Abstract This paper presents an edge preserving and tensor filtering method for diffusion tensor image. The main idea consists in using the Lα Riemannian centers of mass attached to the edge information estimated in the domain of the diffusion tensor so that the image edges not been smoothed in the filtering process. For α ∈ [1, 2], the method encompasses both the standard case of the Riemannian weighted mean filter ( α = 2 ) and the Riemannian weighted median filter ( α = 1 ) in only one filter. Aiming to establish the fundamentals for the well-posedness of the proposed filter, called adaptive Riemannian filter (ARF), we claimed a theoretical result previously stated in the literature on the continuity of the Lα Riemannian centers of mass, with respect to the parameter α and the points in the neighborhood of the filtered tensor.

中文翻译：

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L 黎曼加权质心用于构成扩散张量成像的图像滤波器

摘要 本文提出了一种用于扩散张量图像的边缘保持和张量滤波方法。主要思想在于使用 Lα 黎曼质心附加到在扩散张量域中估计的边缘信息，以便在滤波过程中不会平滑图像边缘。对于 α ∈ [1, 2]，该方法仅在一个滤波器中包含黎曼加权平均滤波器 (α = 2 ) 和黎曼加权中值滤波器 ( α = 1 ) 的标准情况。为了建立所提出的滤波器适定性的基础，称为自适应黎曼滤波器 (ARF)，我们声称先前在文献中陈述的关于 Lα 黎曼质心连续性的理论结果，关于参数 α以及过滤张量附近的点。