Journal ArticleDOI
A Nonlinear Structure Tensor with the Diffusivity Matrix Composed of the Image Gradient
Jooyoung Hahn,Chang-Ock Lee +1 more
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TLDR
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.Abstract:
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.read more
Citations
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Journal ArticleDOI
Orientation-Matching Minimization for Image Denoising and Inpainting
TL;DR: An orientation-matching functional minimization for image denoising and image inpainting that yields a new nonlinear partial differential equation (PDE) for reconstructing denoised and inpainted images which have sharp edges and smooth regions is proposed.
Journal ArticleDOI
Ramp-Preserving Denoising for Conductivity Image Reconstruction in Magnetic Resonance Electrical Impedance Tomography
TL;DR: This paper proposes a ramp-preserving denoising method utilizing a structure tensor and applies it to in vivo animal imaging experiments, showing significant improvements in the quality of reconstructed conductivity images.
Journal ArticleDOI
Introducing diffusion tensor to high order variational model for image reconstruction
TL;DR: A new tensor weighted second order (TWSO) model for image restoration is introduced that effectively reduces both the staircase and blurring effects and outperforms existing approaches for image inpainting and denoising applications.
Journal ArticleDOI
Image Denoising Using Directional Adaptive Variable Exponents Model
TL;DR: An algorithm based on iterative minimization is presented and the numerical experiments demonstrate the possible advantages of the new model over some existing variational and partial differential equations methods.
Book ChapterDOI
Image Denoising Using TV-Stokes Equation with an Orientation-Matching Minimization
TL;DR: In this article, an orientation-matching minimization was proposed for denoising digital images with an additive noise, where instead of finding an image that fits the regularized normal direction from the first step, they minimize an orientation between the image gradient and the regularised normal direction.
References
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Book
Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
Journal ArticleDOI
Nonlinear total variation based noise removal algorithms
TL;DR: In this article, a constrained optimization type of numerical algorithm for removing noise from images is presented, where the total variation of the image is minimized subject to constraints involving the statistics of the noise.
Journal ArticleDOI
Scale-space and edge detection using anisotropic diffusion
Pietro Perona,Jitendra Malik +1 more
TL;DR: A new definition of scale-space is suggested, and a class of algorithms used to realize a diffusion process is introduced, chosen to vary spatially in such a way as to encourage intra Region smoothing rather than interregion smoothing.
Journal ArticleDOI
Image selective smoothing and edge detection by nonlinear diffusion. II
TL;DR: In this article, a new version of the Perona and Malik theory for edge detection and image restoration is proposed, which keeps all the improvements of the original model and avoids its drawbacks.
Journal ArticleDOI
Nonlinear anisotropic filtering of MRI data
TL;DR: In contrast to acquisition-based noise reduction methods a postprocess based on anisotropic diffusion is proposed, which overcomes the major drawbacks of conventional filter methods, namely the blurring of object boundaries and the suppression of fine structural details.