Definition
A binary partition tree (BPT) is a hierarchy, used to represent a set of regions in a grey-scale image. This hierarchy is constructed using the homogeneity between the regions. The leaf nodes represent the basic regions and the other nodes represent the regions obtained by merging pairs of neighboring regions. The root represents the entire image. See Salembier and Garrido (2000) for more details.
Illustration
To illustrate the definition, consider the image on the left of Fig. 1. This image consists of five regions with the grey-scale value as denoted in the brackets. The corresponding binary partition tree is shown on the right.
Figure illustrating the binary partition tree
This is a preview of subscription content, log in via an institution to check access.
Bibliography
Garrido L, Salembier P, Garciá D (1998) Extensive operators in partition lattices for image sequence analysis. Signal Process 66(2):157–180. https://doi.org/10.1016/S0165-1684(98)00004-8
Najman L, Cousty J, Perret B (2013) Playing with Kruskal: algorithms for morphological trees in edge-weighted graphs. In: Hendriks CLL, Borgefors G, Strand R (eds) Mathematical morphology and its applications to signal and image processing, 11th international symposium, ISMM 2013, Uppsala, Sweden, May 27–29, 2013. Proceedings. Lecture notes in computer science, vol 7883. Springer, Heidelberg, pp 135–146. https://doi.org/10.1007/978-3-642-38294-9_12
Perret B, Chierchia G, Cousty J, Guimarães SJF, Kenmochi Y, Najman L (2019) Higra: hierarchical graph analysis. SoftwareX 10:100335. https://doi.org/10.1016/j.softx.2019.100335. http://www.sciencedirect.com/science/article/pii/S235271101930247X
Salembier P, Garrido L (2000) Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval. IEEE Trans Image Process 9(4):561–576. https://doi.org/10.1109/83.841934
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this entry
Cite this entry
Danda, S., Challa, A., Daya Sagar, B.S. (2021). Binary Partition Tree. In: Daya Sagar, B., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-26050-7_54-1
Download citation
DOI: https://doi.org/10.1007/978-3-030-26050-7_54-1
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-26050-7
Online ISBN: 978-3-030-26050-7
eBook Packages: Springer Reference Earth and Environm. ScienceReference Module Physical and Materials ScienceReference Module Earth and Environmental Sciences