We propose a novel hybrid framework for registering retinal images in the presence of extreme geometric distortions that are commonly encountered in ultra-widefield (UWF) fluorescein angiography. Our approach consists of two stages: a feature-based global registration and a vessel-based local refinement. For the global registration, we introduce a modified RANSAC algorithm that jointly identifies robust matches between feature keypoints in reference and target images and estimates a polynomial geometric transformation consistent with the identified correspondences. Our RANSAC modification particularly improves feature point matching and the registration in peripheral regions that are most severely impacted by the geometric distortions. The second local refinement stage is formulated in our framework as a parametric chamfer alignment for vessel maps obtained using a deep neural network. Because the complete vessel maps contribute to the chamfer alignment, this approach not only improves registration accuracy but also aligns with clinical practice, where vessels are typically a key focus of examinations. We validate the effectiveness of the proposed framework on a new UWF fluorescein angiography (FA) dataset and on the existing narrow-field FIRE (fundus image registration) dataset and demonstrate that it significantly outperforms prior retinal image registration methods. The proposed approach enhances the utility of large sets of longitudinal UWF images by enabling: (a) automatic computation of vessel change metrics and (b) standardized and co-registered examination that can better highlight changes of clinical interest to physicians.</div>

<div>We propose a novel hybrid framework for registering retinal images in the presence of extreme geometric distortions that are commonly encountered in ultra-widefield (UWF) fluorescein angiography. Our approach consists of two stages: a feature-based global registration and a vessel-based local refinement. For the global registration, we introduce a modified RANSAC algorithm that jointly identifies robust matches between feature keypoints in reference and target images and estimates a polynomial geometric transformation consistent with the identified correspondences. Our RANSAC modification particularly improves feature point matching and the registration in peripheral regions that are most severely impacted by the geometric distortions. The second local refinement stage is formulated in our framework as a parametric chamfer alignment for vessel maps obtained using a deep neural network. Because the complete vessel maps contribute to the chamfer alignment, this approach not only improves registration accuracy but also aligns with clinical practice, where vessels are typically a key focus of examinations. We validate the effectiveness of the proposed framework on a new UWF fluorescein angiography (FA) dataset and on the existing narrow-field FIRE (fundus image registration) dataset and demonstrate that it significantly outperforms prior retinal image registration methods. The proposed approach enhances the utility of large sets of longitudinal UWF images by enabling: (a) automatic computation of vessel change metrics and (b) standardized and co-registered examination that can better highlight changes of clinical interest to physicians.</div>

Abstract. Locally refined grids for global atmospheric models are attractive since they are expected to provide an alternative to solve local phenomena without the requirement of a global high-resolution uniform grid, whose computational cost may be prohibitive. Spherical centroidal Voronoi tessellation (SCVT), as used in the atmospheric Model for Prediction Across Scales (MPAS), allows a flexible way to build and work with local refinement. In addition, the Andes Range plays a key role in the South American weather, but it is hard to capture its fine-structure dynamics in global models. This paper describes how to generate SCVT grids that are locally refined in South America and that also capture the sharp topography of the Andes Range by defining a density function based on topography and smoothing techniques. We investigate the use of the mimetic finite-volume scheme employed in the MPAS dynamical core on this grid considering the nonlinear classic and moist shallow-water equations on the sphere. We show that the local refinement, even with very smooth transitions from different resolutions, generates spurious numerical inertia–gravity waves that may even numerically destabilize the model. In the moist shallow-water model, wherein physical processes such as precipitation and cloud formation are included, our results show that the local refinement may generate spurious rain that is not observed in uniform-resolution SCVT grids. Fortunately, the spurious waves originate from small-scale grid-related numerical errors and can therefore be mitigated using fourth-order hyperdiffusion. We exploit a grid geometry-based hyperdiffusion that is able to stabilize spurious waves and has very little impact on the total energy conservation. We show that, in some cases, the clouds are better represented in a variable-resolution grid when compared to a respective uniform-resolution grid with the same number of cells, while in other cases, grid effects can affect the cloud and rain representation.

In this paper, an efficient multiscale finite element method via local defect-correction technique is developed. This method is used to solve the Schrödinger eigenvalue problem with three-dimensional domain. First, this paper considers a three-dimensional bounded spherical region, which is the truncation of a three-dimensional unbounded region. Using polar coordinate transformation, we successfully transform the three-dimensional problem into a series of one-dimensional eigenvalue problems. These one-dimensional eigenvalue problems also bring singularity. Second, using local refinement technique, we establish a new multiscale finite element discretization method. The scheme can correct the defects repeatedly on the local refinement grid, which can solve the singularity problem efficiently. Finally, the error estimates of eigenvalues and eigenfunctions are also proved. Numerical examples show that our numerical method can significantly improve the accuracy of eigenvalues.

T-splines have recently been introduced to represent objects of arbitrary shapes using a smaller number of control points than the conventional non-uniform rational B-splines (NURBS) or B-spline representatizons in computer-aided design, computer graphics and reverse engineering. They are flexible in representing complex surface shapes and economic in terms of parameters as they enable local refinement. This property is a great advantage when dense, scattered and noisy point clouds are approximated using least squares fitting, such as those from a terrestrial laser scanner (TLS). Unfortunately, when it comes to assessing the goodness of fit of the surface approximation with a real dataset, only a noisy point cloud can be approximated: (i) a low root mean squared error (RMSE) can be linked with an overfitting, i.e., a fitting of the noise, and should be correspondingly avoided, and (ii) a high RMSE is synonymous with a lack of details. To address the challenge of judging the approximation, the reference surface should be entirely known: this can be solved by printing a mathematically defined T-splines reference surface in three dimensions (3D) and modeling the artefacts induced by the 3D printing. Once scanned under different configurations, it is possible to assess the goodness of fit of the approximation for a noisy and potentially gappy point cloud and compare it with the traditional but less flexible NURBS. The advantages of T-splines local refinement open the door for further applications within a geodetic context such as rigorous statistical testing of deformation. Two different scans from a slightly deformed object were approximated; we found that more than 40% of the computational time could be saved without affecting the goodness of fit of the surface approximation by using the same mesh for the two epochs.

In this paper, an efficient and robust Cartesian Mesh Generation with Local Refinement for an Immersed Boundary Approach is proposed, whose key feature is the capability of high Reynolds number simulations by the use of wall function models, bypassing the need for accurate boundary layer discretization. Starting from the discrete manifold model of the object to be analyzed, the proposed model generates Cartesian adaptive grids for a CFD simulation, with minimal user interactions; the most innovative aspect of this approach is that the automatic generation is based on the segmentation of the surfaces enveloping the object to be analyzed. The aim of this paper is to show that this automatic workflow is robust and enables to get quantitative results on geometrically complex configurations such as marine vehicles. To this purpose, the proposed methodology has been applied to the simulation of the flow past a BB2 submarine, discretized by non-uniform grid density. The obtained results are comparable with those obtained by classical body-fitted approaches but with a significant reduction of the time required for the mesh generation.