Variational image inpainting

Chan, Tony F.; Shen, Jianhong

doi:10.1002/cpa.20075

Cited by 126 publications

(39 citation statements)

References 60 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: 91%

“…The choice of this regularization measure was encouraged by the fact that several inpainting approaches deal with total variation penalties [12,14]. Since in 2 dimensions, 1 sparse wavelet expansions are known to give 'near' minimal total variation solutions, see, e.g., [17,20], this kind of sparsity constraint seems to be well suited for our purpose.…”

Section: Wavelet Frames Joint Sparsity and Recolorization Modelmentioning

confidence: 99%

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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: 91%

Section: Wavelet Frames Joint Sparsity and Recolorization Modelmentioning

confidence: 99%

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

2008

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“…The second type is derived from the diffusion process and based on partial differential equations [20]. It originates from the conventional isotropic heat flow equation and has been widespread used in image filtering [21][22][23][24], segmentation [25][26][27] and inpainting [28][29][30]. And the third type is based on the mathematical morphology [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Mutual Information Criterion-Based Optimal Scale Selection for Image Denoising and Segmentation

Wen¹,

Zhu²,

Gu³

2013

Appl. Math. Inf. Sci.

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Scale-spaces play an important role in many computer vision tasks. Automatic scale selection is at the foundation of multiscale image analysis, but its performance is still very subjective and empirical. To automatically select the appropriate scale for a particular issue, a scale selection model based on information theory is proposed in this paper. The proposed model utilizes mutual information as a measuring criterion of similarity for the optimal scale selection in multi-scale analysis, with applications to image denoising and segmentation. Firstly, we focus on the morphological operator based scale selection to image denoising. This technique does not require the prior knowledge of the noise variance and can effectively eliminate the variation of illumination. Secondly, we develop a clustering based unsupervised image segmentation algorithm by recursively pruning the Huffman coding tree. The proposed clustering algorithm can preserve the maximum amount of information at a specific clustering number from the information-theoretical point of view. Finally, for the feasibility of the proposed algorithms, its theoretical properties are analyzed mathematically and its performance is tested by a series of experiments, which demonstrate that it yields the optimal scale for our developed image denoising and segmentation algorithms.

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“…On the other hands, the image interpolation or restoration techniques for damaged and occluded images are also proposed [5,6,7,8,9,10]. However, some of them can only treat with line-shape scratches [5,6,7], because they are the techniques for restoring old films.…”

Section: Introductionmentioning

confidence: 99%

“…However, some of them can only treat with line-shape scratches [5,6,7], because they are the techniques for restoring old films. It is also required that human operators indicate the region of noises interactively (not automatically) [8,9,10]. At any hand, it is also very difficult to treat large noises and to duplicate the complex textures with these methods.…”

Section: Introductionmentioning

confidence: 99%

Virtual wiper — removal of adherent noises from images of dynamic scenes by using a pan–tilt camera

Yamashita¹,

Harada²,

Kaneko³

et al. 2005

Advanced Robotics

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In this paper, we propose a new method that can remove view-disturbing noises from images of dynamic scenes. One of the thorny problems in outdoor surveillance by a camera is that adherent noises such as waterdrops or mud blobs on the protecting glass surface lens disturb the view from the camera. Therefore, we propose a method for removing adherent noises from images of dynamic scenes taken by changing the direction of a pan-tilt camera, which is often used for surveillance.Our method is based on the comparison of two images, a reference image and a second image taken by a different camera angle. The latter image is transformed by a projective transformation and subtracted from the reference image to extract the regions of adherent noises and moving objects.The regions of adherent noises in the reference image are identified by examining the shapes and distances of regions existing in the subtracted image. Finally, regions of adherent noises can be eliminated by merging two images. Experimental results show the effectiveness of our proposed method.

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Variational image inpainting

Cited by 126 publications

References 60 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

Mutual Information Criterion-Based Optimal Scale Selection for Image Denoising and Segmentation

Virtual wiper — removal of adherent noises from images of dynamic scenes by using a pan–tilt camera

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