1st Edition
by Laurent Najman (Editor), Hugues Talbot (Editor)
Mathematical Morphology
allows for the analysis and processing of geometrical structures using
techniques based on the fields of set theory, lattice theory, topology,
and random functions. It is the basis of morphological image processing,
and finds applications in fields including digital image processing
(DSP), as well as areas for graphs, surface meshes, solids, and other
spatial structures. This book presents an up-to-date treatment of
mathematical morphology, based on the three pillars that made it an
important field of theoretical work and practical application: a solid
theoretical foundation, a large body of applications and an efficient
implementation.
The book is divided into five parts and includes 20 chapters. The five parts are structured as follows:
- Part
I sets out the fundamental aspects of the discipline, starting with a
general introduction, followed by two more theory-focused chapters, one
addressing its mathematical structure and including an updated
formalism, which is the result of several decades of work.
- Part
II extends this formalism to some non-deterministic aspects of the
theory, in particular detailing links with other disciplines such as
stereology, geostatistics and fuzzy logic.
- Part III addresses
the theory of morphological filtering and segmentation, featuring modern
connected approaches, from both theoretical and practical aspects.
- Part
IV features practical aspects of mathematical morphology, in particular
how to deal with color and multivariate data, links to discrete
geometry and topology, and some algorithmic aspects; without which
applications would be impossible.
- Part V showcases all the
previously noted fields of work through a sample of interesting,
representative and varied applications.