  We propose and investigate a new algorithm for quantifying the topological
properties of cosmological density fluctuations. We first motivate this
algorithm by drawing a formal distinction between two definitions of relevant
topological characteristics, based on concepts, on the one hand, from
differential topology and, on the other, from integral geometry. The former
approach leads one to concentrate on properties of the contour surfaces which,
in turn, leads to the algorithms CONTOUR2D and CONTOUR3D familiar to
cosmologists. The other approach, which we adopt here, actually leads to much
simpler algorithms in both two and three dimensions. (The 2D algorithm has
already been introduced to the astronomical literature.) We discuss the 3D case
in some detail and compare results obtained with it to analogous results using
the CONTOUR3D algorithm.
