Mathematical morphology was born in 1964 when G. Matheron was asked to investigate the relationships between the geometry of porous media and their permeabilities, and when at the same time, I was asked to quantify the petrography of iron ores, in order to predict their milling properties. This initial period (1964-1968) has resulted in a first body of theoretical notions (Hit or Miss transformations, openings and closings, Boolean models), and also in the first prototype of the texture analyser. It was also the time of the creation of the Centre de Morphologie Mathematique on the campus of the Paris School of Mines at Fontainebleau (France). Above all, the new group had found its own style, made of a symbiosis between theoretical research, applications and design of devices.
These have the following idea in common: the notion of a geometrical structure, or texture, is not purely objective. It does not exist in the phenomenon itself, nor in the observer, but somewhere in between the two. Mathematical morphology quantifies this intuition by introducing the concept of structuring elements. Chosen by the morphologist, they interact with the object under study, modifying its shape and reducing it to a sort of caricature which is more expressive than the actual initial phenomenon. The power of the approach, but also its difficulty, lies in this structural sorting. Indeed, the need for a general theory for the rules of deformations appeared soon. The method progressed as a result of an interchange between intellectual intuitions and practical demands coming from the applications. This finally lead to the content of this book. On the way, several researchers joined the initial team and constituted what is now called the "Fontainebleau School". Among them, we can quote J.C. Klein, P. Delfiner, H. Digabel, M. Gauthier, D. Jeulin, E. Kolomenski, Y. Sylvestre, Ch. Lantuejoul, F. Meyer and S. Beucher.
A new theory never appears by spontaneous generation. It starts from some initial knowledge and grows in a certain context. The family tree of mathematical morphology essentially comprises the two branches of integral geometry and geometrical probabilities, plus a few collateral ancestors (harmonic analysis, stochastic processes, algebraic topology). Apart from mathematical morphology, three other parallel branches may be considered as current descendants of the same tree. They are stereology, point processes and stochastic geometry as developed by D. G. Kendall's School at Cambridge. Stereology, unlike the other two, is oriented towards applications. The stereologists have succeeded in putting the major theorems of integral geometry into practice. Indeed their society regroups biologists and specialists of the material sciences whose mutual interest lies in the quantitative description of structures, principally at the microscopic scale.