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

Author

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  • da Silva Alves, Charlan Dellon
  • Oliveira, Paulo Roberto
  • Gregório, Ronaldo Malheiros

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.

Suggested Citation

  • da Silva Alves, Charlan Dellon & Oliveira, Paulo Roberto & Gregório, Ronaldo Malheiros, 2021. "Lα Riemannian weighted centers of mass applied to compose an image filter to diffusion tensor imaging," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320305580
    DOI: 10.1016/j.amc.2020.125603
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    References listed on IDEAS

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    1. Gregório, R.M. & Oliveira, P.R. & Alves, C.D.S., 2019. "A two-phase-like proximal point algorithm in domains of positivity," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 67-89.
    2. O. P. Ferreira & P. R. Oliveira, 1998. "Subgradient Algorithm on Riemannian Manifolds," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 93-104, April.
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