Navier-stokes, fluid dynamics, and image and video inpainting

By Marcelo Bertalmío, Andrea L. Bertozzi, Guillermo Sapiro. Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001, 2001

1,213 citations recorded by the source corpus.

Subfields: Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/95498890efa965658d77c118eaec935622634fc0

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Citations in the corpus

Simultaneous cartoon and texture image inpainting using morphological component analysis (MCA) (2005, methodology): “Among the numerous approaches to fill in holes in images, variational methods are very att these were pioneered by Guillermo Sapiro and his collaborators [6,20,21], and followed by Ch Shen [7].”
InstaBoost: Boosting Instance Segmentation via Probability Map Guided Copy-Pasting (2019, methodology): “Inpainting method [5] are adopted to fill in such holes.”
Region filling and object removal by exemplar-based image inpainting (2004, background): “A number of algorithms specifically address the image filling issue for the task of image restoration, where speckles, scratches, and overlaid text are removed [2], [3], [4], [7], [23].”
MVSS-Net: Multi-View Multi-Scale Supervised Networks for Image Manipulation Detection (2021, methodology): “We apply regular data augmentation for training, including flipping, blurring, compression and naive manipulations either by cropping and pasting a squared area or using built-in OpenCV inpainting functions [46], [47].”
Image completion with structure propagation (2005, methodology): “Their method is PDE-based and has its root in the Navier-Stokes equation in fluid dynamics [Bertalmio et al. 2001].”
Space-Time Completion of Video (2007, methodology): “Even when applied to video sequences (as in [4]), the completion was still performed spatially.”
An Image Inpainting Technique Based on the Fast Marching Method (2004, methodology): “Inpaint-ing points in increasing distance order from ∂ Ω i ensures that areas closest to known image points are ﬁ lled in ﬁ rst, thus mimicking manual inpainting techniques [Bertalmio 00, Bertalmio 01].”
VIMPAC: Video Pre-Training via Masked Token Prediction and Contrastive Learning (2021, background): “In the case of images, generative approaches often operate on pixel space [5, 10, 35, 61, 70], which can be extremely expensive for larger input size like videos and has hence limited the widespread adoption of these methods.”
Deep Depth Completion of a Single RGB-D Image (2018, methodology): “Many methods have been proposed for filling holes in depth channels of RGB-D images, including ones that employ smoothness priors [30], fast marching methods [25, 42], Navier-Stokes [6], anisotropic diffusion [41], background surface extrapolation [51, 54, 68], colordepth edge alignment [10, 77, 81]”
Variational PDE models in image processing (2002, neutral): “Other approaches to the inpainting problem can be found in [3, 5, 8]. In particular, it has been just recently pointed out in [ 4 ] that the PDE inpainting model in [5] is closely related to the stream function-vorticity equation in fluid dynamics.”
A level set formulation for Willmore flow (2004, methodology): “Here, higher order methods were presented for instance by Bertalmio et al. [7] [6].”
Mask-Specific Inpainting with Deep Neural Networks (2014, methodology): “Visually our approach performs better than the approaches by [5], [2], [20], [18], [22] and by [1].”
Inpainting and Zooming Using Sparse Representations (2009, background): “Basically, the major mechanisms to get information into the inpainting domain are: • Diffusion and transport PDE/Variational principle: in [3, 4, 5, 6] the PDE is obtained phenomenologically, and axiomatically in [7].”
Aggregated Contextual Transformations for High-Resolution Image Inpainting (2021, background): “pleting large missing regions [1], [9], [29], [30].”
Implicit Neural Representations with Periodic Activation Functions (2020, methodology): “7, where we compare performance on texture images versus Deep Image Prior [41], Navier-Stokes, Fluid Dynamics Image Inpainting [7] (Diffusion), and SIRENs with no prior, total variation prior (TV), and Frobenius norm of Hessian [31, 30] priors (FH) respectively.”
Digital inpainting based on the Mumford–Shah–Euler image model (2002, background): “[10], the transportation process [7] (the first high-order PDE model), the diffusion process [14], and their combination [6, 13].”
Inpainting of Binary Images Using the Cahn–Hilliard Equation (2007, methodology): “In subsequent work with Bertozzi [3], they realized that the method in [1] has intimate connections with 2-”
Spatio-Temporal Image Pattern Prediction Method Based on a Physical Model With Time-Varying Optical Flow (2013, methodology): “However, the purpose in [43] was to propagate a peripheral image of a hole into a missing image region.”