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A method to compute the full hierarchy of the critical subsets of a density field is presented. It is based on a Watershed technique and uses a probability propagation scheme to improve the quality of the segmentation by circumventing the discreteness of the sampling. It can be applied within spaces of arbitrary dimensions and geometry. This recursive segmentation of space yields, for a d-dimensional space, a d -1 succession of n-dimensional subspaces that fully characterize the topology of the density field. The final one-dimensional manifold of the hierarchy is the fully connected network of the primary critical lines of the field: the skeleton. It corresponds to the subset of lines linking maxima to saddle points, and provides a definition of the filaments that compose the cosmic web as a precise physical object, which makes it possible to compute any of its properties such as its length, curvature, connectivity etc.
Sousbie et al. (Thu,) studied this question.