2016
DOI: 10.1186/s13640-016-0110-0
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Directional global three-part image decomposition

Abstract: We consider the task of image decomposition, and we introduce a new model coined directional global three-part decomposition (DG3PD) for solving it. As key ingredients of the DG3PD model, we introduce a discrete multi-directional total variation norm and a discrete multi-directional G-norm. Using these novel norms, the proposed discrete DG3PD model can decompose an image into two or three parts. Existing models for image decomposition Advantages of the DG3PD model over existing ones lie in the properties enfor… Show more

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Cited by 6 publications
(28 citation statements)
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References 54 publications
(110 reference statements)
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“…In the area of computer vision and image processing, important applications include image enhancement, denoising, inpainting, feature extraction and compression. In one subdomain of image processing, these challenges are approached by decomposing images into two or three parts [27], e.g. a cartoon component, which contains piecewise constant or piecewise smooth parts, a texture component, which captures oscillating patterns, and a noise component, which contains small scale objects (corresponding to high frequency parts in the Fourier domain).…”
Section: Discussionmentioning
confidence: 99%
“…In the area of computer vision and image processing, important applications include image enhancement, denoising, inpainting, feature extraction and compression. In one subdomain of image processing, these challenges are approached by decomposing images into two or three parts [27], e.g. a cartoon component, which contains piecewise constant or piecewise smooth parts, a texture component, which captures oscillating patterns, and a noise component, which contains small scale objects (corresponding to high frequency parts in the Fourier domain).…”
Section: Discussionmentioning
confidence: 99%
“…The G3PD method [ 64 ] follows a variational approach to decompose a fingerprint image into three parts and obtains the ROI based on the texture component. The further advanced and more general DG3PD method [ 66 ] has also been applied to latent fingerprint segmentation. The method by Bartůněk [ 65 ] relies on normalisation and local kurtosis estimation as a novel feature for segmentation.…”
Section: Discussionmentioning
confidence: 99%
“…We define a method for restoration of the original noisy/non-noisy image f with a set of known missing regions D . The proposed model is a generalized version of DG3PD [ 35 ] for the inpainting and denoising problem. This modification for our DG3PD inpainting is inspired by Elad et al [ 23 ].…”
Section: Inpainting By Dg3pdmentioning
confidence: 99%
“…Note that if there are no missing regions, i.e. χ c D [ k ] = 1, ∀ k ∈ Ω , the minimization problem ( 2.1 ) becomes the DG3PD model [ 35 ]. Next, we discuss how to solve the DG3PD-inpainting model ( 2.1 ).…”
Section: Inpainting By Dg3pdmentioning
confidence: 99%
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