Image Processing and Analysis with Graphs

6

A Short Tour of Mathematical Morphology on Edge and Vertex Weighted Graphs

Laurent Najman

Université Paris-EstLaboratoire d’Informatique Gaspard-MongeEquipe A3SI - ESIEE ParisFrance

Email: [e-mail]

Fernand Meyer

Centre de Morphologie MathématiqueEcole des Mines de ParisFontainebleau, France

Email: [e-mail]

CONTENTS

6.1    Introduction

6.2    Graphs and lattices

6.2.1    Lattice of Graphs

6.2.2    Lattice of Weights

6.3    Neighborhood Operations on Graphs

6.3.1    Adjunctions on Graphs

6.4    Filters

6.5    Connected Operators and Filtering with the Component Tree

6.6    Watershed Cuts

6.6.1    The Drop of Water Principle

6.6.2    Catchment Basins by a Steepest Descent Property

6.6.3    Minimum Spanning Forests

6.6.4    Illustrations ...