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.