Euler's Elastica and Curvature-Based Inpainting

By Jianhong Shen, S. Kang, Tony F. Chan. SIAM Journal on Applied Mathematics, 2003

673 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/50e2646744ae197f7746a64988a186dcc0b43eb2

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Citations in the corpus

A Combined First and Second Order Variational Approach for Image Reconstruction (2012, neutral): “ kX 2nD(u u 0)k 2 + kvk 1 + kwk 1; such that u= ~u, v= r~u, w= r2u~. We refer the reader to [57] for the details. In Figure 14 we compare our method with harmonic and Euler’s elastica inpainting, see [25, 67]. In the case of harmonic inpainting the regulariser is the square of the L2 norm of the gra”
A framelet-based image inpainting algorithm (2008, methodology): “Many useful techniques have been proposed in recent years to address the problem, see, for example, [1–3,9,11–15,26,27, 29,38].”
Vector-valued image regularization with PDEs: a common framework for different applications (2005, positive): “Color image inpainting : Image inpainting, recently proposed in [4, 7 , 8, 9] consists in filling undesired holes (defined by the user) in images by interpolating the data located at the hole’s neighborhood.”
Inpainting and Zooming Using Sparse Representations (2009, methodology): “By functionalizing Euler’s elastica energy, Masnou and Morel [1, 2], proposed an elastica-based variational inpainting model, and [13] developed its mathematical foundation and a PDE computational scheme.”
Variational PDE models in image processing (2002, methodology): “In the last integrand, the curvature is given by . (Notice that in the absence of the curvature term, the above formula is exactly the co-area formula for smooth functions [31].) This elastica prior model was first studied for inpainting by Masnou and Morel [35], and Chan, Kang, and Shen [ 11 ], and”
Inpainting of Binary Images Using the Cahn–Hilliard Equation (2007, methodology): “[ 7 ] H. B. Barlow, C. Blakemore, and J. D. Pettigrew, “The neural mech-”
Primal‐dual active set methods for Allen–Cahn variational inequalities with nonlocal constraints (2010, methodology): “Other variational models are for example the Euler elastica model [38], the active contour model [114] which is based on the Mumford-Shah segmentation problem, but also higher order variational approaches.”
Optical flow modeling and computation: A survey (2015, methodology): “Inpainting methods can be coarsely divided into two classes, diffusion-based methods [24, 56] and exemplar-based methods [6, 68, 151].”
A level set formulation for Willmore flow (2004, methodology): “Furthermore, curvature based inpainting methods have been proposed by Masnou, Morel [24] [2] and Chan et al. [8].”
Space-Time Completion of Video (2007, background): “, [5], [6], [22]) was defined in a principled way as an edge continuation process, but is restricted to small (narrow) missing image portions in highly structured image data.”
Variable Exponent, Linear Growth Functionals in Image Restoration (2006, background): “6) also has direct application in image processing, as it can be used for image interpolation [13, 27], also referred to as noise-free image inpainting [8, 17, 18].”