HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

The discontinuity issue of total orders on metric spaces and its consequences for mathematical morphology

Abstract : We address here the problem of discontinuities of total orders in a metric space and its implications for mathematical morphology. We first give a rigorous formulation of the problem. Then, a new approach is proposed to tackle the discontinuity issue by adapting the order to the image to be processed. Given an image and a total order we define a cost that evaluates the importance of the discontinuities for morphological processing. The proposed order is then built as a minimization of this cost function. One of the strength of the proposed framework is its generality: the only ingredient required to build the total order is the graph of distances between values of the image. The adapted order can be computed for any image valued in a metric space where the distance is explicitly known. We present results for color images, diffusion tensor images (DTI) and images valued in the hyperbolic upper half-plane.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [18 references]  Display  Hide  Download

Contributor : Emmanuel Chevallier Connect in order to contact the contributor
Submitted on : Thursday, January 15, 2015 - 1:38:04 PM
Last modification on : Wednesday, November 17, 2021 - 12:27:12 PM
Long-term archiving on: : Saturday, April 15, 2017 - 7:11:19 PM


Files produced by the author(s)


  • HAL Id : hal-00948232, version 3


Emmanuel Chevallier, Jesus Angulo. The discontinuity issue of total orders on metric spaces and its consequences for mathematical morphology. 2014. ⟨hal-00948232v3⟩



Record views


Files downloads