by Pierre Gernez, Xavier Descombes, Josiane Zerubia, Éric Slezak and Albert Bijaoui
A joint project between INRIA and the French Riviera Observatory proposes to apply a marked point process to detect a galaxy filament network. The method is based on a model initially developed for road network extraction in remotely sensed images.
Beyond one billion lightyears, when averaged over 30 Mpc, the visible Universe can be seen as a gas of galaxies, uniformly distributed. At smaller spatial scales, astronomical observations and dedicated numerical simulations have shown that the repartition of the luminous matter is not so homogeneous.
The threedimensional distribution of galaxies in the today Universe is indeed characterised by a complex network of filamentary structures which delineates spherical regions of about 100 million lightyears in diameter devoid of objects, suggesting a spongelike or celllike topology for the underlying matter density field. The finite age of the Universe and the low enough peculiar velocity of galaxies imply that information about the initial conditions are preserved at such large spatial scales. Characterising the properties of the galaxy clustering puts therefore strong constraints on the theoretical models for the formation of structures under the influence of gravity in an expanding Universe known to be dominated by dark matter and energy components. Identifying elongated structures like filaments, which might only occupy 10% of the volume, and measuring their statistical properties would allow one to go beyond the information provided by the usual twopoint correlation function measurements which suffer from degeneracies with respect to the topology.

As shown in Figure 1, such a filament is not a single structure with sharp edges, but instead a fuzzy set of points more or less scattered, which makes its detection difficult. Another difficulty in the detection process comes from the difference of spatial scales between sparse and prominent compact features. The gradual disappearance of structures with increasing distance results from the use of a magnitudelimited sample. The apparent luminosity of any object is fainter as distance increases, and only the few galaxies with the highest intrinsic luminosity are then included.
Up to now, there are only a few methods to extract the filamentary structure. The Minimal Spanning Tree (MST) method has been mostly used. Recently, we have adapted a method based on marked point process, initially proposed for road network extraction to this framework. The network of filaments is modelled by a marked point process, that is to say a random set of objects whose number of data points is also a random variable. The objects of this process are segments described by three random variables corresponding to their midpoint, their length and their orientation. The segment distribution is simulated by a density probability. In order to find the segment configuration that better fits the filamentary network, we define a density probability which takes into account the interactions between segments. The configuration of segments composing the filament network is estimated by the minimum of the energy of the system which has two components: the prior term forces the segment configuration to be a network. It takes into account the geometrical constraints of the network: slow curvature and good crossing points between the segments. The network structure is obtained by penalising segments which are not connected. The curvature constraint is optimized by quality functions with respect to the connection angles and the orientation between the segments. The overlaps between segments are forbidden in order to have neat crossing points. The second term is a data term which helps this network to best fit the data. Results are shown on Figure 2 starting from data kindly provided by the center for astrophysics at Harvard.

Link:
http://wwwsop.inria.fr/ariana/personnel/Xavier.Descombes/Resfigaro/Figaro.html
Please contact:
Xavier Descombes, INRIA, France
Tel: +33 4 92 38 76 63
Email: Xavier.Descombessophia.inria.fr