Georges Matheron

Georges François Paul Marie Matheron (1930 — August 7, 2000) was a French mathematician and geologist, known as the founder of geostatistics and a co-founder (together with Jean Serra) of mathematical morphology. In 1968 he created the Centre de Géostatistique et de Morphologie Mathématique at the Paris School of Mines in Fontainebleau. He is known for his contributions on Kriging and mathematical morphology. His seminal work is posted for study and review to the Online Library of the "Centre de Géostatistique", Fontainebleau, France.

Geostatistics

Matheron’s ["Formule des Minerais Connexes"] became his "Note Statistique No 1". In this paper of November 25, 1954, Matheron derived the degree of associative dependence between lead and silver grades of core samples. In his "Rectificatif" of January 13, 1955, he revised the arithmetic mean lead and silver grades because his core samples varied in length. He did derive the length-weighted average lead and silver grades but failed to derive the variances of his weighted averages. Neither did he derive the degree of associative dependence between metal grades of ordered core samples as a measure for spatial dependence between ordered core samples. He did not disclose his primary data set and worked mostly with symbols rather than real measured values such test results for lead and silver in Matheron's core samples. Matheron's "Interprétations des corrélations entre variables aléatoires lognormales" of November 29, 1954, was marked "Note statistisque No 2." In this paper, Matheron explored lognormal variables and set the stage for statistics by symbols. Primary data would have allowed him to assess whether or not lead and silver grades departed from the lognormal distribution, or displayed spatial dependence along core samples in his borehole.

Matheron coined the eponym "krigeage" ("Kriging") for the first time in his 1960 "Krigeage d’un Panneau Rectangulaire par sa Périphérie". In this "Note géostatistique No 28", Matheron derived "k*", his estimateur and a precursor to the kriged estimate or kriged estimator. In mathematical statistics, Matheron’s "k*" is the length-weighted average grade of a single panneau in his set. What Matheron failed to derive in this paper was "var(k*)", the variance of his estimateur. Matheron presented his "Stationary Random Function" at the first colloquium on geostatistics in the USA. He called on Brownian motion to conjecture the continuity of his Riemann integral but did not explain what Brownian motion and ore deposits have in common. Matheron, unlike John von Neumann in 1941 and Anders Hald in 1952, never worked with Riemann sums. It was not Professor Dr Georges Matheron but Dr Frederik P Agterberg who derived the distance-weighted average of a set of measured values determined in samples selected at positions with different coordinates in a sample space. What Agterberg did not do was derive the variance of this function.

Matheron did indeed derive length-weighted average grades of core samples and ore blocks but did not derive the variance of these functions. In time, the length-weighted average grade for Matheron's three-dimensional block grade was replaced with the distance-weighted average grade for Agterberg's zero-dimensional point. Both central values turned into honorific kriged estimates or kriged estimators. An infinite set of Agterberg's zero dimensional points fits within any ore block, along any borehole, or inside any sampling unit or sample space. Matheron's block grades and Agterberg's point grades are unique because both are functions without variances.

Mathematical morphology

In 1964, Matheron was supervising the PhD thesis of Jean Serra, dedicated to quantifying the ore properties of the iron deposit of Lorraine. Serra came up with the idea of using structuring elements for the analysis, which lead to the concept of hit-or-miss transform. The theoretical analysis of this transform lead Matheron to derive and investigate the concepts of erosion, dilation, opening and closing, which became known later as the basic morphological operators. He also developed a tool for granulometry, i.e., the computation of a "size distribution", where he mathematically characterizes the concept of size. In December 1964, Matheron and Serra, together with [http://www.cg.ensmp.fr/bibliotheque/1988/FORMERY/Publication/DOC_00617/FORMERY_Publication_00617.pdf Philippe Formery] , named this approach mathematical morphology. It has since evolved into a theory and method that is applied in a variety of image processing problems and tasks, and is researched worldwide [See, e.g., (Serra and Soille (Eds.) 1994)] ("main article: Mathematical morphology"). Matheron continued to contribute to mathematical morphology during the years, his best-known contribution being the morphological filtering theory, which he developed with Serra in the 1980s.

The Centre de Géostatistique et de Morphologie Mathématique

In 1968, the Paris School of Mines created the "Centre de Morphologie Mathématique", located in Fontainebleau, France, and named Matheron its first director. In 1979, the center was renamed "Centre de Géostatistique et de Morphologie Mathématique", and, in 1986, the latter was split into two separate centers: "Centre de Géostatistique", directed by Matheron, and "Centre de Morphologie Mathématique", directed by Serra.

Notes

References

* [http://www.annales.org/archives/x/matheron.html Matheron at the "Annales des Mines" (French)]
* "Mathematical Morphology and Its Applications to Image Processing", J. Serra and P. Soille (Eds.), proceedings of the 2^nd international symposium on mathematical morphology (ISMM'93), ISBN 0-7923-3093-5 (1994)
* "Image Analysis and Mathematical Morphology" by Jean Serra, ISBN 0126372403 (1982)
* "Image Analysis and Mathematical Morphology, Volume 2: Theoretical Advances" by Jean Serra, ISBN 0-12-637241-1 (1988)
* "An Introduction to Morphological Image Processing" by Edward R. Dougherty, ISBN 0-8194-0845-X (1992)
* "Morphological Image Analysis; Principles and Applications" by Pierre Soille, ISBN 3540-65671-5 (1999)

External links

* [http://cg.ensmp.fr/Presentation/Matheron/Matheron_en.shtml Georges Matheron at the Centre de Géostatistique]
* [http://www.general.monash.edu.au/ss/pdf/vol19no3/Obituaries_01.pdf Obituary] by Dominique Jeulin (Centre de Morphologie Mathématique Ecole des Mines de Paris, October 2000) probably from Image Analysis & Stereology.
* [http://www.geostatscam.com/Adobe/G_Matheron.pdf Georges Matheron - Founder of Spatial Statistics] by Frederik P. Agterberg (Proceedings of the International Association for Mathematical Geology, 2003)
* [http://www.cg.ensmp.fr/bibliotheque/index_byyear.html A chronology of Matheron's seminal work]
* [http://cmm.ensmp.fr/~serra/pdf/birth_of_mm.pdf History of Mathematical Morphology] , by Georges Matheron and Jean Serra
* [http://www.geostatscam.com A website that unscrambles Matheron's new science of geostatistics]