Some Nonlocal Filters Formulation Using Functional Rearrangements

Conference paper

DOI: 10.1007/978-3-319-18461-6_14

Volume 9087 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Galiano G., Velasco J. (2015) Some Nonlocal Filters Formulation Using Functional Rearrangements. In: Aujol JF., Nikolova M., Papadakis N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2015. Lecture Notes in Computer Science, vol 9087. Springer, Cham

Abstract

We present an exact reformulation of a broad class of nonlocal filters, among which the bilateral filters, in terms of two functional rearrangements: the decreasing and the relative rearrangements.

Independently of the image spatial dimension, these filters are expressed as integral operators defined in a one-dimensional space, corresponding to the level sets measures.

We provide some insight into the properties of this new formulation and show some numerical demonstrations to illustrate them.

Keywords

Neighborhood filter Bilateral filter Decreasing rearrangement Relative rearrangement Denoising Segmentation 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversidad de OviedoOviedoSpain