Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIAM Journal on Numerical Analysis
Edge Direction Preserving Image Zooming: A Mathematical and Numerical Analysis
SIAM Journal on Numerical Analysis
Variational Restoration and Edge Detection for Color Images
Journal of Mathematical Imaging and Vision
A Common Framework for Curve Evolution, Segmentation and Anisotropic Diffusion
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Image Deblurring in the Presence of Impulsive Noise
International Journal of Computer Vision
Non-local Regularization of Inverse Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Nonlocal Variational Image Deblurring Models in the Presence of Gaussian or Impulse Noise
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Generalizing the Nonlocal-means to super-resolution reconstruction
IEEE Transactions on Image Processing
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
Deblurring of Color Images Corrupted by Impulsive Noise
IEEE Transactions on Image Processing
From a modified ambrosio-tortorelli to a randomized part hierarchy tree
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree
Journal of Mathematical Imaging and Vision
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We introduce several color image restoration algorithms based on the Mumford-Shah model and nonlocal image information. The standard Ambrosio-Tortorelli and Shah models are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, textures are not local in nature and require semi-local/non-local information to be denoised efficiently. Inspired from recent work (NL-means of Buades, Coll, Morel and NL-TV of Gilboa, Osher), we extend the standard models of Ambrosio-Tortorelli and Shah approximations to Mumford-Shah functionals to work with nonlocal information, for better restoration of fine structures and textures. We present several applications of the proposed nonlocal MS regularizers in image processing such as color image denoising, color image deblurring in the presence of Gaussian or impulse noise, color image inpainting, and color image super-resolution. In the formulation of nonlocal variational models for the image deblurring with impulse noise, we propose an efficient preprocessing step for the computation of the weight function w . In all the applications, the proposed nonlocal regularizers produce superior results over the local ones, especially in image inpainting with large missing regions. Experimental results and comparisons between the proposed nonlocal methods and the local ones are shown.