2. Optimizing spatial and tonal data for PDE-based inpainting

Hoeltgen, Laurent; Mainberger, Markus; Hoffmann, Sebastian; Weickert, Joachim; Tang, Ching Hoo; Setzer, Simon; Johannsen, Daniel; Neumann, Franz‐Josef; Doerr, Benjamin

doi:10.1515/9783110430394-002

Cited by 17 publications

(45 citation statements)

References 120 publications

(208 reference statements)

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“…Instead of quantizing the original pixel values, R-EED chooses the optimal value at each mask position from the quantized co-domain. While this introduces an error to the sparse set K of known data, it has been shown that such brightness optimization can greatly improve the inpainting quality on the inpainting domain Ω \ K [29]. For further technical details of the original R-EED codec, we refer to [3].…”

Section: From Colorization To Compression a Review: Compressionmentioning

confidence: 99%

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Turning Diffusion-Based Image Colorization Into Efficient Color Compression

Peter

Kaufhold

Weickert

2017

IEEE Trans. on Image Process.

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The work of Levin et al. (2004) popularized stroke-based methods that add color to gray value images according to a small amount of user-specified color samples. Even though such reconstructions from sparse data suggest a possible use in compression, only few attempts were made so far in this direction. Diffusion-based compression methods pursue a similar idea: they store only few image pixels and inpaint the missing regions. Despite this close relation and a lack of diffusion-based color codecs, colorization ideas were so far only integrated into transform-based approaches such as JPEG. We address this missing link with two contributions. First, we show the relation between the discrete colorization of Levin et al. and continuous diffusion-based inpainting in the YCbCr color space. It decomposes the image into a luma (brightness) channel and two chroma (color) channels. Our luma-guided diffusion framework steers the diffusion inpainting in the chroma channels according to the structure in the luma channel. We show that making the luma-guided colorization anisotropic outperforms the method of Levin et al. significantly. Second, we propose a new luma preference codec that invests a large fraction of the bit budget into an accurate representation of the luma channel. This allows a high-quality reconstruction of color data with our colorization technique. Simultaneously, we exploit the fact that the human visual system is more sensitive to structural than to color information. Our experiments demonstrate that our new codec outperforms the state of the art in diffusion-based image compression and is competitive to transform-based codecs.

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Section: From Colorization To Compression a Review: Compressionmentioning

confidence: 99%

“…So far, there are no dedicated color codecs, but there is a variety of other specialized compression methods, for example for cartoons [24], depth maps [25]- [27], 3-D data [3], or texture [28]. For a full review of diffusion-based compression, we refer to the in-depth survey of Hoeltgen et al [29].…”

Section: Introductionmentioning

confidence: 99%

Turning Diffusion-Based Image Colorization Into Efficient Color Compression

Peter

Kaufhold

Weickert

2017

IEEE Trans. on Image Process.

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“…For the defective area in the image, starting from the edge of the target area, using the structure of the non-target area and texture information, the unknown area is predicted and patched according to the matching criteria, so that the filled image is visually reasonable and real [6]. According to different principles, digital image inpainting algorithms can be divided into two categories: structural propagation methods based on partial differential equations (PDEs) [7] and texture synthesis methods based on sample block [8].…”

Section: Introductionmentioning

confidence: 99%

“…The confidence of the pixels in the repaired area is mainly updated, and then the next pixel is prepared for inpainting. Steps (2)(3)(4)(5)(6)(7)(8) are repeated until the face image is repaired. 9.…”

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An Adaptive Face Image Inpainting Algorithm Based on Feature Symmetry

Niu

Yao

et al. 2020

Symmetry

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Face image inpainting technology is an important research direction in image restoration. When the current image restoration methods repair the damaged areas of face images with weak texture, there are problems such as low accuracy of face image decomposition, unreasonable restoration structure, and degradation of image quality after inpainting. Therefore, this paper proposes an adaptive face image inpainting algorithm based on feature symmetry. Firstly, we locate the feature points of the face, and segment the face into four feature parts based on the feature point distribution to define the feature search range. Then, we construct a new mathematical model, introduce feature symmetry to improve priority calculation, and increase the reliability of priority calculation. After that, in the process of searching for matching blocks, we accurately locate similar feature blocks according to the relative position and symmetry criteria of the target block and various feature parts of the face. Finally, we introduced the HSV (Hue, Saturation, Value) color space to determine the best matching block according to the chroma and brightness of the sample, reduce the repair error, and complete the face image inpainting. During the experiment, we firstly performed visual evaluation and texture analysis on the inpainting face image, and the results show that the face image inpainting by our algorithm maintained the consistency of the face structure, and the visual observation was closer to the real face features. Then, we used the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) as objective evaluation indicators; among the five sample face images inpainting results given in this paper, our method was better than the reference methods, and the average PSNR value improved from 2.881–5.776 dB using our method when inpainting 100 face images. Additionally, we used the time required for inpainting the unit pixel to evaluate the inpainting efficiency, and it was improved by 12%–49% with our method when inpainting 100 face images. Finally, by comparing the face image inpainting experiments with the generative adversary network (GAN) algorithm, we discuss some of the problems with the method in this paper based on graphics in repairing face images with large areas of missing features.

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“…Further applications include the works of Bloor and Wilson (1989) [5], who studied partial differential equations for generating blend surfaces. Finally, refer to [23,45] for a broad overview on PDE-based inpainting and the closely related problem of PDE-based image compression.…”

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confidence: 99%

Theoretical foundation of the weighted Laplace inpainting problem

et al. 2019

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Laplace interpolation is a popular approach in image inpainting using partial differential equations. The classic approach considers the Laplace equation with mixed boundary conditions. Recently a more general formulation has been proposed where the differential operator consists of a point-wise convex combination of the Laplacian and the known image data. We provide the first detailed analysis on existence and uniqueness of solutions for the arising mixed boundary value problem. Our approach considers the corresponding weak formulation and aims at using the Theorem of Lax-Milgram to assert the existence of a solution. To this end we have to resort to weighted Sobolev spaces. Our analysis shows that solutions do not exist unconditionally. The weights need some regularity and fulfil certain growth conditions. The results from this work complement findings which were previously only available for a discrete setup.

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2. Optimizing spatial and tonal data for PDE-based inpainting

Cited by 17 publications

References 120 publications

Turning Diffusion-Based Image Colorization Into Efficient Color Compression

Turning Diffusion-Based Image Colorization Into Efficient Color Compression

An Adaptive Face Image Inpainting Algorithm Based on Feature Symmetry

Theoretical foundation of the weighted Laplace inpainting problem

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