Abstract
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.
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Boutry, N., Géraud, T., Najman, L. (2014). On Making nD Images Well-Composed by a Self-dual Local Interpolation. In: Barcucci, E., Frosini, A., Rinaldi, S. (eds) Discrete Geometry for Computer Imagery. DGCI 2014. Lecture Notes in Computer Science, vol 8668. Springer, Cham. https://doi.org/10.1007/978-3-319-09955-2_27
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DOI: https://doi.org/10.1007/978-3-319-09955-2_27
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09954-5
Online ISBN: 978-3-319-09955-2
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