Mathematical Morphology Exercises With Mamba (solutions included) CMM/Mines ParisTech/Mamba-Image Publication, June 2016

This document contains about fifty Mathematical Morphology exercises with their solutions using the Mamba Image library. This manual replaces the previous one where no solution was provided. These exercises address the following domains: basic notions, filtering, measure, residual operators, feature extraction, image segmentation.

Region-based color correction [co-authors Dieu-Sang Ly, Michel Bilodeau], CMM publication (pre-print), January 2014

Maxima and Minima: A Review CMM/Mines-ParisTech publication, September 2013

The purpose of this document is just to provide additional information about the concepts of maxima and minima in MM. I have indeed noticed, when giving a class on the geodesic transforms, that these concepts were misleading. This paper must simply be considered as a clarification (I hope!) of these notions. Mamba implementations of the operators are also provided.

Basic Morphological Operators Applied On Partitions CMM/Mines-ParisTech publication, March 2013

This document describes morphological operators designed for partitions (mosaic) images. Two approaches are addressed. Either each cell of the partition is processed independently of the other cells or the partition is considered as an image representation of a graph where some basic morphological operators (erosion and dilation) can be defined. An implementation of these operators in the Mamba image library is also given.

Towards a unification of waterfalls, standard and P algorithms CMM/Mines ParisTech publication, January 2012

This document is an extension of the paper: P algorithm, a dramatic enhancement of the waterfall transformation (see below). It has mainly two purposes. Firstly, it comes back to the waterfalls, standard and P algorithms to propose a general segmentation scheme which covers and unifies these different processes. Secondly, it contains the source code for the implementation of these waterfalls, standard and P operators with the MAMBA Image software library.

About a problem of definition of the geodesic erosion CMM/Mines ParisTech publication, September 2011

This note is the english translation of the paper: Sur un problème de définition de l'érosion géodésique (see below).

How to simulate a volume-controlled flooding with mathematical morphology operators? CMM/Mines ParisTech publication, November 2011

This note discusses some ideas for simulating a (real) flood on a (real) topographic surface by means of morphological tools. This work has been initiated following exchanges with some partners of the THESEUS project (Innovative technologies for safer European coasts in a changing climate) regarding the use of mathematical morphology tools for flooding simulations

(note that the CMM does not belong to the THESEUS consortium, this contribution has no other motive than promoting morphological tools in this research domain!).

This note (in french, see the english translation above) addresses a problem of definition of the geodesic erosion in the numerical case. It shows that the binary geodesic erosion does not correspond to the definition currently used in the numerical case. It also defines a new numerical geodesic erosion which really extends the binary operator. Update (october 2011): two annexes have been added, the first one describing all the new geodesic elementary operators and the second one containing the sources of these new operators for the MAMBA library (these operators are available in the current version 1.1.1).

Hierarchical Queues: general description and implementation in MAMBA Image library

Nicolas BEUCHER and Serge BEUCHER. www.mamba-image.org/CMM/Mines ParisTech publication, April 2011

This paper describes thoroughly the hierarchical queues (HQ) which are implemented in the MAMBA image library. The use of these HQ to realize watershed transforms and geodesic reconstructions is fully explained. The extension of these morphological operators to 32-bit images is also described.

Fast implementation of large erosions and dilations in Mamba CMM/Mines ParisTech publication, October 2010

This document explains how to implement fast erosions and dilations when large structuring elements are needed. These structuring elements can be squares, hexagons, octogons or dodecagons. This implementation, realized in the Mamba library brings a dramatic increase of the computation speed. This increase is all the more important as the size of the structuring element is large.

MAMBA related publications

This page contains documents and notes related to the Mamba software library (algorithmic descriptions, software implementations, courses, lectures, presentations, etc.). New papers are added periodically. Some of them (not all) are also duplicated in this page.

P algorithm, a dramatic enhancement of the waterfall transformation.

Serge BEUCHER and Beatriz MARCOTEGUI. CMM/Mines Paristech publication, 86 pages. September 2009.

This document describes an efficient enhancement of the waterfall algorithm, a hierarchical segmentation algorithm defined from the watershed transformation. The first part of the document recalls the definition of the waterfall algorithm, its various avatars as well as its links with the geodesic reconstruction. The second part starts by analyzing the different shortcomings of the algorithm and introduces several strategies to palliate them. Two enhancements are presented, the first one named standard algorithm and the second one, P algorithm. The different properties of P algorithm are analyzed. This analysis is detailed in the last part of the document. The performances of the two algorithms, in particular, are addressed and their analogies with perception mechanisms linked to the brightness constancy phenomenon are discussed.

Real-time contrast medium detection in X-ray images by mathematical morphology operators [co-authors Dieu-Sang Ly, Michel Bilodeau], Journal of Electronic Imaging, Special Section on Ultrawide Context- and Content-Aware Imaging, 24(6):061202 doi:10.1117/1.JEI.24.6.061202, 2015.

A multi-scale and morphological gradient preserving contrast [co-authors Jean-Charles Bricola, Michel Bilodeau], 14th International Conference on Stereology and Image Analysis, Liège, Belgium. July 7-10, 2015.

Appariements de Régions pour l'estimation de cartes de profondeur [co-authors Jean-Charles Bricola, Michel Bilodeau], Congrès des jeunes chercheurs en vision par ordinateur ORASIS, Amiens, France, June 15-19, 2015.

A Top-Down Approach to the Estimation of Depth Maps Driven by Morphological Segmentations [co-authors Jean-Charles Bricola, Michel Bilodeau], Lecture Notes in Computer Science, vol. 9082, pp. 122-133, ISMM 2015 Reykjavik, Iceland, May 27-29, 2015.

Color Correction Through Region Matching Leveraged by Point Correspondences [co-authors Dieu-Sang Ly, Michel Bilodeau], IEEE International Conference on Image Processing (ICIP 2014), Paris, October 2014.

A top-down methodology to depth map estimation controlled by morphological segmentation [co-authors Jean-Charles Bricola, Michel Bilodeau], HAL publication (hal-01063384), September 2014.

Depth map estimation: a region-based approach [co-authors Jean-Charles Bricola, Michel Bilodeau], Technical Report, HAL publication (hal-00995034), May 2014.

Depth map estimation: a region-based approach [co-authors Jean-Charles Bricola, Michel Bilodeau], HAL publication (hal-00995034), May 2014.

You may have a look at the corresponding pdf presentation.

You may have a look at the corresponding pdf presentation.

From moving edges to moving regions [co-authors L. BIANCARDINI, E. DOKLADALOVA, L. LETELLIER]. IbPRIA 2005, Iberian Conference on Pattern Recognition and Image Analysis.

Extraction des objets en mouvement: une approche mixte contours-régions [co-authors L. BIANCARDINI, L. LETELLIER]. ORASIS 2005, 9ème Congrès Jeunes Chercheurs en Vision par Ordinateurs,

Paper introducing the strong connections between the Waterfall algorithm and dual geodesic reconstructions of the watershed image.

This paper introduces the concept of adaptative transform (and of generalized geodesy).

This paper and the following ones introduce the concept of geodesic transformation.

First introduction of the morphological gradient and the top-hat transformation.

Lecture slides, in french, of the morphological segmentation lessons for the Optics, Image, Vision Master course. These slides are without background (more easily printable)..

Segmentation d'image & Morphologie Mathématique. Cours du Master OIV, Université Jean Monnet, Saint Etienne, France, Janvier 2010.

Lecture slides, in french (old version).

Géodésie et transformations géodésiques. Cours Mines ParisTech, Novembre 2013.

Lecture slides, in french (updated release, the old one is here).

Residus. Cours Mines ParisTech, Novembre 2013.

French version of the slides below (updated version, the old release is here).

From Watersheds to Waterfalls and Beyond. Lecture at 11th European Congress of Stereology and Image Analysis (ECS11), Kaiserlautern, Germany, July 8-12, 2013.

Slides of the lecture on recent tools in Mathematical Morphology for supervised and unsupervised image segmentation.

Recent developments and Tools for Image Segmentation by Mathematical Morphology (The segmentation user's guide revisited...). Invited Conference, 13th International Congress of Stereology (ICS13), Beijing, PR of China, October 19-22, 2011.

This PDF presentation describes some new segmentation tools based on residual transforms and introduces a general extension of the hierarchical algorithms (waterfalls and P algorithms).

Morphological Image Segmentation: A User’s Guide. CMM-ITWM Joint Meeting, Fontainebleau, 21-23 march 2011.

These slides provide a short presentation of P algorithm. For a detailed description, see this paper.

These slides (in french) introduce the "Critical Balls" concept and give some algorithms based on residues to extract them from the skeleton.

Conference slides.

The sequel of the note below....

Serge BEUCHER, Jean-Marc BLOSSEVILLE, François LENOIR, Brevet n° FR2609566,14 janvier 1987.

Analyse de diagraphies électriques par morphologie mathématique CMM/Ecole des Mines de Paris, February 1989

This report (released in february 1989) describes the various algorithms which have been used to analyse electrical logging images. This report introduces many tools which can be found also in my PhD thesis. Among them, various types of morphological gradients, operators using the generalised geodesic distance and new residual operators, in particular ultimate openings (directional ultimate openings). Warning! It is a huge file...

This document addresses different approaches for the parallelisation of the watershed transform by hierarchical queues. This study was performed in 1997 (for the former THOMSON company) but this algorithmic implementation remains an issue. You may also have a look at this paper where the watershed parallelisation is briefly discussed again.

This document describes the algorithms implemented in the TITAN traffic measurement system (research project realised in collaboration with INRETS in 1986-1987). Many new concepts and algorithms were introduced during this project. Among them, the concept of adaptive algorithms and the notion of extended maxima and minima.

Last update July 7 , 2016