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...terested readers are referred to this work for more details, examples, and theoretical results. The two main ingredients of the decomposition developed in [31] are the total variation minimization of =-=[27]-=- for image denoising and restoration, and the space of oscillating functions introduced in [23] to model texture or noise. Let be a given observed image, . could be just a noisy version of a true unde...

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... follows the techniques introduced in [21], [27], as well as numerous examples and applications, see [5]. Note in particular that at every numerical step of (8), a step of anisotropic diffusion, [1], =-=[25]-=-, is applied [5]. Multiresolution can also be applied to speed-up the convergence [5]. For image inpainting alternatives to this approach, see [2], [3]. In particular, [3] shows the relationship of th...

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...fter this paper was accepted for publication, we learned that a number of new papers on inpainting, inspired by [5], will be published at SIGGRAPH 2003 and CVPR 2003. functions of bounded variation , =-=[12]-=-, allowing for edges where is a tuning parameter. The second term in the energy is a fidelity term, while the first term is a regularizing term, to remove noise or small details, while keeping importa...

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...hind the algorithms that have been proposed in the literature is to fill-in these regions with available information from their surroundings. This information can be automatically detected as in [5], =-=[10]-=-, or hinted by the user as in more classical texture filling techniques [8], [14], [28]. Manuscript received August 8, 2002; revised April 15, 2003. This work was supported in part by the Office of Na...

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...en replace the current pixel being filled-in in the lost block by the value of the corresponding pixel next to the selected block. This algorithm is considerably faster when using the improvements in =-=[9]-=-, [13], [33]. Note also that a segmentation algorithm (to the texture image ) can be added to aid this texture synthesis algorithm. IV. IMAGE INPAINTING We now describe the third key component of our ...

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...the current pixel being filled-in in the lost block by the value of the corresponding pixel next to the selected block. This algorithm is considerably faster when using the improvements in [9], [13], =-=[33]-=-. Note also that a segmentation algorithm (to the texture image ) can be added to aid this texture synthesis algorithm. IV. IMAGE INPAINTING We now describe the third key component of our proposed sch...

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...ea behind the algorithms that have been proposed in the literature is to fill-in these regions with available information from their surroundings. This information can be automatically detected as in =-=[5]-=-, [10], or hinted by the user as in more classical texture filling techniques [8], [14], [28]. Manuscript received August 8, 2002; revised April 15, 2003. This work was supported in part by the Office...

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...which follows the techniques introduced in [21], [27], as well as numerous examples and applications, see [5]. Note in particular that at every numerical step of (8), a step of anisotropic diffusion, =-=[1]-=-, [25], is applied [5]. Multiresolution can also be applied to speed-up the convergence [5]. For image inpainting alternatives to this approach, see [2], [3]. In particular, [3] shows the relationship...

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... The two main ingredients of the decomposition developed in [31] are the total variation minimization of [27] for image denoising and restoration, and the space of oscillating functions introduced in =-=[23]-=- to model texture or noise. Let be a given observed image, . could be just a noisy version of a true underlying image , or could be a textured image, then being a simple sketchy approximation or a car...

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...these regions with available information from their surroundings. This information can be automatically detected as in [5], [10], or hinted by the user as in more classical texture filling techniques =-=[8]-=-, [14], [28]. Manuscript received August 8, 2002; revised April 15, 2003. This work was supported in part by the Office of Naval Research, the National Science Foundation, the National Institute of He...

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...decomposed into the sum of two images, one capturing the basic image structure and one capturing the texture (and random noise), second row. This follows the recent work by Vese and Osher reported in =-=[30]-=-, [31]. The first image is inpainted following the work by Bertalmio-Sapiro-CasellesBallester described in [5], while the second one is filled-in with a texture synthesis algorithm following the work ...

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...u). Digital Object Identifier 10.1109/TIP.2003.815261 1057-7149/03$17.00 © 2003 IEEE The algorithms reported in the literature best perform for pure texture, [10], [14], [28], or pure structure, [2],=-= [3]-=-, [5]. This means that for ordinary images such as the one in Fig. 1, different techniques work better for different parts. In [26], it was shown how to automatically switch between the pure texture a...

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...mn.edu). Digital Object Identifier 10.1109/TIP.2003.815261 1057-7149/03$17.00 © 2003 IEEE The algorithms reported in the literature best perform for pure texture, [10], [14], [28], or pure structure,=-= [2]-=-, [3], [5]. This means that for ordinary images such as the one in Fig. 1, different techniques work better for different parts. In [26], it was shown how to automatically switch between the pure text...

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...ns with available information from their surroundings. This information can be automatically detected as in [5], [10], or hinted by the user as in more classical texture filling techniques [8], [14], =-=[28]-=-. Manuscript received August 8, 2002; revised April 15, 2003. This work was supported in part by the Office of Naval Research, the National Science Foundation, the National Institute of Health, the Of...

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...s. All these works were in part inspired by [22], [24]. Full details can also be found at http://mountains.ece.umn.edu/~guille/inpainting.htm. Additional related work is described in [7], [15], [16], =-=[19]-=-, and [20], while [6], [11], [18], and [32] provide literature on inpainting as done by professional restorators. Comments on these contributions and comparisons with the work just described are provi...

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... the hole , propagation done in the direction of minimal change (the isophotes, ). For details on the numerical implementation of this inpainting technique, which follows the techniques introduced in =-=[21]-=-, [27], as well as numerous examples and applications, see [5]. Note in particular that at every numerical step of (8), a step of anisotropic diffusion, [1], [25], is applied [5]. Multiresolution can ...

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...t perform for pure texture, [10], [14], [28], or pure structure, [2], [3], [5]. This means that for ordinary images such as the one in Fig. 1, different techniques work better for different parts. In =-=[26]-=-, it was shown how to automatically switch between the pure texture and pure structure filling-in process. This is done by analyzing the area surrounding the region to be filled-in (inspired by [17]),...

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...e the steady state V(AI)sVI = 0. The work in [2] presents a formal variational approach that leads to a system of coupled second order differential equations. All these works were in part inspired by =-=[21, 23]-=-. Full details can also be found at mountains.ece.umn.edu/guille/inpainting.htm. Additional related work is described in [7, 14, 15, 18, 19], while [6, 10, 17, 30] provides literature on inpainting as...

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... regions with available information from their surroundings. This information can be automatically detected as in [5], [10], or hinted by the user as in more classical texture filling techniques [8], =-=[14]-=-, [28]. Manuscript received August 8, 2002; revised April 15, 2003. This work was supported in part by the Office of Naval Research, the National Science Foundation, the National Institute of Health, ...

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...ial equations. All these works were in part inspired by [22], [24]. Full details can also be found at http://mountains.ece.umn.edu/~guille/inpainting.htm. Additional related work is described in [7], =-=[15]-=-, [16], [19], and [20], while [6], [11], [18], and [32] provide literature on inpainting as done by professional restorators. Comments on these contributions and comparisons with the work just describ...

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...erential equations. All these works were in part inspired by [22], [24]. Full details can also be found at http://mountains.ece.umn.edu/~guille/inpainting.htm. Additional related work is described in =-=[7]-=-, [15], [16], [19], and [20], while [6], [11], [18], and [32] provide literature on inpainting as done by professional restorators. Comments on these contributions and comparisons with the work just d...

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...uations. All these works were in part inspired by [22], [24]. Full details can also be found at http://mountains.ece.umn.edu/~guille/inpainting.htm. Additional related work is described in [7], [15], =-=[16]-=-, [19], and [20], while [6], [11], [18], and [32] provide literature on inpainting as done by professional restorators. Comments on these contributions and comparisons with the work just described are...

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... The two main ingredients of the decomposition developed in [29] are the total variation minimization of [26] for image denoising and restoration, and the space of oscillating functions introduced in =-=[22]-=- to model texture or noise. Let I: 2 _sbe a given observed image, I C L2(). I could be just a noisy version of a true underlying image u, or could be a textured image, u then being a simple sketchy ap...

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...n [26], it was shown how to automatically switch between the pure texture and pure structure filling-in process. This is done by analyzing the area surrounding the region to be filled-in (inspired by =-=[17]-=-), and selecting either a texture synthesis or a structure inpainting technique. Since most image areas are not pure texture or pure structure, this approach provides just a first attempt in the direc...

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... [22], [24]. Full details can also be found at http://mountains.ece.umn.edu/~guille/inpainting.htm. Additional related work is described in [7], [15], [16], [19], and [20], while [6], [11], [18], and =-=[32]-=- provide literature on inpainting as done by professional restorators. Comments on these contributions and comparisons with the work just described are provided in [5]. Fig. 6. Comparison of our propo...

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...place the current pixel being filled-in in the lost block by the value of the corresponding pixel next to the selected block. This algorithm is considerably faster when using the improvements in [9], =-=[13]-=-, [33]. Note also that a segmentation algorithm (to the texture image ) can be added to aid this texture synthesis algorithm. IV. IMAGE INPAINTING We now describe the third key component of our propos...

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...nspired by [22], [24]. Full details can also be found at http://mountains.ece.umn.edu/~guille/inpainting.htm. Additional related work is described in [7], [15], [16], [19], and [20], while [6], [11], =-=[18]-=-, and [32] provide literature on inpainting as done by professional restorators. Comments on these contributions and comparisons with the work just described are provided in [5]. Fig. 6. Comparison of...

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...e in part inspired by [22], [24]. Full details can also be found at http://mountains.ece.umn.edu/~guille/inpainting.htm. Additional related work is described in [7], [15], [16], [19], and [20], while =-=[6]-=-, [11], [18], and [32] provide literature on inpainting as done by professional restorators. Comments on these contributions and comparisons with the work just described are provided in [5]. Fig. 6. C...

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...s. All these works were in part inspired by [21, 23]. Full details can also be found at mountains.ece.umn.edu/guille/inpainting.htm. Additional related work is described in [7, 14, 15, 18, 19], while =-=[6, 10, 17, 30]-=- provides literature on inpainting as done by professional restorators. Comments on these contributions and comparisons with the work just described are provided in [5]. 5 Experimental results We now ...

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...2. to achieve the steady state . The work in [2] presents a formal variational approach that leads to a system of coupled second order differential equations. All these works were in part inspired by =-=[22]-=-, [24]. Full details can also be found at http://mountains.ece.umn.edu/~guille/inpainting.htm. Additional related work is described in [7], [15], [16], [19], and [20], while [6], [11], [18], and [32] ...

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...n [25], it was shown how to automatically switch between the pure texture and pure structure filling-in process. This is done by analyzing the area surrounding the region to be filled-in (inspired by =-=[16]-=-), and selecting either a texture synthesis or a structure inpainting technique. Since most image areas are not pure texture or pure structure, this approach provides just a first attempt in the direc...