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Register a new userMesh Total Generalized Variation for Denoising
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Added by
Zheng Liu
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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Total Generalized Variation (TGV) has recently been proven certainly successful in image processing for preserving sharp features as well as smooth transition variations. However, none of the existing works aims at numerically calculating TGV over triangular meshes. In this paper, we develop a novel numerical framework to discretize the second-order TGV over triangular meshes. Further, we propose a TGV-based variational model to restore the face normal field for mesh denoising. The TGV regularization in the proposed model is represented by a combination of a first- and second-order term, which can be automatically balanced. This TGV regularization is able to locate sharp features and preserve them via the first-order term, while recognize smoothly curved regions and recover them via the second-order term. To solve the optimization problem, we introduce an efficient iterative algorithm based on variable-splitting and augmented Lagrangian method. Extensive results and comparisons on synthetic and real scanning data validate that the proposed method outperforms the state-of-the-art methods visually and numerically.
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We consider the total variation (TV) minimization problem used for compressive sensing and solve it using the generalized alternating projection (GAP) algorithm. Extensive results demonstrate the high performance of proposed algorithm on compressive sensing, including two dimensional images, hyperspectral images and videos. We further derive the Alternating Direction Method of Multipliers (ADMM) framework with TV minimization for video and hyperspectral image compressive sensing under the CACTI and CASSI framework, respectively. Connections between GAP and ADMM are also provided.
In this paper, we propose a regularization technique for noisy-image super-resolution and image denoising. Total variation (TV) regularization is adopted in many image processing applications to preserve the local smoothness. However, TV prior is prone to oversmoothness, staircasing effect, and contrast losses. Nonlocal TV (NLTV) mitigates the contrast losses by adaptively weighting the smoothness based on the similarity measure of image patches. Although it suppresses the noise effectively in the flat regions, it might leave residual noise surrounding the edges especially when the image is not oversmoothed. To address this problem, we propose the bilateral spectrum weighted total variation (BSWTV). Specially, we apply a locally adaptive shrink coefficient to the image gradients and employ the eigenvalues of the covariance matrix of the weighted image gradients to effectively refine the weighting map and suppress the residual noise. In conjunction with the data fidelity term derived from a mixed Poisson-Gaussian noise model, the objective function is decomposed and solved by the alternating direction method of multipliers (ADMM) algorithm. In order to remove outliers and facilitate the convergence stability, the weighting map is smoothed by a Gaussian filter with an iteratively decreased kernel width and updated in a momentum-based manner in each ADMM iteration. We benchmark our method with the state-of-the-art approaches on the public real-world datasets for super-resolution and image denoising. Experiments show that the proposed method obtains outstanding performance for super-resolution and achieves promising results for denoising on real-world images.
Feature-preserving mesh denoising has received noticeable attention recently. Many methods often design great weighting for anisotropic surfaces and small weighting for isotropic surfaces, to preserve sharp features. However, they often disregard the fact that small weights still pose negative impacts to the denoising outcomes. Furthermore, it may increase the difficulty in parameter tuning, especially for users without any background knowledge. In this paper, we propose a novel clustering method for mesh denoising, which can avoid the disturbance of anisotropic information and be easily embedded into commonly-used mesh denoising frameworks. Extensive experiments have been conducted to validate our method, and demonstrate that it can enhance the denoising results of some existing methods remarkably both visually and quantitatively. It also largely relaxes the parameter tuning procedure for users, in terms of increasing stability for existing mesh denoising methods.
Total generalization variation (TGV) is a very powerful and important regularization for various inverse problems and computer vision tasks. In this paper, we proposed a semismooth Newton based augmented Lagrangian method to solve this problem. The augmented Lagrangian method (also called as method of multipliers) is widely used for lots of smooth or nonsmooth variational problems. However, its efficiency usually heavily depends on solving the coupled and nonlinear system together and simultaneously, which is very complicated and highly coupled for total generalization variation. With efficient primal-dual semismooth Newton methods for the complicated linear subproblems involving total generalized variation, we investigated a highly efficient and competitive algorithm compared to some efficient first-order method. With the analysis of the metric subregularities of the corresponding functions, we give both the global convergence and local linear convergence rate for the proposed augmented Lagrangian methods.
We consider variations of the Rudin-Osher-Fatemi functional which are particularly well-suited to denoising and deblurring of 2D bar codes. These functionals consist of an anisotropic total variation favoring rectangles and a fidelity term which measure the L^1 distance to the signal, both with and without the presence of a deconvolution operator. Based upon the existence of a certain associated vector field, we find necessary and sufficient conditions for a function to be a minimizer. We apply these results to 2D bar codes to find explicit regimes ---in terms of the fidelity parameter and smallest length scale of the bar codes--- for which a perfect bar code is recoverable via minimization of the functionals. Via a discretization reformulated as a linear program, we perform numerical experiments for all functionals demonstrating their denoising and deblurring capabilities.
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