The multiscale morphology filter: identifying and extracting spatial patterns in the galaxy distribution

Abstract

Aims. We present here a new method, MMF, for automatically segmenting cosmic structure into its basic components: clusters, filaments, and walls. Importantly, the segmentation is scale independent, so all structures are identified without prejudice as to their size or shape. The method is ideally suited for extracting catalogues of clusters, walls, and filaments from samples of galaxies in redshift surveys or from particles in cosmological N-body simulations: it makes no prior assumptions about the scale or shape of the structures. Methods. Our Multiscale Morphology Filter (MMF) method has been developed on the basis of visualization and feature extraction techniques in computer vision and medical research. The density or intensity field of the sample is smoothed over a range of scales. The smoothed signals are processed through a morphology response filter whose form is dictated by the particular morphological feature it seeks to extract, and depends on the local shape and spatial coherence of the intensity field. The morphology signal at each location is then defined to be the one with the maximum response across the full range of smoothing scales. The success of our method in identifying anisotropic features such as filaments and walls depends critically on the use of an optimally defined intensity field. This is accomplished by applying the DTFE reconstruction methodology to the sample particle or galaxy distribution. Results. We have tested our MMF Filter against a set of heuristic models of weblike patterns such as are seen in the Megaparsec cosmic matter distribution. To test its effectiveness in the context of more realistic configurations we also present preliminary results from the MMF analysis of an N-body model. Comparison with alternative prescriptions for feature extraction shows that MMF is a remarkably strong structure finder

The Vainshtein mechanism in the cosmic web

“…The halos themselves have different morphologies; they can be in overdense or underdense environments, and they can inhabit different types of structures in the cosmic web. Halos in simulations, and galaxies in observations, are found in filaments, walls, and voids, and obviously there are many in clusters and superclusters [22,23,48,49]. In this section, we investigate the morphological dependence of the Vainshtein mechanism for dark matter halos.…”

“…While voids are underdense regions and halos are density peaks, it is now understood that density alone is not the salient feature that distinguishes these structures. Rather, it is the dynamics of the nonlinear gravitational collapse that fundamentally distinguishes between expanding voids, walls collapsing along one dimension, filaments collapsing along two, and halos collapsing along three orthogonal dimensions [19][20][21][22][23][24][25]. While the chameleon mechanism has been found to depend on the density of the halo environment [26], the dimensionality dependence of the Vainshtein mechanism suggests it may depend instead on the morphology of the cosmic web.…”

SPECTROSCOPIC STUDY OF STAR-FORMING GALAXIES IN FILAMENTS AND THE FIELD ATz∼ 0.5: EVIDENCE FOR ENVIRONMENTAL DEPENDENCE OF ELECTRON DENSITY

“…To further investigate the reality of this structure, we used the 2D version of the Multi-scale Morphology Filter (MMF) algorithm (Aragón-Calvo et al 2007;Darvish et al 2014), which is able to disentangle the cosmic web into its components such as filaments and clusters. This algorithm describes the local geometry of each point in the density field based on the signs and the ratio of eigenvalues of the Hessian matrix (second-order derivative of the density field).…”

Towards understanding the structure of voids in the cosmic web

“…The characteristic diameter of these supervoids is of the order of 100 h −1 Mpc Kirshner et al 1981;Einasto et al 1994bEinasto et al , 1997b. Supervoids are not empty, but contain a hierarchy of voids (Einasto et al 1989;Martel & Wasserman 1990;van de Weygaert & van Kampen 1993;Lindner et al 1995;Müller et al 2000;Gottlöber et al 2003;Aragón-Calvo et al 2007;von Benda-Beckmann & Müller 2008;Aragon-Calvo et al 2010a;Jones et al 2010).…”