Blanc SIMI 2 - Sciences de l'information, de la matière et de l'ingénierie : Sciences de l’information, simulation

Knowledge Integration for Digital convolution, Image Segmentation and Measurement – KIDICO


Knowledge Integration for Digital convolution, Image Segmentation and <br />Measurement

Developing new frameworks for image analysis

In image processing, the solution to any problem requires the use of knowledge concerning the acquisition device and the imaging domain.<br /><br />Our research deals with the development of approaches in image processing and segmentation based on discrete geometry, discrete topology and mathematical morphology, through which we expect to extract geometrical, differential, topological and morphological information in images, and to use this information in the image segmentation process.<br /><br />For image segmentation, we must also set into collaboration geometrical, topological and morphological methods, and combine them with tools from other domains (probability, statistics, differential approaches, artificial intelligence, etc.).

The KIDICO project is composed of the following five taks :

1. Models for discretization and models for topological information ;
2. Reconstruction of geometrical and morphological information ;
3. Digital differential geometry and estimation of differential parameters ;
4. New concepts for the exact solution to inverse problems ;
5. Knowledge-based image segmentation.

The tools used for implementing these five tasks come from discrete geometry, discrete topology and mathematical morphology.

General facts and results concerning production and organisation :

* A good scientific production : see below.
* Hiring of 3 PhD students on the topics of the project, among whom one is financed by a partner's own budget.
* It has been decided to integrate discrete geometry software developed within the project into an existing library : Dgtal ( Also, morphological software will be integrated into the Olena and Pink libraries.

Outstanding scientific results :

* Elaboration of a topology for label images in cellular complexes.
* Generalization of the 3 interval property to parabolas.
* Invention of a new estimator for derivatives on discrete signals, based on stairhead convolutions, having a better complexity than binomial convolutions.
* Advances towards the generation of discrete planes by a better understanding of different models of continuous fractions in dimension 3 and by the use of symbolic dynamic and arithmetic.
* Study of orders and hierarchies of partitions for connective segmentation.

* The various topics of the 5 tasks will keep being deepened.

* The software tools to be developed before the end of the project, will be integrated within the Dgtal library ( for the discrete geometry part and the Olena and Pink libraries for the mathematical morphology part.

Up to now, the project has given rise to 85 publications : 29 articles in international journals, 3 articles in national journals and 53 communications in international conference proceedings (among which 5 publications in international journals and 5 in international conferences resulting from works conducted jointly by two partners).

The KIDICO project spans 4 years. It regroups teams from 7 research
laboratories: LSIIT (Strasbourg / Illkirch), LAIC (Clermont) IGM
(Noisy / Marne la Vallée), LIRMM (Montpellier), LAMA (Chambéry), LORIA
(Nancy) and I3M (Montpellier).

It deals with the modeling, extraction and use of knowledge in image
processing and segmentation. The sought knowledge will be of
geometrical, differential, topological and morphological nature, and
the processing will be based on discrete geometry, discrete topology
and mathematical morphology. Indeed, these specialties abide by visual
intuition, which allows an easier planning of processing and improves
ergonomy for the user. However most works based on these approaches
use only a small part of the available information, which leads to the
proposal of a research dealing both with the extraction of information
from images and the integration of knowledge in image segmentation.

More specifically, the following topics will be studied:

(1) Discretization models and topological models for imaging:

Extension of discretization models;

Reconstruction of geometrical properties;

Reconstruction of topological informations from Hausdorff
discretizations or projections;

Topological reduction, simple points / sets, and topology in label

Separated discrete topologies.

(2) Reconstruction of geometrical and morphological information:

Estimation of geometrical parameters from sets or grey-level images;

Study of the discretization error;

Taking noise into account;

Reconstruction of discrete sets from noisy projections;

Tomographic estimation of geometrical parameters.

(3) Digital differential geometry and estimation of differential parameters:

Conformal differential geometry and differential estimators;

Discrete differential geometry;

Digital differential geometry on cubical polyhedral surfaces;

Sparse convolution.

(4) New concepts for exact solution to inverse problems:

Arithmetical study of discrete planes and appplication to the study of
their patterns;

Convolution of binary functions, tilings by translation and

Convolution in word combinatorics

(5) Knowledge-based segmentation:

Segmentation by topology-preserving transforms;


Geometrical and morphological descriptors for image segmentation;

Connective segmentation;

Lattice of watersheds.

Possible applications of theoretical results lie in medical,
astronomical and satellite imaging, in geographic information systems,

The design of software platforms implementing the results will be
achieved during the two last years of the project. The source codes of
the developed primitives will be distributed on the project web
site. The scientific communication will be achieved through an
international summer school and publications.

For the smooth running of the project, we request the financing of two
and a half doctoral theses (each lasting 36 months), as well as of
travels and computing equipment.

Project coordination


The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.



Help of the ANR 501,200 euros
Beginning and duration of the scientific project: - 48 Months

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