Centre de Morphologie Mathématique

35, rue St-Honoré

77305 Fontainebleau


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(+33) 01 64 69 47 06

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(+33) 01 64 69 47 07


[ Accueil ]

[ Curriculum Vitae ]

[ Liste des publications ]

[ Quelques Publications ]

[ Quelques exposés ]

[ Cours ]



Papers on line



All my papers, together with a list of the most interesting ones, are detailed in my CV. Moreover, the heading



of this web-site shows the class marks of these documents at the School of Mines library from 1992, and even before for some of them.

However, as these two lists do not give a direct access to the texts themselves, I put on line most of my publications from 1994, together with some technical reports, which can be downloaded from this page. These articles, communications and technical reports deal with the following themes :

  Connectivity : 1995 IEEE paper [A-65], written with Ph. Salembier, describes the connected filters properties for numerical functions (pyramids, commutativity, contours) for image compression. The mathematical study  [A-74]enlarges the connection notion to complete lattices, which had been introduced in 1989 in the set lattices framework [0-6_2]. Two more simple presentations [A-75] and [C-63] come back on the general case and on the set one, and take up with the filtering again [A-65]



  Segmentation : In publication [A-77], in collaboration with Ch. Ronse, we tried to extend to the numerical functions the “geodesic” dilations, which had only been set wise oriented up to that moment. It was a trial to link the connection and the segmentation of numerical functions. Afterwards, I preferred the approach developed in the note [NI-212] and presented in both communications [C-71] (in French, published in « Traitement du Signal » Vol. 20 n° 3) and [C-75] (in English, cf. CIC 2002 congress proceedings). These beginnings have led to the main text about this subject, i.e. the technical report [NI-238]], which is accepted by JIMV for publication in 2005. In this document, segmentation is studied like the research of optimum partitions according to connected criteria. This way of looking at things turns out to be a solution to the paradox between segmentation, considered as an optimum (therefore as a global result) and the fact that it often comes among other operations. We will find other results about mixed partitions in [C-81].



  Interpolation : the following research line is independent from the previous paragraphs, and  originates in the video images interpolations to be compressed. Several quite close lines were also followed by S. Beucher, J.R. Casas, Ph. Salembier and F. Meyer. For my part, I proved that Hausdorff metric accepts several geodesics). Some of them can be made symmetrical, which leads to quite high quality interpolators, and which broaden to numerical functions [C-61]. With M. Iwanowski, we studied the extension to affine versions [C-64] as well as to colour vector functions [C-62]. Some examples of these interpolations can be seen [fly.avi] ; [multi.avi] ; [ren_morph_c.avi].


  Colour : I had to face colour problems when I was working on interpolation. At the same time, A. Hanbury and I were wondering how we could construct morphological operations for data defined on the unit circle, such as directions or colours (see [A-79], published in IEEE in 2001). This drove us to pay more attention the luminance/saturation/colour systems of polar coordinates, such as HLS or HSV. And we realized they were contradictory with Newton’s disk famous experience, because of a wrong definition of saturation [NI-230][C-77][T-38]. We proposed some alternatives (see [A-81], published in IAS {Image Analysis and Stereology} in 2001, or the most detailed version [NI-205], or [C-68]).  On that point, as some robotics staff had asked us to detect reflections on colour pictures, J. Angulo and I were brought to study again the various systems of polar coordinates for colour, and to compare their results. The norm L1 based system proved to be very informative, as the reflection regions are represented by straight lines in the Luminance / Saturation histogram. This new step led me to propose an original model for light space distribution [C-82]. Finally, combining my studies on maximum partition segmentation with the saturation function as “colour measuring”, J. Angulo and I have created a segmentation method for colour images, presented in English in [C-79], in French in [NI-236] and in Spanish in [C-76]Another possibility consists in building a total order, named lexicographic, on colour lattices [C-80]. An application of this method to map segmentation is proposed in the paper [C-81].

The reference [NI-239] gives an overview of the works on colour at CMM, from 1998 to 2003 (in French). Finally, a series of examples is published in the book dedicated to G. Matheron (2005, in English) [CDL-8].

  3-Dimensions morphology : In 1999, within a few months, two embryology problems were submitted to me, from two totally independent directions, and both used to involve 3-dimensional structures. Dr Bertram (Melbourne University) was aiming at giving a quantitative description of kidneys embryos development which were growing in-vitro, and Dr. Staub (CHU Lariboisière-Saint Denis, Paris) was working on the morphogenesis of long bones, such as the shinbone, for orthopedic research. From a morphological viewpoint, both questions are based on geodesic (i.e. submitted to constraints) wave front propagations within the three-dimensional environment. Branchings, bottle necks, extremities, etc can be detected and study this way [A-80] (French version [NI-194]). Also, thanks to these studies, I could extend a more formal research [C-60] in which I had proposed the cube-octahedron as a better digital substitute to the sphere.



  Viscous lattices and other theoretical studies : Propagations by Euclidean geodesic wave fronts consider the singletons as the smallest moving particles. But what if the smallest moving element is not the point anymore, but a small ball which radius r>0, as if there were space quanta ? This question is dealt with in the viscous lattices study [NI-237] (accepted in 2005 for publication by JIMV). As we are mentioning theory, let us quote a note that was written after J. Barrera’s work on the operators decomposition. I added several constraints in order to channel this too large problem [NI-209]. On the other side, [NI-216] is a research over Euclidean functions classes, that are suitable to morphological operations (they must make up complete lattices, closed under the multiplication by -1, and continuous enough). As this study turns us towards equi-continuous functions, I kept it up and created a probabilistic version of equi-continuous classes [C-55].



  Biological applications  : There are many forays of mathematical morphology into biology. Dozens could be mentioned : for instance, I took part to a study over the early detection of transplanted kidneys (Dr D. Seron’s team in Barcelona), which was rewarded as the best paper for the year 1996 in “Kidney International”. To mention more recent studies, publication [A-82] in “Bioinformatics” in 2003 offers a methodology to read bio-chips, which was created by J. Angulo, and which is presently used as an international reference (particularly in the USA) for genetic analysis. Another study, more medicine-related, was carried out with Prof. Z. Massy’s team at Necker Hospital, and deals with the aorta calcification ([A-83], published in IAS in 2003). Finally, a larger study, carried out with Prof. Flandrin (Necker Hospital, Paris), led  to an automatic classification of lymphocytes. I select three communications, written with J. Angulo, two in English, dealing  with the chromatin structure [C-67] and cells recognition [C-74], and another one in Spanish, about telemedicine applications [C-70].

  Other Applications : Bio-medical applications are not the only ones the Center of Mathematical Morphology is involved in. At present, many other fields are opened, but more particularly material sciences and multi-media. As an example, here are two studies from these two themes. The first one [C-65] was undertaken with M. Młynarczuk (Krakow), and  synthesizes  petrography information obtained from the polarizer. The second one, with E. Decencière and M.E. Díaz (Valencia), allows us to cancel vertical lines in old movies [NI-187]]. Some of these applications tackle unusual physics fields and do not always refer to models. The invited lecture  [C-66] to ICPR 2000 congress (Barcelona) wonders if shape recognition may be considered as physics.



  Courses : My courses are displayed as transparencies or written texts. For the first ones, they are listed into the “transparencies” heading. For the second ones, I have given access to five of them from this page. The first one, [T-34],  is a general text over deterministic morphological methods. It was written for the first franco-scandinavian mathematics school, that Prof. Ch. Kiselman (Uppsala University) and I organised at Lake Erken (Sweden, 2002). This course includes a part of the material on 3-D morphology from [T-36] course, lectured at Bordeaux Stereology congress in 2002, but teh Bordeaux course is more specific to 3-D. Both third course about random sets and functions [T-37], with its exercises [T-37b], fourth one on colour [T-39], lectured at Lille University in 2005 are totally independent from the two first courses (i.e. Lake Erken and Bordeaux). Finally, reference [NI-216] that I mentioned before, about models of numerical functions, is one of the chapters of my next book to be published.



  Envoi : This skimming through would not be complete without paper [C-72] regarding the birth of mathematical morphology, published in 2002, but written in 1998 with G. Matheron and myself. It was his last text, and an answer to some inaccurate remarks heard at the School of Mines at that time. As extremes often meet, I added my very first paper on mathematical morphology, quite in its infancy (1965) [C-2].


P.S. the classification marks used here as links are also those of my publications list, where O, A, C, NI and T are respectively standing for books, papers, communications with acts, internal notes and courses. Pdf files that can be downloaded here are often slightly different from the final publications, as they consist in first versions, presented in congresses or to journals.