Computer Vision, Graphics, and Image Processing
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Feature-oriented image enhancement using shock filters
SIAM Journal on Numerical Analysis
Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow
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
Signal and image restoration using shock filters and anisotropic diffusion
SIAM Journal on Numerical Analysis
A Theoretical Framework for Convex Regularizers in PDE-Based Computation of Image Motion
International Journal of Computer Vision
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
Image Processing Based on Partial Differential Equations: Proceedings of the International Conference on PDE-Based Image Processing and Related Inverse ... 8-12, 2005 (Mathematics and Visualization)
Image and Vision Computing
Digital Image Processing
Noise removal using smoothed normals and surface fitting
IEEE Transactions on Image Processing
The staircasing effect in neighborhood filters and its solution
IEEE Transactions on Image Processing
Image Denoising Using TV-Stokes Equation with an Orientation-Matching Minimization
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Orientation-Matching Minimization for Image Denoising and Inpainting
International Journal of Computer Vision
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We propose a nonlinear partial differential equation (PDE) for regularizing a tensor which contains the first derivative information of an image such as strength of edges and a direction of the gradient of the image. Unlike a typical diffusivity matrix which consists of derivatives of a tensor data, we propose a diffusivity matrix which consists of the tensor data itself, i.e., derivatives of an image. This allows directional smoothing for the tensor along edges which are not in the tensor but in the image. That is, a tensor in the proposed PDE is diffused fast along edges of an image but slowly across them. Since we have a regularized tensor which properly represents the first derivative information of an image, the tensor is useful to improve the quality of image denoising, image enhancement, corner detection, and ramp preserving denoising. We also prove the uniqueness and existence of solution to the proposed PDE.