The Computation of Visible-Surface Representations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
International Journal of Computer Vision
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Coherence-Enhancing Diffusion Filtering
International Journal of Computer Vision
Orthonormal Vector Sets Regularization with PDE's and Applications
International Journal of Computer Vision
Numerical Methods for p-Harmonic Flows and Applications to Image Processing
SIAM Journal on Numerical Analysis
Regularized Laplacian Zero Crossings as Optimal Edge Integrators
International Journal of Computer Vision
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional
International Journal of Computer Vision
An Improved LOT Model for Image Restoration
Journal of Mathematical Imaging and Vision
A Nonlinear Structure Tensor with the Diffusivity Matrix Composed of the Image Gradient
Journal of Mathematical Imaging and Vision
Anisotropic Smoothing Using Double Orientations
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Inpainting by Flexible Haar-Wavelet Shrinkage
SIAM Journal on Imaging Sciences
Image and Vision Computing
A TV-stokes denoising algorithm
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Interpolating orientation fields: an axiomatic approach
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Filling-in by joint interpolation of vector fields and gray levels
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Noise removal using smoothed normals and surface fitting
IEEE Transactions on Image Processing
A Short- Time Beltrami Kernel for Smoothing Images and Manifolds
IEEE Transactions on Image Processing
Augmented Lagrangian Method for Generalized TV-Stokes Model
Journal of Scientific Computing
A New TV-Stokes Model with Augmented Lagrangian Method for Image Denoising and Deconvolution
Journal of Scientific Computing
A coupled variational model for image denoising using a duality strategy and split Bregman
Multidimensional Systems and Signal Processing
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In this paper, we propose an orientation-matching functional minimization for image denoising and image inpainting. Following the two-step TV-Stokes algorithm (Rahman et al. in Scale space and variational methods in computer vision, pp. 473---482, Springer, Heidelberg, 2007; Tai et al. in Image processing based on partial differential equations, pp. 3---22, Springer, Heidelberg, 2006; Bertalmio et al. in Proc. conf. comp. vision pattern rec., pp. 355---362, 2001), a regularized tangential vector field with zero divergence condition is first obtained. Then a novel approach to reconstruct the image is proposed. Instead of finding an image that fits the regularized normal direction from the first step, we propose to minimize an orientation matching cost measuring the alignment between the image gradient and the regularized normal direction. This functional yields a new nonlinear partial differential equation (PDE) for reconstructing denoised and inpainted images. The equation has an adaptive diffusivity depending on the orientation of the regularized normal vector field, providing reconstructed images which have sharp edges and smooth regions. The additive operator splitting (AOS) scheme is used for discretizing Euler-Lagrange equations. We present the results of various numerical experiments that illustrate the improvements obtained with the new functional.