Lα Riemannian weighted centers of mass applied to compose an image filter to diffusion tensor imaging

作者：

Highlights：

• Based on the convexity of the centers of mass in Hadamard manifolds, we proposed a kind of extension of the Median and Average filters to the Riemannian case.

• Optimization problems in manifolds and their applications among them the image processing in diffusion tensor magnetic resonance imaging (DT-MRI).

• The weighted average and median Riemannian filter in a continuous way for filtering and smoothing images, using the conduction coefficient of the brightness function to compose the degree of smoothing of the filter function.

• Using a new proximal point algorithm in domains of positivity for filter solutions in DT-MRI.

摘要

•Based on the convexity of the centers of mass in Hadamard manifolds, we proposed a kind of extension of the Median and Average filters to the Riemannian case.•Optimization problems in manifolds and their applications among them the image processing in diffusion tensor magnetic resonance imaging (DT-MRI).•The weighted average and median Riemannian filter in a continuous way for filtering and smoothing images, using the conduction coefficient of the brightness function to compose the degree of smoothing of the filter function.•Using a new proximal point algorithm in domains of positivity for filter solutions in DT-MRI.

论文关键词：Centers of mass,Image processing,Riemannian weighted averages,Riemannian weighted median,Diffusion tensor imaging

论文评审过程：Received 23 May 2020, Accepted 9 August 2020, Available online 2 September 2020, Version of Record 2 September 2020.

论文官网地址：https://doi.org/10.1016/j.amc.2020.125603