2,098 research outputs found
Sobolev gradients and image interpolation
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 -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
Inpainting of Cyclic Data using First and Second Order Differences
Cyclic data arise in various image and signal processing applications such as
interferometric synthetic aperture radar, electroencephalogram data analysis,
and color image restoration in HSV or LCh spaces. In this paper we introduce a
variational inpainting model for cyclic data which utilizes our definition of
absolute cyclic second order differences. Based on analytical expressions for
the proximal mappings of these differences we propose a cyclic proximal point
algorithm (CPPA) for minimizing the corresponding functional. We choose
appropriate cycles to implement this algorithm in an efficient way. We further
introduce a simple strategy to initialize the unknown inpainting region.
Numerical results both for synthetic and real-world data demonstrate the
performance of our algorithm.Comment: accepted Converence Paper at EMMCVPR'1
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