Inpainting and Zooming Using Sparse Representations

Fadili, M.J.; Starck, Jean-Luc; Murtagh, Fionn

doi:10.1093/comjnl/bxm055

Cited by 288 publications

(237 citation statements)

References 55 publications

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“…This work can be seen as a development of the theory of Euler's elastica curves by Mumford [40]. Chan and Shen contributed to inpainting with other models similar or related to the ones previously cited, see [11,12,13,14] and also [25,27,37]. In simple words, mathematical inpainting is the attempt to guess the morphology of the image in a relatively small missing part from the level curves of the relevant known part.…”

Section: Mathematical Inpainting and Recolorizationmentioning

confidence: 92%

The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem

2008

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On March 11, 1944, the famous Eremitani Church in Padua (Italy) was destroyed in an Allied bombing along with the inestimable frescoes by Andrea Mantegna et al. contained in the Ovetari Chapel. In the last 60 years, several attempts have been made to restore the fresco fragments by traditional methods, but without much success. One of the authors contributed to the development of an efficient pattern recognition algorithm to map the original position and orientation of the fragments, based on comparisons with an old gray level image of the fresco prior to the damage. This innovative technique allowed for the partial reconstruction of the frescoes. Unfortunately, the surface covered by the colored fragments is only 77 m 2 , while the original area was of several hundreds. This means that we can reconstruct only a fraction (less than 8%) of this inestimable artwork. In particular the original color of the blanks is not known. This begs the question of whether it is possible to estimate mathematically the original colors of the frescoes by making use of the potential information given by the available fragments and the gray level of the pictures taken before the damage. Moreover, is it possible to estimate how faithful such a restoration is? In this paper we retrace the development of the recovery of the frescoes as an inspiring and challenging real-life problem for the development of new mathematical methods. Then we shortly review two models recently studied independently by the authors for the recovery of vector valued functions from incomplete data, with applications to the recolorization problem. The models are based on the minimization of a functional which is formed by the discrepancy with respect to the data and additional regularization constraints. The latter refer to joint sparsity measures with respect to frame expansions, in particular wavelet or curvelet expansions, for the first functional and functional total variation for the second. We establish relations between these two models. As a major contribution of this work we perform specific numerical test on the real-life problem of the A. Mantegna's frescoes and we compare the results due to the two methods.MSC: 15A29, 47A52, 68U10, 94A08, 94A40

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Section: Mathematical Inpainting and Recolorizationmentioning

confidence: 92%

The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem

2008

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“…Almost all previous methods for image inpainting or completion (e.g., [8], [12], [13], etc.) need information about the support Ω of the corrupted regions.…”

Section: Sparse Low-rank Texture Repairingmentioning

confidence: 99%

“…Recently, there have also been works (see [12][13][14] and references therein) which perform inpainting based on sparse structures of image patches: patches inside the missing pixel region are synthesized as a sparse linear combination of elements from a patch dictionary. Furthermore, Bugeau et al [15] combine geometric partial differential equation (PDEs) and patch-based texture synthesis in a variational model and performs image inpainting by minimizing the proposed energy function.…”

Section: Introductionmentioning

confidence: 99%

Repairing Sparse Low-Rank Texture

Liang

Ren

Zhang

et al. 2012

Computer Vision – ECCV 2012

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Abstract. In this paper, we show how to harness both low-rank and sparse structures in regular or near regular textures for image completion. Our method leverages the new convex optimization for low-rank and sparse signal recovery and can automatically correctly repair the global structure of a corrupted texture, even without precise information about the regions to be completed. Through extensive simulations, we show our method can complete and repair textures corrupted by errors with both random and contiguous supports better than existing low-rank matrix recovery methods. Through experimental comparisons with existing image completion systems (such as Photoshop) our method demonstrate significant advantage over local patch based texture synthesis techniques in dealing with large corruption, non-uniform texture, and large perspective deformation.

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“…The authors in [13] proposed an algorithm to inpaint an image using sparse representation based iterative algorithm. The results prove that it recovers different structural components in the image.…”

Section: Related Workmentioning

confidence: 99%

Automatic Detection and Inpainting of Text Images

Bhuvaneswari¹,

Subashini²

2013

IJCA

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The proposed system detects text using connect component labelling and a set of selection/ rejection criteria which helps to retain the text region alone. The detected text region is then inpainted using fast marching algorithm which uses the pixel information that is present in the non-text region of the image for inpainting the detected text region. This work is done in two steps. The first step detects the text region from the image without the user manually marking it and in the second step the text is de-occluded from the image using the existing fast marching inpainting algorithm.

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Inpainting and Zooming Using Sparse Representations

Cited by 288 publications

References 55 publications

The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem

The application of joint sparsity and total variation minimization algorithms to a real-life art restoration problem

Repairing Sparse Low-Rank Texture

Automatic Detection and Inpainting of Text Images

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