Pde based inpainting algorithms: performance evaluation of the Cahn-Hillard model

Image inpainting consists in restoring a missing or a damaged part of an image on the basis of the signal information in the pixels sur- rounding the missing domain. To this aim a suitable image model is needed to represent the signal features to be reproduced within the inpainting domain, also depending on the size of the missing area. With no claim of completeness, in this paper the main streamline of the development of the PDE based models is retraced. Then, the Cahn-Hillard model for binary images is analyzed in detail and its performances are evaluated on some numerical experiments

Combined Structure and Texture Image Inpainting Algorithm for Natural Scene Image Completion

Image inpainting or image completion refers to the task of filling in the missing or damaged regions of an image in a visually plausible way. Many works on this subject have been proposed these recent years. We present a hybrid method for completion of images of natural scenery, where the removal of a foreground object creates a hole in the image. The basic idea is to decompose the original image into a structure and a texture image. Reconstruction of each image is performed separately. The missing information in the structure component is reconstructed using a structure inpainting algorithm, while the texture component is repaired by an improved exemplar based texture synthesis technique. Taking advantage of both the structure inpainting methods and texture synthesis techniques, we designed an effective image reconstruction method. A comparison with some existing methods on different natural images shows the merits of our proposed approach in providing high quality inpainted images. Keywords: Image inpainting, Decomposition method, Structure inpainting, Exemplar based, Texture synthesi

Investigation of Optimal Image Inpainting Techniques for Image Reconstruction and Image Restoration Applications

People in today's society take a lot of pictures with their smartphones and also make an effort to keep their old photographs safe, but with time, those photographs deteriorate. Image inpainting is the art of reconstructing damaged or missing parts of an image. Repairing scratches in photographs or film negatives, or adding or removing elements like stamped dates or "red-eye," are all possible through inpainting. In order to restore the image many techniques have been developed, significant techniques include exemplar based inpainting, coherent based inpainting and method for correction of non-uniform illumination. The four main applications of these image inpainting techniques are scratch removal, text removal, object removal and image restoration. However, all the four image inpainting applications cannot be implemented using a single technique. According to the literature, there has been relatively less work done in the field of image inpainting applications. Investigation has been carried out to find the suitability of these three techniques for the four above mentioned image inpainting applications based on two performance metrics

p-Laplace Variational Image Inpainting Model Using Riesz Fractional Differential Filter

In this paper, p-Laplace variational image inpainting model with symmetric Riesz fractional differential filter is proposed. Variational inpainting models are very useful to restore many smaller damaged regions of an image. Integer order variational image inpainting models (especially second and fourth order) work well to complete the unknown regions. However, in the process of inpainting with these models, any of the unindented visual effects such as staircasing, speckle noise, edge blurring, or loss in contrast are introduced. Recently, fractional derivative operators were applied by researchers to restore the damaged regions of the image. Experimentation with these operators for variational image inpainting led to the conclusion that second order symmetric Riesz fractional differential operator not only completes the damaged regions effectively, but also reducing unintended effects. In this article, The filling process of damaged regions is based on the fractional central curvature term. The proposed model is compared with integer order variational models and also GrunwaldLetnikov fractional derivative based variational inpainting in terms of peak signal to noise ratio, structural similarity and mutual information

Regularised Diffusion-Shock Inpainting

We introduce regularised diffusion--shock (RDS) inpainting as a modification of diffusion--shock inpainting from our SSVM 2023 conference paper. RDS inpainting combines two carefully chosen components: homogeneous diffusion and coherence-enhancing shock filtering. It benefits from the complementary synergy of its building blocks: The shock term propagates edge data with perfect sharpness and directional accuracy over large distances due to its high degree of anisotropy. Homogeneous diffusion fills large areas efficiently. The second order equation underlying RDS inpainting inherits a maximum--minimum principle from its components, which is also fulfilled in the discrete case, in contrast to competing anisotropic methods. The regularisation addresses the largest drawback of the original model: It allows a drastic reduction in model parameters without any loss in quality. Furthermore, we extend RDS inpainting to vector-valued data. Our experiments show a performance that is comparable to or better than many inpainting models, including anisotropic processes of second or fourth order

Cell Path Reconstruction Using 3D Digital Inpainting

Digital inpainting is the reconstruction of a missing or damaged region in a digital image. Intensity values in the missing region are approximated using information near the boundary of the region. Some applications include repair of chipped paintings, repair of rips in paper photographs, and removal of unwanted objects from photographs. In this thesis, we review 2D digital inpainting techniques, examine the application of 3D digital inpainting to cell path reconstruction, and propose a new inpainting technique inspired by the cell path reconstruction problem. Cell path reconstruction is the estimation of the shape and position of living cells in videos recorded using fluorescence microscopy. This procedure is necessary because in a particular phase of the life cycle of some cells, fluorescent light passes through the cells with an undetectable change in wavelength and they vanish from the frame. This leads to misleading results when, for example, the number of cells in a particular frame is counted. We transform the position/shape estimation problem into a 3D shape reconstruction problem by stacking the frames of the video to form a 3D volume. In this volume, cell paths form tubes with missing segments where cells have vanished. We apply elastica inpainting to the 3D tube reconstruction problem and introduce a new 3D inpainting model to overcome difficulties with a direct generalization to 3D of 2D elastica

CNN-based Euler's Elastica Inpainting with Deep Energy and Deep Image Prior

Euler's elastica constitute an appealing variational image inpainting model. It minimises an energy that involves the total variation as well as the level line curvature. These components are transparent and make it attractive for shape completion tasks. However, its gradient flow is a singular, anisotropic, and nonlinear PDE of fourth order, which is numerically challenging: It is difficult to find efficient algorithms that offer sharp edges and good rotation invariance. As a remedy, we design the first neural algorithm that simulates inpainting with Euler's Elastica. We use the deep energy concept which employs the variational energy as neural network loss. Furthermore, we pair it with a deep image prior where the network architecture itself acts as a prior. This yields better inpaintings by steering the optimisation trajectory closer to the desired solution. Our results are qualitatively on par with state-of-the-art algorithms on elastica-based shape completion. They combine good rotation invariance with sharp edges. Moreover, we benefit from the high efficiency and effortless parallelisation within a neural framework. Our neural elastica approach only requires 3x3 central difference stencils. It is thus much simpler than other well-performing algorithms for elastica inpainting. Last but not least, it is unsupervised as it requires no ground truth training data.Comment: In Proceedings of the 10th European Workshop on Visual Information Processing, Lisbon, 202