# MorphoGraph and Imagery

## Goal

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.