Galaxy Filament Detection using the Quality Candy Model- II

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 magnitude-limited 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.