Topographical Tools for Filtering and Segmentation 2

Flooding and Marker-based Segmentation on Node- or Edge-weighted Graphs

Topographical Tools for Filtering and Segmentation 2

Fernand Meyer, MINES ParisTech, France

ISBN : 9781786304070

Publication Date : January 2019

Hardcover 284 pp

145.00 USD



Mathematical morphology has developed a powerful methodology for segmenting images, based on connected filters and watersheds. We have chosen the abstract framework of node- or edge-weighted graphs for an extensive mathematical and algorithmic description of these tools.

Volume 2 proposes two physical models for describing valid flooding on a node- or edge-weighted graph, and establishes how to pass from one to another. Many new flooding algorithms are derived, allowing parallel and local flooding of graphs.

Watersheds and flooding are then combined for solving real problems. Their ability to model a real hydrographic basin represented by its digital elevation model constitutes a good validity check of the underlying physical models.

The last part of Volume 2 explains why so many different watershed partitions exist for the same graph. Marker-based segmentation is the method of choice for curbing this proliferation. This book proposes new algorithms combining the advantages of the previous methods which treated node- and edge-weighted graphs differently.


Part 1. Flooding
1. Modelling Flooding in Edge- or Node-weighted Graphs.
2. Lakes and Regional Minima.
3. Among all Possible Floodings, Choosing One.
4. Flooding and Flooding Distances.
5. Graph Flooding via Dendrograms.

Part 2. Modeling a Real Hydrographic Basin
6. The Hydrographic Basin of a Digital Elevation Model.

Part 3. Watershed Partitions
7. Minimum Spanning Forests and Watershed Partitions.
8. Marker-based Segmentation.

About the authors

Fernand Meyer has been working at the Center for Mathematical Morphology of MINES ParisTech since 1975. He participated actively in the development of mathematical morphology, particularly in the field of segmentation and filtering.