Book description
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.
