  We present a study on galaxy detection and shape classification using
topometric clustering algorithms. We first use the DBSCAN algorithm to extract,
from CCD frames, groups of adjacent pixels with significant fluxes and we then
apply the DENCLUE algorithm to separate the contributions of overlapping
sources. The DENCLUE separation is based on the localization of pattern of
local maxima, through an iterative algorithm which associates each pixel to the
closest local maximum. Our main classification goal is to take apart elliptical
from spiral galaxies. We introduce new sets of features derived from the
computation of geometrical invariant moments of the pixel group shape and from
the statistics of the spatial distribution of the DENCLUE local maxima
patterns. Ellipticals are characterized by a single group of local maxima,
related to the galaxy core, while spiral galaxies have additional ones related
to segments of spiral arms. We use two different supervised ensemble
classification algorithms, Random Forest, and Gradient Boosting. Using a sample
of ~ 24000 galaxies taken from the Galaxy Zoo 2 main sample with spectroscopic
redshifts, and we test our classification against the Galaxy Zoo 2 catalog. We
find that features extracted from our pipeline give on average an accuracy of ~
93%, when testing on a test set with a size of 20% of our full data set, with
features deriving from the angular distribution of density attractor ranking at
the top of the discrimination power.
