Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Coherence-Enhancing Diffusion Filtering
International Journal of Computer Vision
Numerical Methods for p-Harmonic Flows and Applications to Image Processing
SIAM Journal on Numerical Analysis
A Nonlinear Structure Tensor with the Diffusivity Matrix Composed of the Image Gradient
Journal of Mathematical Imaging and Vision
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
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Noise removal using smoothed normals and surface fitting
IEEE Transactions on Image Processing
A New TV-Stokes Model with Augmented Lagrangian Method for Image Denoising and Deconvolution
Journal of Scientific Computing
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In this paper, we propose an orientation-matching minimization for denoising digital images with an additive noise. Inspired by the two-step algorithm in the TV-Stokes denoising process [1,2,3], the regularized tangential vector field with the zero divergence condition is used in the first step. The present work suggests a different approach in order to reconstruct a denoised image in the second step. Namely, instead of finding an image that fits the regularized normal direction from the first step, we minimize an orientation between the image gradient and the regularized normal direction. It gives a nonlinear partial differential equation (PDE) for reconstructing denoised images, which has the diffusivity depending on an orientation of a regularized normal vector field and the weighted self-adaptive force term depending on the direction between the gradient of an image and the vector field. This allows to obtain a denoised image which has sharp edges and smooth regions, even though an original image has smoothly changing pixel values near sharp edges. The additive operator splitting scheme is used for discretizing Euler-Lagrange equations. We show improved qualities of results from various numerical experiments.