On Making nD Images Well-Composed by a Self-dual Local Interpolation

Natural and synthetic discrete images are generally not well-composed, leading to many topological issues: connectivities in binary images are not equivalent, the Jordan Separation theorem is not true anymore, and so on. Conversely, making images well-composed solves those problems and then gives ac...

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Bibliographic Details
Published inDiscrete Geometry for Computer Imagery pp. 320 - 331
Main Authors Boutry, Nicolas, Géraud, Thierry, Najman, Laurent
Format Book Chapter
LanguageEnglish
Published Cham Springer International Publishing 01.01.2014
SeriesLecture Notes in Computer Science
Subjects
Digital topology
gray-level images
well-composed images
well-composed sets
Online AccessGet full text
ISBN9783319099545
331909954X
ISSN0302-9743
1611-3349
DOI10.1007/978-3-319-09955-2_27

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Summary:Natural and synthetic discrete images are generally not well-composed, leading to many topological issues: connectivities in binary images are not equivalent, the Jordan Separation theorem is not true anymore, and so on. Conversely, making images well-composed solves those problems and then gives access to many powerful tools already known in mathematical morphology as the Tree of Shapes which is of our principal interest. In this paper, we present two main results: a characterization of 3D well-composed gray-valued images; and a counter-example showing that no local self-dual interpolation satisfying a classical set of properties makes well-composed images with one subdivision in 3D, as soon as we choose the mean operator to interpolate in 1D. Then, we briefly discuss various constraints that could be interesting to change to make the problem solvable in nD.
ISBN:9783319099545
331909954X
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-319-09955-2_27