Space, structure, and randomness: these are the three key concepts
underlying Georges Matherona (TM)s scientific work. He first
encountered them at the beginning of his career when working as a
mining engineer, and then they resurfaced in fields ranging from
meteorology to microscopy. What could these radically different
types of applications possibly have in common? First, in each one
only a single realisation of the phenomenon is available for study,
but its features repeat themselves in space; second, the sampling
pattern is rarely regular, and finally there are problems of change
of scale.
This volume is divided in three sections on random sets,
geostatistics and mathematical morphology. They reflect his
professional interests and his search for underlying unity. Some
readers may be surprised to find theoretical chapters mixed with
applied ones. We have done this deliberately. GM always considered
that the distinction between the theory and practice was purely
academic.
When GM tackled practical problems, he used his skill as a
physicist to extract the salient features and to select variables
which could be measured meaningfully and whose values could be
estimated from the available data. Then he used his outstanding
ability as a mathematician to solve the problems neatly and
efficiently. It was his capacity to combine a physicista (TM)s
intuition with a mathematiciana (TM)s analytical skills that
allowed him to produce new and innovative solutions to difficult
problems.
The book should appeal to graduate students and researchers
working in mathematics, probability, statistics, physics, spatial
data analysis, and image analysis. In addition it will be of
interest tothose who enjoy discovering links between scientific
disciplines that seem unrelated at first glance. In writing the
book the contributors have tried to put GMa (TM)s ideas into
perspective. During his working life, GM was a genuinely creative
scientist. He developed innovative concepts whose usefulness goes
far beyond the confines of the discipline for which they were
originally designed. This is why his work remains as pertinent
today as it was when it was first written.
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