ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

The Birth of Mathematical Morphology

Georges Matheron and Jean Serra

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 1

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000•

Context

Before considering how Mathematical
Morphology originated in 1964, we will
describe briefly the backgrounds of its
two founders at the beginning of thatyear,

• even though they were hardly aware of
the theoretical turn they would take a few
months later.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 2

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000•

First Protagonist

Georges Matheron was a mining engineer
from the Corps des Mines, 34 years old,working with the B.R.G.M. ( i.e. geologicalsurvey) , in Paris.

• At the end of 1963, he had just achieved thedoctrinal body of his theory concerning theestimation of deposits, called Geostatistics,
and started in Algeria ten years before.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 3

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

First Protagonist (II)• It was time for a break and forinvestigating new horizons beyond themining world.
• His publication of reports paused at thattime, decreasing from fifty in ten years tonone in ten months. He wouldn't return togeostatistics until January 1969, five years
later, via universal kriging.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 4

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Second Protagonist• Jean Serra was a civil engineer from theEcole des Mines de Nancy. He was 24 years
old and was completing a bachelor's degreein philosophy focus on Gestalt psychology.
• One year before, he had been hired by
IRSID as a PhD student for a detailed
inventory of Lorraine iron deposit bygeostatistics .
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 5

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000•

Lorraine Iron Orebody

Three different scales were to beconsidered. First of all, best profitableareas had to be estimated within the 600
Km of the deposit.

• But the panels to be kriged at the 100m
scale were affected by a strong “nugget
effect” acting at the metric scale, due tolocal migrations of calcite.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 6

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

2nd scale : Calcite migration

Calcite migration provokes a bias in the drillings
grades which had to be quantified.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 7

3rd scale : Petrography (100 µm)

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

– in brown, olites of limonite ( Φ : 100µm to 300µm ) ;– in green, chlorite cement with (poor) iron ;– in white, quartz and calcite.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 8

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Petrography (II)• For the enrichment of the ore, which had
become essential, the grade of iron was lessimportant than its petrographic distribution
between oolites and chlorite cement .
• Therefore quantifying meant estimating the
proportions of the petrographic phases andmeasuring their sizes.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 9

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Nested Phenomena• In parallel with these economic objectives,
J. S. also hoped to link the three scales
through a point variogram, which would
serve as a vital lead for this huge structural
zoom and would cover the space from themicron to the hundred kilometer scale.

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 10

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Chronology : Spring 1964

• Quantitative study of the above thin section
by J. S. by means of a slide projector. The
thin section was projected screen equippedwith a square grid.
• The phases found in each of the 6.000 gridvertices were read manually. Direct andcross variograms were calculated in the 4basic directions on a 1410 IBM computer.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 11

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Chronology : Oct. 1964

• G.M. report, entitled ''Fonctions aléatoires
du type tout ou rien'', in which he attempts tomodel petrography in random terms,
through the classical approach of the spatiallaw, based on a finite number of points.
• First sketch of the Boolean
calculation of its covariance.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )model,

Birth of Math. Morph. 12

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Chronology : Dec. 1964

• J.S. report, entitled « l'analyse pétrographiquequantitative ».
• This report, which detailed the results ofpetrographic surveys, introduced the twoconcepts ofa structuring element, called ''spot'',
and of the hit or miss transformation.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 13

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Chronology : Dec. 1964 (II)• J.S. could not link variograms to the desired
size properties. Hence he proposed to startfrom shapes which would be given a priori the structuring elements - and to make theminteract with the objects under study.
• According to their geometry (circle, straight
line, pair of points), they would reveal thevarious structural features of the objects .
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 14

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Chronology : Dec. 1964 (III)• G.M. report, entitled ''Etude théorique desgranulométries'', starts from this first study
to introduce number of new ideas ;• J. S. begings the construction of a devoted
device, the “texture Analyser”, with J.C.
Klein.
These two texts and the device form the very
start of Mathematical Morphology.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 15

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Chronology : Dec. 1964 (IV)• Limiting Hit-or-Miss mapping to one-phasestructuring elements, G.M. described its
algebraic properties and finds the analyticalrepresentation for erosion and dilation ;• He re-formulated the Boolean model in aconvenient framework, which forecast thetheory of random sets, and uses the erosion
formalism to find the functional Q(B).
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 16

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Chronology : Dec. 1964 (V)In addition, in the same report, G. M.
• introduced the concepts of the adjunctopening and closing,• found their main algebraic properties,• and interpreted openings according todiscs of increasing radius as size
descriptors : the granulometries .
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 17

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Chronology : July 1965

• Registration of the first patent of the texture
analyser, inventor : J. S., company : IRSID.
• This ended the first year of Mathematical
Morphology :- G.M. report was the basis for “éléments
pour une théorie des milieux poreux” (1967);- J.S. report was published in the ''bullein
du BRGM” in 1966 .
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 18

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

G. Matheron, J. Serra

Texture Analyser Patent (I)Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 19

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

G. Matheron, J. Serra

Texture Analyser Patent (II)Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 20

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Chronology : 1965

• Surprisingly, the first year, which was sorich in fruitful exchanges, was followed by
two years of almost complete silence on thesubject. G. M. turned to hydrodynamics(eight studies written during that period)
The main reason for this situation was thedevelopment of the texture analyser thattook the entire year of 1965
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 21

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000•

Chronology : 1966

The whole year of 1966 was devoted tothe inventory of ''good'' structuring elements
and to establishing logical relations between
them.

• the machine allowed the construction of
every possible structuring element based onoone or two straight lines, whcih was asmall technical revolution.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 22

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Chronology : 1967 (I)• Looking back on the year 1967, it appears
that G.M. and J.S. were both busy finishingprevious work, and preparing the creation of
C.M.M., even if they did not suspect it yet.
• The national service in a military research
center allowing some free time, J. S. ended
his mining studies, with a PhD and two
publications respectively.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 23

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000•

Chronology : 1967 (II)Still in 1967, G. M., after he had chosen
to take some distance from Geostatistics,
left B.R.G.M. and wrote the first version of“Random sets and Integral Geometry”.

• Also, he gathered his morphological papers
and some texts on hydrodynamics in thebook ’Eléments pour une théorie des milieux
poreux’
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 24

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000•

Chronology : End of the Begining

On April 20, 1968, The Ecole des Mines
created the '‘Centre de Morphologie
Mathématique'', and appointed G.M.
director.

• Despite the imposing size of the building,the center was reduced to two people:
G.M. and J. S. , The later had just been
hired as ''Maître de Recherches'' by theEcole des Mines, and appointed to C.M.M.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 25

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

From 1968• From 1968, some previous results were to
be developed (Boolean model, hit or misstransformation), others less (star, radii ofcurvature), and the original machine
evolved rapidly to other proptotypes andcommercial devices (Leitz, Allen Bradeley) ;…But a specific approach was drawn.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 26

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Comments• Chronology sharpens the events, makes
more precise their apparitions, but says
nothing about their reasons.
• And also , some questions arise , which arestill open...

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 27

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Questions• What happened during the three years wehave just skipped through, and above all
during the first one ?
• What kind of impulse did these two men
give by working together with practicallyno intellectual connection with the people
around them ?
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 28

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

• Why did this methodology gradually
gain in influence instead of another ? Is it
due to a better ability to render theconcepts of the time, and integrate theminto a unified approach ?
• Or is it just the result of the evolution incomputer science that enabled thesynchronized development of Math.
Morphology as a sort of by-product ?

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 29

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000•

First Outside : the Stereologists

G. M. had rediscovered the set addition
defined by H. Minkowski (1903) andstudied in detail by H. Hadwiger in 1957.

• This oriented G.M. and J.S. towards Integral
Geometry and the int. Society for stereology

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 30

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000•

The Stereologists (II)When the new ideas were presented
before the Stereologists, in 1971 , they werereceived with rather mixed feelings.

• The postulate that one can study a set only
by associating it with numbers was so
deeply rooted in their minds, that they
were just unable to imagine other ways ofthinking.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 31

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

The Stereologists (III)• The physical intuition of morphology thatperceiving a set, or an image, means totransform it, either qualitatively or
quantitatively, was too far removed fromtheirs.

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 32

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

• And yet the new approach used to open
number of questions : dilation was to be amore robust operation than erosion,
although no experiment could verify it ;• Also, one could wonder whether such atheory would apply to gray level images,
or uniquely to binary ones. Etc..
But the stereologists did not pay attention totheses aspects…

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 33

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

Are ideas just the fruits of technologicalevolution ?
From this point of view, the evolution of
Mathematical Morphology over the past
thirty years is instructive :- Two-dimensional operators were discovered
four years before television technology
enabled their implementation (1969);
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 34

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

-the memory of the size of an image, with itsvery peculiar loop functioning, occurredin 1973, simultaneously with a growinginterest for binary iterative algorithms(ultimate erosion, skeleton, thinning).
-Five years later, the numerical memory
opened the door to gray tone image
processing , precisely at the time whenmorphological filtering and the watershedalgorithm were invented.

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 35

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

-More recently, the morphological theory forconnection,thatgoverns
automatic
segmentation of images and sequences, wasdeveloped during the nineties, just whenthe multimedia applications arose.
What a lot of coincidences !

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 36

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

How an idea was born ? (I)• Even if we are not always aware of it, we all''surf'' on successive technological waves.
However, this this subconscious pressure
applies uniformly over all the 1500 image
processing laboratories in the world.
• Why then strong ideas do crystallize in a
few places only, and at some privileged
periods ?
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 37

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

How an idea was born ? (II)• Take the casegranulometry

of

the

notionofa• The first question was : how to know the sizeof oolites and of chlorite cement in Lorraine
iron ores (at least one mean volume
parameter, and more if possible) ?
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 38

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

How an idea was born ? (III)• First answer : The results of the first point
variograms led J.S. to the following

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 39

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

How an idea was born ? (IV)

• J.S. was wrong when considering dilations
or distance functions as granulometric
tools, but he did feel the need for convex
structuring elements.
• He formulated the question differently interms of set Æ set transformations (and notof sets Æ numbers) which was new, andintroduced the paradigm for this type ofoperations.

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 40

ISMM 2000 ,Xeros Center
Palo-Alto, June2000•

How an idea was born ? (V)Second step : G.M. revived the idea oftransforming sets and showed that dilations
using disks should be combined with theirdual operations to obtain a size result

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 41

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 42

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

How an idea was born ? (VI)

• Once again a good insight emerged out of aquestionable mathematical statement : thefunction Sλ was certainly not decreasing,but the same was true already for dilations
according to disks.

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 43

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

How an idea was born ? (VII)• The strength of G.M. approach actuallycame from the introduction of idempotent
operators. Indeed, this property wasproved for opening a few pages before, but
its author did not venture yet to substituteit (with two other axioms) as constitutive of
the physical concept of granulometry.

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 44

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Dialectics• Thus, ideas first need time to take shape,
then to expand and link together.
• Platonists are not always aware of thispoint. Those who try to construct amathematical structure are sometimes
lured by the strong impression that ''it
does exist'' somewhere, outside thesensible world.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 45

ISMM 2000 ,Xeros Center
Palo-Alto, June2000

• But because they interpret this impression
from a retrospective, therefore static, pointof view, they tend to forget that they feelthat ''it does exist'' because ''it does
resist'' (a feeling that is not so Platonic..)• In this story, experimental facts are neverused to verify ready-made formulas. They
appear on the contrary as a support tohelp an idea under construction to find its
structure and shape.

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 46

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Internal reports (I)Georges Matheron• Fonctions aléatoires du type tout ou rien, October 1964
• Etude théorique des granulométries, December 1964
• Axiomatique des milieux poreux aléatoires, March 1965
• Pour une théorie des structures aléatoires, Aug.-Sept.
1967

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 47

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Internal reports (II)Jean Serra• Contribution à l'analyse pétrographique quantitative,
December 1964
• La transformation en tout ou rien. February 1965
• L'Analyse des Textures par la géométrie aléatoire, May
1965• Morphologie mathématique et genèse des concrétions
carbonatées des minerais de fer de Lorraine, April 1967

G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 48

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Publications (I)Georges Matheron• Haas A., Matheron G., Serra J. :Morphologie Mathématique etgranulométries en place. Annales des Mines, XI, 1967, 736-753, and XII,
1967, 767-782.
• Eléments pour une théorie des milieux poreux. Masson, Paris, 1967.
• Théorie des ensembles aléatoires - Les Cahiers du Centre de Morphologie
Mathématique, Fasc. 4 - Paris : ENSMP, 1969, 54 p.
• Random sets theory and its applications in stereology. - 3rd Int.
Congress Stereology, Berne, 28-31 Aug. 1971. J. of Microscopy,Vol. 95,
Pt 1, Feb. 1972, 15-23.
• Random Sets and Integral Geometry. New York: Wiley, 1975.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 49

ISMM 2000 ,Xeros Center
Palo-Alto, June
2000

Publications (II)Jean Serra• Patent : Dispositif d'analyse de textures, Inventor : J. SERRA,
Registered by IRSID, July 2, 1965 (23 273), Canada, Great-Britain,
France, Japan, Sweden, U.S.A.
• L'analyse des textures par la géométrie aléatoire. Comptes-rendus duComité Scientifique de l'IRSID}, 2 Nov. 1965, 7 p.
• Remarque sur une lame mince de minerai lorrain. Bulletin du B.R.G.M
n°6 Dec. 1966, 26 p.
• Buts et réalisation de l'analyseur de textures. Revue de l'Industrie
Minérale, vol. 49, Sept. 1967, 9 p.
• Morphologie Mathématique et genèse des concrétions carbonaté}esdes minerais de fer de Lorraine. Sedimentology, Oct. 1968, 183-208.
• Stereology and structuring elements. - 3rd Int. Congress Stereology,
Berne, 28-31 Aug. 1971 J. of Microscopy, Vol.95(1), 1972, 93-103.
G. Matheron, J. Serra

Ecole des Mines de Paris ( 2000 )Birth of Math. Morph. 50