This book discusses the basic geometric contents of an image and presents a
treedatastructuretohandleite?ciently.Itanalyzesalsosomemorphological operators that simplify
this geometric contents and their implementation in termsofthe
datastructuresintroduced.It?nallyreviewsseveralapplications to image comparison and
registration to edge and corner computation and the selection of features associated to a
given scale in images. Let us ?rst say that to avoid a long list we shall not give references
in this summary they are obviously contained in this monograph. A gray level image is usually
modeled as a function de?ned in a bounded N domain D? R (typically N = 2 for usual snapshots
N=3formedical images or movies) with values in R. The sensors of a camera or a CCD array
transform the continuum of light energies to a ?nite interval of values by means of a nonlinear
function g. The contrast change g depends on the pr- ertiesofthesensors
butalsoontheilluminationconditionsandthere?ection propertiesofthe objects
andthoseconditionsaregenerallyunknown.Images are thus observed modulo an arbitrary and unknown
contrast change.
