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Digital Geometry (2019-2020)

Description

In digital images, an object is represented by a set of pixels/voxels. In such a digital world, the axioms and properties of conventional Euclidean geometry are no longer valid. Digital geometry aims at designing discrete models that allow to solve geometric and topological probelms of such discrete objects. Its main application areas are image analysis and computer graphics.

This course will focus on computerized modeling of geometric and topological shapes in digital world. We will study algorithms and data structures for creating, manipulating and analyzing digital shapes.

The whole course is divided into two parts, which are given by Michel Couprie and myself. The following information in this page concerns only my part.

Schedule and Detail

My part of the course contains the following five lectures and three laboratory sessions.

Lecture 1

Time: 13:45-15:45 on Wednesday 2nd October 2019
Place: Room 1305 (ESIEE Paris)
Topic: Introduction: continuous vs. digital shape analysis
Slides: dg1.pdf

Lecture 2

Time: 8:00-10:00 on Thursday 3rd October 2019
Place: Room 1103 (ESIEE Paris)
Topic: Digital topology: object boundaries and curves/surfaces
Slides: dg2.pdf

Laboratory session 1

Time: 10:00-12:00 on Thursday 3rd October 2019
Place: Room 5309V (ESIEE Paris)
Topic: Pixelation of 2D shapes
Experiment subject: dg_tp1.pdf
Report and code due date: 17/10/2019

Lecture 3

Time: 13:45-15:45 on Wednesday 16th October 2019
Place: Room 1407 (ESIEE Paris)
Topic: Digital lines: definition and recognition
Slides: dg3.pdf

Laboratory session 2

Time: 8:00-10:00 on Friday 18th October 2019
Place: Room 5101+ (ESIEE Paris)
Topic: Counting and measuring grains
Experiment subject: dg_tp2.pdf
Report and code due date: 13/11/2019

Lecture 4

Time: 10:00-12:00 on Friday 18th October 2019
Place: Room 1105 (ESIEE Paris)
Topic: Geometric measurements of digital shapes
Slides: dg4.pdf

Lecture 5

Time: 13:45-15:45 on Thursday 14th November 2019
Place: Room 1105 (ESIEE Paris)
Topic: Digitized geometric transformations
Slides: dg5.pdf (Be careful of the file size, which is more than 20MB!)

Laboratory session 3

Time: 16:00-18:00 on Thursday 14th November 2019
Place: Room 5301V (ESIEE Paris)
Topic: Digital shape registration
Experiment subject: dg_tp3.pdf
Report and code due date: 20/12/2019

Textbooks

R. Klette and A. Rosenfeld.
"Digital geometry: geometric methods for digital picture analysis", San Diego: Morgan Kaufmann, 2004.

D. Coeurjolly, A. Montanvert et J.-M. Chassery.
"Géométrie discrète et images numériques", Hermès, 2007.

Useful links

DGtal: Open source C++ library of Digital Geometry Tools and Algorithms

PINK: Image processing library in C

Fiji: Image processing package with Java

Data sets at IAPR - TC18 Discrete Geometry and Mathematical Morphology