How to Make n-D Plain Maps Defined on Discrete Surfaces Alexandrov-Well-Composed in a Self-Dual Way

In 2013, Najman and Géraud proved that by working on a well-composed discrete representation of a gray-level image, we can compute what is called its tree of shapes , a hierarchical representation of the shapes in this image. This way, we can proceed to morphological filtering and to image segmentat...

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Bibliographic Details
Published in:Journal of mathematical imaging and vision 2019-07, Vol.61 (6), p.849-873
Main Authors: Boutry, Nicolas, Géraud, Thierry, Najman, Laurent
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computer Science
Computer Vision and Pattern Recognition
Discrete Mathematics
Geometric Topology
Image filters
Image Processing and Computer Vision
Image segmentation
Mathematical Methods in Physics
Mathematics
Representations
Signal and Image Processing
Signal,Image and Speech Processing
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Summary:In 2013, Najman and Géraud proved that by working on a well-composed discrete representation of a gray-level image, we can compute what is called its tree of shapes , a hierarchical representation of the shapes in this image. This way, we can proceed to morphological filtering and to image segmentation . However, the authors did not provide such a representation for the non-cubical case. We propose in this paper a way to compute a well-composed representation of any gray-level image defined on a discrete surface , which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is self-dual in the sense that it treats bright and dark components in the image the same way. This paper can be seen as an extension to gray-level images of the works of Daragon et al. on discrete surfaces.
ISSN:0924-9907
1573-7683
DOI:10.1007/s10851-019-00873-4