Efficient Algorithms to Implement the Confinement Tree

  • Julian Mattes
  • Jacques Demongeot
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)

Abstract

The aim of this paper is to present a new algorithm to calculate the confinement tree of an image - also known as component tree or dendrone - for which we can prove that its worst-case complexity is O(n log n) where n is the number of pixels. More precisely, in a first part, we present an algorithm which separates the different kinds of operations - which we call scanning, fusion, propagation, and attribute operations - such that we can separately apply complexity analysis on them and such that all operations except propagation stay in O(n). The implementation of the propagation operations is presented in a second part, first in O(n2n), where nn is the number of nodes in the tree (n n = n). This is suficient if the number of pixels is much larger than the number of nodes (n n << n). Else, we show how to obtain O(n n log n n ) complexity for propagation. We construct two example images to investigate the behavior of two known algorithms for which we can show worst-case complexity of O(n2 log n) and O(n2), respectively, and we compare it to our algorithm. Finally, a practical evaluation will be opposed to the theoretical results. Several variations of the implementation will show which operations are time consuming in practice.

Keywords

Grey Level Unique Representation Practical Evaluation Attribute Operation Fast Execution Time 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Julian Mattes
    • 1
    • 2
  • Jacques Demongeot
    • 1
  1. 1.TIMC-IMAG, Faculty of MedicineLa TroncheFrance
  2. 2.iBioS, DKFZ HeidelbergHeidelbergGermany

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