Publications/geraud.13.ismm

Authors

Thierry Géraud, Edwin Carlinet, Sébastien Crozet, Laurent Najman

Where

Mathematical Morphology and Its Application to Signal and Image Processing -- Proceedings of the 11th International Symposium on Mathematical Morphology (ISMM)

Place

Uppsala, Sweden

Type

inproceedings

Publisher

Springer

Projects

Image"Image" is not in the list (Vaucanson, Spot, URBI, Olena, APMC, Tiger, Climb, Speaker ID, Transformers, Bison, ...) of allowed values for the "Related project" property.

Keywords

Image

Date

2013-03-14

Abstract

To compute the morphological self-dual representation of images, namely the tree of shapes, the state-of-the-art algorithms do not have a satisfactory time complexity. Furthermore the proposed algorithms are only effective for 2D images and they are far from being simple to implement. That is really penalizing since a self-dual represen- tation of images is a structure that gives rise to many powerful operators and applications, and that could be very useful for 3D images. In this paper we propose a simple-to-write algorithm to compute the tree of shapes; it works for nD images and has a quasi-linear complexity when data quantization is low, typically 12 bits or less. To get that result, this paper introduces a novel representation of images that has some amazing properties of continuitywhile remaining discrete.

Documents

• Paper

Bibtex (lrde.bib)

@InProceedings{	  geraud.13.ismm,
  author	= {Thierry G\'eraud and Edwin Carlinet and S\'ebastien Crozet
		  and Laurent Najman},
  title		= {A quasi-linear algorithm to compute the tree of shapes of
		  {$n$-D} images.},
  booktitle	= {Mathematical Morphology and Its Application to Signal and
		  Image Processing -- Proceedings of the 11th International
		  Symposium on Mathematical Morphology (ISMM)},
  year		= 2013,
  editor	= {C.L. Luengo Hendriks and G. Borgefors and R. Strand},
  volume	= 7883,
  series	= {Lecture Notes in Computer Science Series},
  address	= {Uppsala, Sweden},
  publisher	= {Springer},
  pages		= {98--110},
  abstract	= {To compute the morphological self-dual representation of
		  images, namely the tree of shapes, the state-of-the-art
		  algorithms do not have a satisfactory time complexity.
		  Furthermore the proposed algorithms are only effective for
		  2D images and they are far from being simple to implement.
		  That is really penalizing since a self-dual represen-
		  tation of images is a structure that gives rise to many
		  powerful operators and applications, and that could be very
		  useful for 3D images. In this paper we propose a
		  simple-to-write algorithm to compute the tree of shapes; it
		  works for nD images and has a quasi-linear complexity when
		  data quantization is low, typically 12 bits or less. To get
		  that result, this paper introduces a novel representation
		  of images that has some amazing properties of continuity,
		  while remaining discrete.}
}