Skip to Main content Skip to Navigation
Conference papers

A quasi-linear algorithm to compute the tree of shapes of n-D images

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 representation 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.
Complete list of metadata

Cited literature [22 references]  Display  Hide  Download
Contributor : Laurent Najman <>
Submitted on : Saturday, March 9, 2013 - 6:02:55 PM
Last modification on : Wednesday, June 9, 2021 - 5:28:03 PM
Long-term archiving on: : Sunday, April 2, 2017 - 10:48:14 AM


Files produced by the author(s)


  • HAL Id : hal-00798620, version 1


Thierry Géraud, Edwin Carlinet, Sébastien Crozet, Laurent Najman. A quasi-linear algorithm to compute the tree of shapes of n-D images. International Symposium on Mathematical Morphology, May 2013, Uppsala, Sweden. pp.97-108. ⟨hal-00798620⟩



Record views


Files downloads