摘要
Nonlocal filters are simple and powerful techniques for image denoising. In this paper, we give new insights into the analysis of one kind of them, the Neighborhood filter, by using a classical although not commonly used transformation: the decreasing rearrangement of a function. Independently of the dimension of the image, we reformulate the Neighborhood filter and its iterative variants as an integral operator defined in a one-dimensional space. The simplicity of this formulation allows to perform a detailed analysis of its properties. Among others, we prove that the filtered image is a contrast change of the original image, an that the filtering procedure behaves asymptotically as a shock filter combined with a border diffusive term, responsible for the staircaising effect and the loss of contrast.
- 出版日期2015-2