Stability of the Tree of Shapes to Additive Noise

From LRDE

Abstract

The tree of shapes (ToS) is a famous self-dual hierarchical structure in mathematical morphology, which represents the inclusion relationship of the shapes (i.e. the interior of the level lines with holes filled) in a grayscale image. The ToS has already found numerous applications in image processing tasks, such as grain filtering, contour extraction, image simplification, and so on. Its structure consistency is bound to the cleanliness of the level lines, which are themselves deeply affected by the presence of noise within the image. However, according to our knowledge, no one has measured before how resistant to (additive) noise this hierarchical structure is. In this paper, we propose and compare several measures to evaluate the stability of the ToS structure to noise.


Bibtex (lrde.bib)

@InProceedings{	  boutry.21.dgmm.3,
  author	= {Nicolas Boutry and Guillaume Tochon},
  title		= {Stability of the Tree of Shapes to Additive Noise},
  booktitle	= {Proceedings of the IAPR International Conference on
		  Discrete Geometry and Mathematical Morphology (DGMM)},
  year		= 2021,
  month		= {May},
  address	= {Uppsala, Sweden},
  publisher	= {Springer},
  pages		= {365--377},
  abstract	= {The tree of shapes (ToS) is a famous self-dual
		  hierarchical structure in mathematical morphology, which
		  represents the inclusion relationship of the shapes
		  (\textit{i.e.} the interior of the level lines with holes
		  filled) in a grayscale image. The ToS has already found
		  numerous applications in image processing tasks, such as
		  grain filtering, contour extraction, image simplification,
		  and so on. Its structure consistency is bound to the
		  cleanliness of the level lines, which are themselves deeply
		  affected by the presence of noise within the image.
		  However, according to our knowledge, no one has measured
		  before how resistant to (additive) noise this hierarchical
		  structure is. In this paper, we propose and compare several
		  measures to evaluate the stability of the ToS structure to
		  noise.},
  doi		= {10.1007/978-3-030-76657-3_26}
}