MorphoGraph and Imagery

ESIEE Paris, Département Informatique


This course is an introduction to the fundamentals of graph theory, graph algorithms, and mathematical morphology. Each graph notion/algorithm is used to define/implement a morphological operator that solves a practical problem of 2D or 3D image analysis. It aims to provide attendees with the ability to:

- formalize a given (image analysis) problem in terms of graphs;
- identify whether the problem has a known solution or not; and
- in case there is no known solution, suggest a new algorithm to solve it and evaluate its complexity.

Course material

Lectire 0 - Introduction

Lecture 1 - Graphs: basic notions

Lecture 2 - Mathematical morphology: basic operators

Practical session 1 - Dilation and Erosion: implementation and first applications

Lecture 3 - Connectivity in graphs

Exercises 1 - Cyber-profiler

Practical session 2 - Friends, bipartite graphs and cycles of odd length

Lecture 4 - Shortest paths

Exercises 2 - Back tracking a shortest path (lecture 4, slide 20) - Floyd algorithm

Practical session 3 - A journey in the metro

Lecture 5 - Distance maps, dilations and medial axis

Lecture 6 - Introduction to morphological filtering - Introduction to grayscale image processing by mathematical morphology

Practical session 4 - Application of morphological operators by structuring elements to binary and grayscale image processing

Lecture 7 - Trees

Lecture 8 - Connected operators

Practical session 5 - Application of morphological connected operators to binary and grayscale images

Lecture 9 - Minimum spanning tree

Exercise 3 - In the wood - Spy games - Analysis of trajectories

Practical session 6 - Analysis of trajectories in a bubble chamber

Lecture 10 - Watershed segmentation

Working environment

On a windows operating system, the working environment settled at ESIEE for the practical sessions can be reproduced through the Linux virtual machine whose image is provided here.

In order to play this virtual machine you need to install a VMware player such as the one that can be downloaded here.

In order to uncompress it , any archiving program such as 7-zip, which can be downloaded here, can be used.

Once your virtual machine is running, you can use the account whose user id is "user" and password is "azerty".

This course is proposed by Jean Cousty.
A part of it is inspired by the courses "Graphes et algorithmes" and "Algorithmique et applications en imagerie" given by Michel Couprie and Gilles Bertrand at ESIEE Paris.