EAN: 9781461272007

SYSTEMS & CONTROL FOUNDATIONS & APPLICATIONS ...

The analysis  processing  evolution  optimization and or regulation  and control of shapes and
images appear naturally in engineering (shape optimization  image processing  visual control) 
numerical analysis (interval analysis)  physics (front propagation)  biological morphogenesis 
population dynamics (migrations)  and dynamic economic theory. These problems are currently
studied with tools forged out of differential geometry and functional analysis  thus requiring
shapes and images to be smooth. However  shapes and images are basically sets  most often not
smooth. J.-P. Aubin thus constructs another vision  where shapes and images are just any
compact set. Hence their evolution -- which requires a kind of differential calculus -- must be
studied in the metric space of compact subsets. Despite the loss of linearity  one can transfer
most of the basic results of differential calculus and differential equations in vector spaces
to mutational calculus and mutational equations in any mutational space  including naturally
the space of nonempty compact subsets. Mutational and Morphological Analysis offers a structure
that embraces and integrates the various approaches  including shape optimization and
mathematical morphology. Scientists and graduate students will find here other powerful
mathematical tools for studying problems dealing with shapes and images arising in so many
fields.

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