Directional Total Generalized Variation Regularization

Kongskov, Rasmus Dalgas; Dong, Yiqiu; Knudsen, Kim

doi:10.48550/arxiv.1701.02675

Cited by 3 publications

(6 citation statements)

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“…Second, higher order regularization such as the total generalized variation [40] has been proven useful for natural images. This naturally leads to the directional total generalized variation which combines higher order smoothness with structural a-priori knowledge as presented in this work, thereby generalizing the definition of [36]. Similarly, other kernel regularization functionals such as the total generalized variation or the H 1 -semi-norm will be considered in future investigations to better model the smoothness of the kernel.…”

Section: Discussionmentioning

confidence: 95%

“…Similar versions of the directional total variation have been used before [17,19,29] and it is related to other anisotropic priors [14,30,31] and the notion of parallel level sets [32][33][34]. Note that the directional total variation generalizes the usual total variation (7) for ξ = 0 and other versions of the directional total variation [35,36] where the direction ξ is constant and not depending in the pixel location i. With the isotropic choice P i = w i I, 0 ≤ w i ≤ 1 it reduces to weighted total variation [18,29,[37][38][39].…”

Section: The Forward Operatormentioning

confidence: 95%

“…[18] for the latter) such that the side information image has sufficiently much influence. Extensive studies of this parameter are performed in [36] where the authors obtain their best results for small values of a := 1 − γ 2 . An example photograph, its gray scale version and the corresponding vector-field are shown in figure 4.…”

Section: The Forward Operatormentioning

confidence: 99%

“…Thus, both parameters ε and γ in general will depend on the given side information v but can be chosen without considering a particular data set f. Note that in practice, one chooses γ very close or even equal to 1 (see [18] for the latter) such that the side information image has sufficiently much influence. Extensive studies of this parameter are performed in [36] where the authors obtain their best results for small values of a := 1 − γ 2 . An example photograph, its gray scale version and the corresponding vector-field are shown in figure 4.…”

Section: Definition (Directional Total Variationmentioning

confidence: 99%

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Blind image fusion for hyperspectral imaging with the directional total variation

et al. 2018

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Hyperspectral imaging is a cutting-edge type of remote sensing used for mapping vegetation properties, rock minerals and other materials. A major drawback of hyperspectral imaging devices is their intrinsic low spatial resolution. In this paper, we propose a method for increasing the spatial resolution of a hyperspectral image by fusing it with an image of higher spatial resolution that was obtained with a different imaging modality. This is accomplished by solving a variational problem in which the regularization functional is the directional total variation. To accommodate for possible mis-registrations between the two images, we consider a non-convex blind super-resolution problem where both a fused image and the corresponding convolution kernel are estimated. Using this approach, our model can realign the given images if needed. Our experimental results indicate that the non-convexity is negligible in practice and that reliable solutions can be computed using a variety of different optimization algorithms. Numerical results on real remote sensing data from plant sciences and urban monitoring show the potential of the proposed method and suggests that it is robust with respect to the regularization parameters, mis-registration and the shape of the kernel.AMS classification scheme numbers: 49M37, 65K10, 90C30, 90C90 PACS numbers: 42.30. Va, 42.68.Wt, 95.75.Pq, 95.75.Rs Figure 1. Three example data for image fusion in remote sensing. They each consist of a hyperspectral image (small image, only one channel shown) and an image of higher spatial resolution (large image). The goal is to create an image that has both high spatial and high spectral resolution.

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Section: Discussionmentioning

confidence: 95%

Section: The Forward Operatormentioning

confidence: 95%

Section: The Forward Operatormentioning

confidence: 99%

Section: Definition (Directional Total Variationmentioning

confidence: 99%

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Blind image fusion for hyperspectral imaging with the directional total variation

et al. 2018

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“…Beyond anisotropic PDEs, non-smooth anisotropic regularisers for variational imaging models are also considered. In [17,25,26,33,34], for instance, directionality is used to define the anisotropic total-variation and total-generalised-variation functionals. This is classically done by considering a re-parametrised version of the gradient operator depending on the local orientation of the image, which allows to enforce diffusion along certain directions only.…”

Section: Anisotropic Diffusionmentioning

confidence: 99%

Anisotropic osmosis filtering for shadow removal in images

Parisotto¹,

Calatroni²,

Caliari³

et al. 2019

Inverse Problems

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We present an anisotropic extension of the isotropic osmosis model that has been introduced by Weickert et al. [38] for visual computing applications, and we adapt it specifically to shadow removal applications. We show that in the integrable setting, linear anisotropic osmosis minimises an energy that involves a suitable quadratic form which models local directional structures. In our shadow removal applications we estimate the local structure via a modified tensor voting approach [24] and use this information within an anisotropic diffusion inpainting that resembles edge-enhancing anisotropic diffusion inpainting [39,13]. Our numerical scheme combines the nonnegativity preserving stencil of Fehrenbach and Mirebeau [10] with an exact time stepping based on highly accurate polynomial approximations of the matrix exponential. The resulting anisotropic model is tested on several synthetic and natural images corrupted by constant shadows. We show that it outperforms isotropic osmosis, since it does not suffer from blurring artefacts at the shadow boundaries.

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Tomographic Reconstruction Methods for Decomposing Directional Components

Kongskov¹,

Dong²

2017

Preprint

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Directional Total Generalized Variation Regularization

Cited by 3 publications

References 5 publications

Blind image fusion for hyperspectral imaging with the directional total variation

Blind image fusion for hyperspectral imaging with the directional total variation

Anisotropic osmosis filtering for shadow removal in images

Tomographic Reconstruction Methods for Decomposing Directional Components

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