Geometric description of images as topographic maps (Q1043891)

This book discusses the basic geometric content of an image viewed as a surface in an extended Morse theory design and with the help of Mathematical Morphology. The book is mainly mathematics oriented and often considers images as continuous functions over a subdomain of \(\mathbb{R}^n\). The book is divided into eight chapters: {\parindent=5mm \begin{itemize}\item[1.] The Introduction that recalls Morse theory and level set properties; \item[2.] The tree of shapes of an image is investigated and finiteness properties are proven; \item[3.] ``Grain filters'' is devoted to special filters which are contrast invariant (grain and extrema filters) and provides algorithmic solutions to their computations; \item[4.] ``A topological description of the topographic map'' weakens the Morse assumption to allow for image transitions by use of upper semicontinuity; \item[5.] ``Merging the component trees'' describes an algorithm to construct the tree of shapes by merging the trees of connected components; \item[6.] ``Computation of the tree of shapes of a digital image'' specifies the construction with data structures and implementation details for this more applicative issue; \item[7.] ``Computation of the tree of bilinear level lines'' also describes algorithmic issues for interpolations of level lines; \item[8.] Finally, ``Applications'' treats image filtering, registration and other applications, such as corner detection, using the developed principles. \end{itemize}} Of course a conclusion speaks about future perspectives and extensions of the theory.