The concept of ridges has appeared numerous times in the image
processing liter- ature. Sometimes the term is used in an intuitive
sense. Other times a concrete definition is provided. In almost all
cases the concept is used for very specific ap- plications. When
analyzing images or data sets, it is very natural for a scientist to
measure critical behavior by considering maxima or minima of the data.
These critical points are relatively easy to compute. Numerical packages
always provide support for root finding or optimization, whether it be
through bisection, Newton's method, conjugate gradient method, or other
standard methods. It has not been natural for scientists to consider
critical behavior in a higher-order sense. The con- cept of ridge as a
manifold of critical points is a natural extension of the concept of
local maximum as an isolated critical point. However, almost no
attention has been given to formalizing the concept. There is a need for
a formal development. There is a need for understanding the computation
issues that arise in the imple- mentations. The purpose of this book is
to address both needs by providing a formal mathematical foundation and
a computational framework for ridges. The intended audience for this
book includes anyone interested in exploring the use- fulness of ridges
in data analysis.
