A Nonlinear Structure Tensor with the Diffusivity Matrix Composed of the Image Gradient

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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.
Publisher
SPRINGER
Issue Date
2009-06
Language
English
Article Type
Article
Keywords

SHOCK FILTERS; ANISOTROPIC DIFFUSION; EDGE-DETECTION

Citation

JOURNAL OF MATHEMATICAL IMAGING AND VISION, v.34, no.2, pp.137 - 151

ISSN
0924-9907
DOI
10.1007/s10851-009-0138-1
URI
http://hdl.handle.net/10203/97116
Appears in Collection
MA-Journal Papers(저널논문)
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