2,368 research outputs found

    Towards unifying diffusion and exemplar-based inpainting

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    A novel framework for image inpainting is proposed, relying on graph-based diffusion processes. Depending on the construction of the graph, both flow-based and exemplar-based inpainting methods can be implemented by the same equations, hence providing a unique framework for geometry and texture-based approaches to inpainting. Furthermore, the use of a variational framework allows to overcome the usual sensitivity of exemplar-based methods to the heuristic issues by providing an evolution criterion. The use of graphs also makes our framework more flexible than former non-local variational formulations, allowing for example to mix spatial and non-local constraints and to use a data term to provide smoother blending between the initial image and the result

    Sobolev gradients and image interpolation

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    We present here a new image inpainting algorithm based on the Sobolev gradient method in conjunction with the Navier-Stokes model. The original model of Bertalmio et al is reformulated as a variational principle based on the minimization of a well chosen functional by a steepest descent method. This provides an alternative of the direct solving of a high-order partial differential equation and, consequently, allows to avoid complicated numerical schemes (min-mod limiters or anisotropic diffusion). We theoretically analyze our algorithm in an infinite dimensional setting using an evolution equation and obtain global existence and uniqueness results as well as the existence of an ω\omega-limit. Using a finite difference implementation, we demonstrate using various examples that the Sobolev gradient flow, due to its smoothing and preconditioning properties, is an effective tool for use in the image inpainting problem
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